0213_0231_0321_1203_2103<br /><br />

Counting sequence:<br />
1, 1, 2, 6, 19, 56, 156, 428, 1181, 3283, 9151, 25497, 70974, 197479, 549468, 1529021, 4255131, 11841744, 32954352, 91707701, 255210172, 710216466, 1976441904, 5500188027, 15306326325, 42595559419, 118538016529, 329876204252, 918003486391, 2554686876164, 7109368465657, 19784467648153, 55057655459626, 153218447822922, 426387439927991, 1186581978549668, 3302106628958184, 9189342486078908, 25572770601474297, 71165765909813043, 198045269183704171, 551134778706685749, 1533737945635027518, 4268197502252785351, 11877850430756264024, 33054546042191629333, 91986594748338051883, 255986985953306929832, 712379202173313026620, 1982460654393017558209, 5516935691309262500280, 15352929882666859298270, 42725249879819814880968, 118898932727748343618471, 330880597388264017320613, 920798591007569732512519, 2562465287762438892100133, 7131014768172531133619828, 19844706528024221364967807, 55225292610679819110005752, 153684960754058302774275937, 427685686130865971032666177, 1190194832492088399197895666, 3312160741468960993200329086, 9217321801303603982826784411, 25650633474722888835904016992, 71382448376872333772514024100, 198648268913050356234241373836, 552812850209503876394038556309, 1538407805056279552313734253859, 4281193126681395474830127770327, 11914015599572122333334749435185, 33155189104229184401071575834686, 92266671581047491265640840054295, 256766404133070207417688340808676, 714548223770213628755000343507485, 1988496765443494749728529355473611, 5533733420140468360476581483480704, 15399675824139371906967009711447672, 42855337885532408660571937534597773, 119260951091208356927842557214056644, 331888048419312835146583690867982714, 923602199007619030856853318734967104, 2570267372008417155973403996702226867, 7152726975649565575784098651354657221, 19905128838097173838771214144929402323, 55393440209601467966061416319356180473, 154152894121534301160356246473633533132, 428987885138176542897960263525527723543, 1193818686597187277068860799807652009948, 3322245466231702240231899497961789137401, 9245386306824714516301552709703997107641, 25728733421788806816380473058236812040026, 71599790589693827464908547739607598904994, 199253104629959023360238796803831764997759, 554496031031578600138467792957902099871212, 1543091883063908114944993404538820779263696, 4294228319629058186809878861378944088634780, 11950290882542659423893566939196720221608241, 33256138599942516844803553657809177425182819, 92547601179668489722069356578265607826364099<br /><br />


Generating function in Maple syntax:<br />
(x-1)^3/(x^5+x^4+4*x^3-5*x^2+4*x-1)<br /><br />



Generating function in latex syntax:<br />
\frac{\left(x -1\right)^{3}}{x^{5}+x^{4}+4 x^{3}-5 x^{2}+4 x -1}<br /><br />



Generating function in sympy syntax:<br />
(x - 1)**3/(x**5 + x**4 + 4*x**3 - 5*x**2 + 4*x - 1)<br /><br />



Implicit equation for the generating function in Maple syntax:<br />
(x^5+x^4+4*x^3-5*x^2+4*x-1)*F(x)-(x-1)^3 = 0<br /><br />



Implicit equation for the generating function in latex syntax:<br />
\left(x^{5}+x^{4}+4 x^{3}-5 x^{2}+4 x -1\right) F \! \left(x \right)-\left(x -1\right)^{3} = 0<br /><br />



Explicit closed form in Maple syntax:<br />
-1486664225/3177548674624*((((RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-1822/16075)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-1822/16075*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-542/16075)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)+(-1822/16075*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-542/16075)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-542/16075*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-179/3215)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)+((-1822/16075*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-542/16075)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-542/16075*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-179/3215)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)+(-542/16075*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-179/3215)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-179/3215*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+35933/16075)*((((295255/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-1)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^2+(-77295/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-203013/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)+19892/92483+18716/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^3+((295255/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-1)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^3+(125477/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-517225/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^2+(-261592/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-6600840/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)+739824/92483+38608/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^2+((-77295/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-203013/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^3+(-261592/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-6600840/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^2+(2233298/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-5275258/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)+457547/92483+422529/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)+(19892/92483+18716/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^3+(739824/92483+38608/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^2+(457547/92483+422529/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)-619611/92483-262385/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^(-n+1)+(((-18716/92483+77295/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-295255/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^2+(-33531/92483+132084/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+77295/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)-33531/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-18716/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^2-781/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^2+((-33531/92483+132084/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+77295/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^2+(8682508/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-332496/92483+132084/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)-33531/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^2-467789/92483-332496/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)+(-33531/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-18716/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^2-781/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^2+(-33531/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^2-467789/92483-332496/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)-824234/92483-467789/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-781/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)^(-n+1)+(((1-295255/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)+RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+221729/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^4+((314212/92483-202772/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)+314212/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+6659340/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^3+((591661/92483-1088537/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)+591661/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+7324527/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^2+((1214689/92483+2706883/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)+1214689/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+1104717/4021)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)+(14251/4021*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-341953/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-3499339/92483-341953/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^(-n+1)+(((295255/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-1)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^2+(-77295/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-203013/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)+19892/92483+18716/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^2+((-77295/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-203013/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^2+(-6384188/92483-132084/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)+33531/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)+720713/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)+(19892/92483+18716/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^2+(33531/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)+720713/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)+204623/92483+781/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^(-n+2)+(((1-295255/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)+RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+221729/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^3+((314212/92483-202772/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)+314212/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+6659340/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^2+((216652/92483+129508/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)+216652/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+6418500/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)+(-5077/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-19111/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-515309/92483-19111/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^(-n+2)+(((1-295255/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)+RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+221729/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^2+((203013/92483+77295/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)+203013/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+6417719/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)+(-18716/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-19892/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-719932/92483-19892/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^(-n+3)+(((34356/4021+860676/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)+34356/4021*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+766692/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)+(34356/4021*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+766692/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)+28688716/92483+766692/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^(-n+1)+(((-375009/92483+1218045/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-375009/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-906027/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)+(-375009/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-906027/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-26265753/92483-906027/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^(-n+2)+(((-111199/92483+280067/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-111199/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-241621/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)+(-111199/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-241621/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-7157543/92483-241621/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^(-n+3)+(((-1+295255/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-221729/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)+(-RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-221729/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-6437611/92483-221729/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^(-n+4)+(((-RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-221729/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^2+(-203013/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-6417719/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)+719932/92483+19892/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^3-((RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)+221729/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^2+(203013/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)+6417719/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)-719932/92483-19892/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4))*(RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)+1)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^2+((-203013/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-6417719/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^3+(-183121/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-5697787/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^2+(778650/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-26511714/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)+2578552/92483-297880/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)+(719932/92483+19892/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^3+(719932/92483+19892/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^2+(2578552/92483-297880/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)-13784896/92483-490688/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^(-n)+(((-19892/92483+203013/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^2+(-720713/92483+6384188/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+203013/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)-720713/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-19892/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^2-204623/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^2+((-720713/92483+6384188/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+203013/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^2+(5721412/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-1223216/92483+6384188/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)-720713/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^2-695311/92483-1223216/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)+(-720713/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-19892/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^2-204623/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^2+(-720713/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^2-695311/92483-1223216/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)-14714062/92483-695311/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-204623/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)^2)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)^(-n)+(((RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+221729/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)+6437611/92483+221729/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^4+((RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+221729/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)+6437611/92483+221729/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^3+((886916/92483+4*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)+886916/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)+25750444/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^2+((-1560770/92483+1570810/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-1560770/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-33468630/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)+(-377448/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-301176/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-10086952/92483-301176/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)^(-n)+(((-452125/92483+2033225/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-452125/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-1280575/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 2)+(-452125/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3)-1280575/92483)*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 4)-36059125/92483-1280575/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 3))*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 1)^(-n)-14260544/92483*RootOf(_Z^5+_Z^4+4*_Z^3-5*_Z^2+4*_Z-1,index = 5)^(-n))<br /><br />



Explicit closed form in latex syntax:<br />
-\frac{1486664225 \left(\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{1822}{16075}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{1822 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{16075}-\frac{542}{16075}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{1822 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{16075}-\frac{542}{16075}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{542 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{16075}-\frac{179}{3215}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\left(-\frac{1822 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{16075}-\frac{542}{16075}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{542 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{16075}-\frac{179}{3215}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{542 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{16075}-\frac{179}{3215}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{179 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{3215}+\frac{35933}{16075}\right) \left(\left(\left(\left(\frac{295255 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{77295 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}-\frac{203013}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{19892}{92483}+\frac{18716 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(\frac{295255 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(\frac{125477 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}-\frac{517225}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{261592 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}-\frac{6600840}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{739824}{92483}+\frac{38608 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{77295 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}-\frac{203013}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{261592 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}-\frac{6600840}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{2233298 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}-\frac{5275258}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{457547}{92483}+\frac{422529 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{19892}{92483}+\frac{18716 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(\frac{739824}{92483}+\frac{38608 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{457547}{92483}+\frac{422529 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{619611}{92483}-\frac{262385 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}+\left(\left(\left(-\frac{18716}{92483}+\frac{77295 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{295255 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{33531}{92483}+\frac{132084 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}+\frac{77295 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{33531 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{18716 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{92483}-\frac{781}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{33531}{92483}+\frac{132084 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}+\frac{77295 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{8682508 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{332496}{92483}+\frac{132084 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{33531 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{92483}-\frac{467789}{92483}-\frac{332496 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{33531 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{18716 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{92483}-\frac{781}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{33531 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{92483}-\frac{467789}{92483}-\frac{332496 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{824234}{92483}-\frac{467789 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{781 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}+\left(\left(\left(1-\frac{295255 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{221729}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{4}+\left(\left(\frac{314212}{92483}-\frac{202772 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{314212 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}+\frac{6659340}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(\frac{591661}{92483}-\frac{1088537 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{591661 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}+\frac{7324527}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{1214689}{92483}+\frac{2706883 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{1214689 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}+\frac{1104717}{4021}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{14251 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{4021}-\frac{341953}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{3499339}{92483}-\frac{341953 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}+\left(\left(\left(\frac{295255 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}-1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{77295 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}-\frac{203013}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{19892}{92483}+\frac{18716 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{77295 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}-\frac{203013}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{6384188}{92483}-\frac{132084 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{33531 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}+\frac{720713}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{19892}{92483}+\frac{18716 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{33531 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}+\frac{720713}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{204623}{92483}+\frac{781 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}+\left(\left(\left(1-\frac{295255 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{221729}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(\frac{314212}{92483}-\frac{202772 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{314212 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}+\frac{6659340}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{216652}{92483}+\frac{129508 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{216652 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}+\frac{6418500}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{5077 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{19111}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{515309}{92483}-\frac{19111 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}+\left(\left(\left(1-\frac{295255 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{221729}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(\frac{203013}{92483}+\frac{77295 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{203013 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}+\frac{6417719}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{18716 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{19892}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{719932}{92483}-\frac{19892 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}+\left(\left(\left(\frac{34356}{4021}+\frac{860676 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{34356 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{4021}+\frac{766692}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(\frac{34356 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{4021}+\frac{766692}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{28688716}{92483}+\frac{766692 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}+\left(\left(\left(-\frac{375009}{92483}+\frac{1218045 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{375009 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{906027}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{375009 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{906027}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{26265753}{92483}-\frac{906027 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}+\left(\left(\left(-\frac{111199}{92483}+\frac{280067 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{111199 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{241621}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{111199 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{241621}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{7157543}{92483}-\frac{241621 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}+\left(\left(\left(-1+\frac{295255 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{221729}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)-\frac{221729}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{6437611}{92483}-\frac{221729 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}+\left(\left(\left(-\mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{221729}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{203013 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}-\frac{6417719}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{719932}{92483}+\frac{19892 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}-\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{221729}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{203013 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}+\frac{6417719}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{719932}{92483}-\frac{19892 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}\right) \left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+1\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{203013 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}-\frac{6417719}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(-\frac{183121 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}-\frac{5697787}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{778650 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}-\frac{26511714}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\frac{2578552}{92483}-\frac{297880 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(\frac{719932}{92483}+\frac{19892 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{3}+\left(\frac{719932}{92483}+\frac{19892 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{2578552}{92483}-\frac{297880 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{13784896}{92483}-\frac{490688 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}+\left(\left(\left(-\frac{19892}{92483}+\frac{203013 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}+\mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{720713}{92483}+\frac{6384188 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}+\frac{203013 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{720713 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{19892 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{92483}-\frac{204623}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{720713}{92483}+\frac{6384188 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}+\frac{203013 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(\frac{5721412 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{1223216}{92483}+\frac{6384188 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{720713 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{92483}-\frac{695311}{92483}-\frac{1223216 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{720713 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{19892 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{92483}-\frac{204623}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{2}+\left(-\frac{720713 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{92483}-\frac{695311}{92483}-\frac{1223216 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)-\frac{14714062}{92483}-\frac{695311 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{204623 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)^{2}}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}+\left(\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{221729}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{6437611}{92483}+\frac{221729 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{4}+\left(\left(\mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)+\frac{221729}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{6437611}{92483}+\frac{221729 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{3}+\left(\left(\frac{886916}{92483}+4 \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)+\frac{886916 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}+\frac{25750444}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{2}+\left(\left(-\frac{1560770}{92483}+\frac{1570810 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{1560770 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{33468630}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)+\left(-\frac{377448 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{301176}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{10086952}{92483}-\frac{301176 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}+\left(\left(\left(-\frac{452125}{92483}+\frac{2033225 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{452125 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{1280575}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =2\right)+\left(-\frac{452125 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}-\frac{1280575}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =4\right)-\frac{36059125}{92483}-\frac{1280575 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =3\right)}{92483}\right) \mathit{RootOf}\! \left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}-\frac{14260544 \mathit{RootOf}\left(\textit{\_Z}^{5}+\textit{\_Z}^{4}+4 \textit{\_Z}^{3}-5 \textit{\_Z}^{2}+4 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{92483}\right)}{3177548674624}<br /><br />



  
    Recurrence in maple format:<br />
    
      a(0) = 1<br />
    
      a(1) = 1<br />
    
      a(2) = 2<br />
    
      a(3) = 6<br />
    
      a(4) = 19<br />
    
    a(n+5) = a(n)+a(n+1)+4*a(n+2)-5*a(n+3)+4*a(n+4), n >= 5<br /><br />

    Recurrence in latex format:<br />
    
      a \! \left(0\right) = 1<br />
    
      a \! \left(1\right) = 1<br />
    
      a \! \left(2\right) = 2<br />
    
      a \! \left(3\right) = 6<br />
    
      a \! \left(4\right) = 19<br />
    
    a \! \left(n +5\right) = a \! \left(n \right)+a \! \left(n +1\right)+4 a \! \left(n +2\right)-5 a \! \left(n +3\right)+4 a \! \left(n +4\right), \quad n \geq 5<br /><br />
  



  Specification 1<br />
  Strategy pack name: point_placements<br />
  Tree: http://www.permpal.com/tree/20246/<br />
  System of equations in Maple syntax:<br />
  
    F[0,x] = F[1,x]+F[2,x]<br />
  
    F[1,x] = 1<br />
  
    F[2,x] = F[3,x]<br />
  
    F[3,x] = F[4,x]*F[5,x]<br />
  
    F[4,x] = x<br />
  
    F[5,x] = F[14,x]+F[6,x]<br />
  
    F[6,x] = F[1,x]+F[7,x]<br />
  
    F[7,x] = F[8,x]<br />
  
    F[8,x] = F[4,x]*F[9,x]<br />
  
    F[9,x] = F[10,x]+F[6,x]<br />
  
    F[10,x] = F[11,x]<br />
  
    F[11,x] = F[12,x]<br />
  
    F[12,x] = F[13,x]*F[4,x]<br />
  
    F[13,x] = F[1,x]+F[11,x]<br />
  
    F[14,x] = F[15,x]+F[2,x]<br />
  
    F[15,x] = F[16,x]+F[17,x]+F[76,x]<br />
  
    F[16,x] = 0<br />
  
    F[17,x] = F[18,x]*F[4,x]<br />
  
    F[18,x] = F[19,x]+F[29,x]<br />
  
    F[19,x] = F[20,x]+F[7,x]<br />
  
    F[20,x] = F[16,x]+F[21,x]+F[23,x]<br />
  
    F[21,x] = F[22,x]*F[4,x]<br />
  
    F[22,x] = F[19,x]<br />
  
    F[23,x] = F[24,x]*F[4,x]<br />
  
    F[24,x] = F[10,x]+F[25,x]<br />
  
    F[25,x] = F[26,x]<br />
  
    F[26,x] = F[27,x]<br />
  
    F[27,x] = F[28,x]*F[4,x]<br />
  
    F[28,x] = F[11,x]+F[26,x]<br />
  
    F[29,x] = F[30,x]+F[38,x]<br />
  
    F[30,x] = F[31,x]<br />
  
    F[31,x] = F[32,x]*F[4,x]<br />
  
    F[32,x] = F[33,x]+F[34,x]<br />
  
    F[33,x] = F[2,x]+F[30,x]<br />
  
    F[34,x] = F[35,x]<br />
  
    F[35,x] = F[36,x]<br />
  
    F[36,x] = F[37,x]*F[4,x]<br />
  
    F[37,x] = F[2,x]+F[35,x]<br />
  
    F[38,x] = 2*F[16,x]+F[39,x]+F[51,x]<br />
  
    F[39,x] = F[4,x]*F[40,x]<br />
  
    F[40,x] = F[41,x]<br />
  
    F[41,x] = F[30,x]+F[42,x]<br />
  
    F[42,x] = 2*F[16,x]+F[43,x]+F[45,x]<br />
  
    F[43,x] = F[4,x]*F[44,x]<br />
  
    F[44,x] = F[41,x]<br />
  
    F[45,x] = F[4,x]*F[46,x]<br />
  
    F[46,x] = F[34,x]+F[47,x]<br />
  
    F[47,x] = F[48,x]<br />
  
    F[48,x] = F[49,x]<br />
  
    F[49,x] = F[4,x]*F[50,x]<br />
  
    F[50,x] = F[35,x]+F[48,x]<br />
  
    F[51,x] = F[4,x]*F[52,x]<br />
  
    F[52,x] = F[53,x]+F[75,x]<br />
  
    F[53,x] = F[54,x]<br />
  
    F[54,x] = F[16,x]+F[36,x]+F[55,x]<br />
  
    F[55,x] = F[4,x]*F[56,x]<br />
  
    F[56,x] = F[57,x]+F[63,x]<br />
  
    F[57,x] = F[11,x]+F[58,x]<br />
  
    F[58,x] = F[16,x]+F[59,x]+F[61,x]<br />
  
    F[59,x] = F[4,x]*F[60,x]<br />
  
    F[60,x] = F[57,x]<br />
  
    F[61,x] = F[4,x]*F[62,x]<br />
  
    F[62,x] = F[11,x]<br />
  
    F[63,x] = F[35,x]+F[64,x]<br />
  
    F[64,x] = 2*F[16,x]+F[65,x]+F[73,x]<br />
  
    F[65,x] = F[4,x]*F[66,x]<br />
  
    F[66,x] = F[67,x]<br />
  
    F[67,x] = F[35,x]+F[68,x]<br />
  
    F[68,x] = 2*F[16,x]+F[69,x]+F[71,x]<br />
  
    F[69,x] = F[4,x]*F[70,x]<br />
  
    F[70,x] = F[67,x]<br />
  
    F[71,x] = F[4,x]*F[72,x]<br />
  
    F[72,x] = F[35,x]<br />
  
    F[73,x] = F[4,x]*F[74,x]<br />
  
    F[74,x] = F[54,x]<br />
  
    F[75,x] = F[49,x]<br />
  
    F[76,x] = F[4,x]*F[77,x]<br />
  
    F[77,x] = F[33,x]+F[53,x]<br />
  
  System of equations in latex syntax:<br />
  
    F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)<br />
  
    F_{1}\! \left(x \right) = 1<br />
  
    F_{2}\! \left(x \right) = F_{3}\! \left(x \right)<br />
  
    F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)<br />
  
    F_{4}\! \left(x \right) = x<br />
  
    F_{5}\! \left(x \right) = F_{14}\! \left(x \right)+F_{6}\! \left(x \right)<br />
  
    F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)<br />
  
    F_{7}\! \left(x \right) = F_{8}\! \left(x \right)<br />
  
    F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)<br />
  
    F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{6}\! \left(x \right)<br />
  
    F_{10}\! \left(x \right) = F_{11}\! \left(x \right)<br />
  
    F_{11}\! \left(x \right) = F_{12}\! \left(x \right)<br />
  
    F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)<br />
  
    F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{2}\! \left(x \right)<br />
  
    F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)+F_{76}\! \left(x \right)<br />
  
    F_{16}\! \left(x \right) = 0<br />
  
    F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{29}\! \left(x \right)<br />
  
    F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{7}\! \left(x \right)<br />
  
    F_{20}\! \left(x \right) = F_{16}\! \left(x \right)+F_{21}\! \left(x \right)+F_{23}\! \left(x \right)<br />
  
    F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{22}\! \left(x \right) = F_{19}\! \left(x \right)<br />
  
    F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{24}\! \left(x \right) = F_{10}\! \left(x \right)+F_{25}\! \left(x \right)<br />
  
    F_{25}\! \left(x \right) = F_{26}\! \left(x \right)<br />
  
    F_{26}\! \left(x \right) = F_{27}\! \left(x \right)<br />
  
    F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{28}\! \left(x \right) = F_{11}\! \left(x \right)+F_{26}\! \left(x \right)<br />
  
    F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{38}\! \left(x \right)<br />
  
    F_{30}\! \left(x \right) = F_{31}\! \left(x \right)<br />
  
    F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)<br />
  
    F_{33}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)<br />
  
    F_{34}\! \left(x \right) = F_{35}\! \left(x \right)<br />
  
    F_{35}\! \left(x \right) = F_{36}\! \left(x \right)<br />
  
    F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)<br />
  
    F_{37}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)<br />
  
    F_{38}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{39}\! \left(x \right)+F_{51}\! \left(x \right)<br />
  
    F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)<br />
  
    F_{40}\! \left(x \right) = F_{41}\! \left(x \right)<br />
  
    F_{41}\! \left(x \right) = F_{30}\! \left(x \right)+F_{42}\! \left(x \right)<br />
  
    F_{42}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{43}\! \left(x \right)+F_{45}\! \left(x \right)<br />
  
    F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)<br />
  
    F_{44}\! \left(x \right) = F_{41}\! \left(x \right)<br />
  
    F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)<br />
  
    F_{46}\! \left(x \right) = F_{34}\! \left(x \right)+F_{47}\! \left(x \right)<br />
  
    F_{47}\! \left(x \right) = F_{48}\! \left(x \right)<br />
  
    F_{48}\! \left(x \right) = F_{49}\! \left(x \right)<br />
  
    F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)<br />
  
    F_{50}\! \left(x \right) = F_{35}\! \left(x \right)+F_{48}\! \left(x \right)<br />
  
    F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)<br />
  
    F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{75}\! \left(x \right)<br />
  
    F_{53}\! \left(x \right) = F_{54}\! \left(x \right)<br />
  
    F_{54}\! \left(x \right) = F_{16}\! \left(x \right)+F_{36}\! \left(x \right)+F_{55}\! \left(x \right)<br />
  
    F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)<br />
  
    F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{63}\! \left(x \right)<br />
  
    F_{57}\! \left(x \right) = F_{11}\! \left(x \right)+F_{58}\! \left(x \right)<br />
  
    F_{58}\! \left(x \right) = F_{16}\! \left(x \right)+F_{59}\! \left(x \right)+F_{61}\! \left(x \right)<br />
  
    F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)<br />
  
    F_{60}\! \left(x \right) = F_{57}\! \left(x \right)<br />
  
    F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)<br />
  
    F_{62}\! \left(x \right) = F_{11}\! \left(x \right)<br />
  
    F_{63}\! \left(x \right) = F_{35}\! \left(x \right)+F_{64}\! \left(x \right)<br />
  
    F_{64}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{65}\! \left(x \right)+F_{73}\! \left(x \right)<br />
  
    F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)<br />
  
    F_{66}\! \left(x \right) = F_{67}\! \left(x \right)<br />
  
    F_{67}\! \left(x \right) = F_{35}\! \left(x \right)+F_{68}\! \left(x \right)<br />
  
    F_{68}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{69}\! \left(x \right)+F_{71}\! \left(x \right)<br />
  
    F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)<br />
  
    F_{70}\! \left(x \right) = F_{67}\! \left(x \right)<br />
  
    F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)<br />
  
    F_{72}\! \left(x \right) = F_{35}\! \left(x \right)<br />
  
    F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)<br />
  
    F_{74}\! \left(x \right) = F_{54}\! \left(x \right)<br />
  
    F_{75}\! \left(x \right) = F_{49}\! \left(x \right)<br />
  
    F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)<br />
  
    F_{77}\! \left(x \right) = F_{33}\! \left(x \right)+F_{53}\! \left(x \right)<br />
  
  System of equations in sympy syntax:<br />
  
    Eq(F_0(x), F_1(x) + F_2(x))<br />
  
    Eq(F_1(x), 1)<br />
  
    Eq(F_2(x), F_3(x))<br />
  
    Eq(F_3(x), F_4(x)*F_5(x))<br />
  
    Eq(F_4(x), x)<br />
  
    Eq(F_5(x), F_14(x) + F_6(x))<br />
  
    Eq(F_6(x), F_1(x) + F_7(x))<br />
  
    Eq(F_7(x), F_8(x))<br />
  
    Eq(F_8(x), F_4(x)*F_9(x))<br />
  
    Eq(F_9(x), F_10(x) + F_6(x))<br />
  
    Eq(F_10(x), F_11(x))<br />
  
    Eq(F_11(x), F_12(x))<br />
  
    Eq(F_12(x), F_13(x)*F_4(x))<br />
  
    Eq(F_13(x), F_1(x) + F_11(x))<br />
  
    Eq(F_14(x), F_15(x) + F_2(x))<br />
  
    Eq(F_15(x), F_16(x) + F_17(x) + F_76(x))<br />
  
    Eq(F_16(x), 0)<br />
  
    Eq(F_17(x), F_18(x)*F_4(x))<br />
  
    Eq(F_18(x), F_19(x) + F_29(x))<br />
  
    Eq(F_19(x), F_20(x) + F_7(x))<br />
  
    Eq(F_20(x), F_16(x) + F_21(x) + F_23(x))<br />
  
    Eq(F_21(x), F_22(x)*F_4(x))<br />
  
    Eq(F_22(x), F_19(x))<br />
  
    Eq(F_23(x), F_24(x)*F_4(x))<br />
  
    Eq(F_24(x), F_10(x) + F_25(x))<br />
  
    Eq(F_25(x), F_26(x))<br />
  
    Eq(F_26(x), F_27(x))<br />
  
    Eq(F_27(x), F_28(x)*F_4(x))<br />
  
    Eq(F_28(x), F_11(x) + F_26(x))<br />
  
    Eq(F_29(x), F_30(x) + F_38(x))<br />
  
    Eq(F_30(x), F_31(x))<br />
  
    Eq(F_31(x), F_32(x)*F_4(x))<br />
  
    Eq(F_32(x), F_33(x) + F_34(x))<br />
  
    Eq(F_33(x), F_2(x) + F_30(x))<br />
  
    Eq(F_34(x), F_35(x))<br />
  
    Eq(F_35(x), F_36(x))<br />
  
    Eq(F_36(x), F_37(x)*F_4(x))<br />
  
    Eq(F_37(x), F_2(x) + F_35(x))<br />
  
    Eq(F_38(x), 2*F_16(x) + F_39(x) + F_51(x))<br />
  
    Eq(F_39(x), F_4(x)*F_40(x))<br />
  
    Eq(F_40(x), F_41(x))<br />
  
    Eq(F_41(x), F_30(x) + F_42(x))<br />
  
    Eq(F_42(x), 2*F_16(x) + F_43(x) + F_45(x))<br />
  
    Eq(F_43(x), F_4(x)*F_44(x))<br />
  
    Eq(F_44(x), F_41(x))<br />
  
    Eq(F_45(x), F_4(x)*F_46(x))<br />
  
    Eq(F_46(x), F_34(x) + F_47(x))<br />
  
    Eq(F_47(x), F_48(x))<br />
  
    Eq(F_48(x), F_49(x))<br />
  
    Eq(F_49(x), F_4(x)*F_50(x))<br />
  
    Eq(F_50(x), F_35(x) + F_48(x))<br />
  
    Eq(F_51(x), F_4(x)*F_52(x))<br />
  
    Eq(F_52(x), F_53(x) + F_75(x))<br />
  
    Eq(F_53(x), F_54(x))<br />
  
    Eq(F_54(x), F_16(x) + F_36(x) + F_55(x))<br />
  
    Eq(F_55(x), F_4(x)*F_56(x))<br />
  
    Eq(F_56(x), F_57(x) + F_63(x))<br />
  
    Eq(F_57(x), F_11(x) + F_58(x))<br />
  
    Eq(F_58(x), F_16(x) + F_59(x) + F_61(x))<br />
  
    Eq(F_59(x), F_4(x)*F_60(x))<br />
  
    Eq(F_60(x), F_57(x))<br />
  
    Eq(F_61(x), F_4(x)*F_62(x))<br />
  
    Eq(F_62(x), F_11(x))<br />
  
    Eq(F_63(x), F_35(x) + F_64(x))<br />
  
    Eq(F_64(x), 2*F_16(x) + F_65(x) + F_73(x))<br />
  
    Eq(F_65(x), F_4(x)*F_66(x))<br />
  
    Eq(F_66(x), F_67(x))<br />
  
    Eq(F_67(x), F_35(x) + F_68(x))<br />
  
    Eq(F_68(x), 2*F_16(x) + F_69(x) + F_71(x))<br />
  
    Eq(F_69(x), F_4(x)*F_70(x))<br />
  
    Eq(F_70(x), F_67(x))<br />
  
    Eq(F_71(x), F_4(x)*F_72(x))<br />
  
    Eq(F_72(x), F_35(x))<br />
  
    Eq(F_73(x), F_4(x)*F_74(x))<br />
  
    Eq(F_74(x), F_54(x))<br />
  
    Eq(F_75(x), F_49(x))<br />
  
    Eq(F_76(x), F_4(x)*F_77(x))<br />
  
    Eq(F_77(x), F_33(x) + F_53(x))<br />
  
  Pack JSON:<br />{&#34;expansion_strats&#34;: [[{&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;extra_basis&#34;: [], &#34;ignore_parent&#34;: false, &#34;maxreqlen&#34;: 1, &#34;one_cell_only&#34;: false, &#34;strategy_class&#34;: &#34;CellInsertionFactory&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;dirs&#34;: [0, 1, 2, 3], &#34;ignore_parent&#34;: false, &#34;partial&#34;: false, &#34;point_only&#34;: false, &#34;strategy_class&#34;: &#34;PatternPlacementFactory&#34;}]], &#34;inferral_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.row_and_col_separation&#34;, &#34;ignore_parent&#34;: true, &#34;inferrable&#34;: true, &#34;possibly_empty&#34;: false, &#34;strategy_class&#34;: &#34;RowColumnSeparationStrategy&#34;, &#34;workable&#34;: true}, {&#34;class_module&#34;: &#34;tilings.strategies.obstruction_inferral&#34;, &#34;strategy_class&#34;: &#34;ObstructionTransitivityFactory&#34;}], &#34;initial_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;interleaving&#34;: null, &#34;strategy_class&#34;: &#34;FactorFactory&#34;, &#34;tracked&#34;: false, &#34;unions&#34;: false, &#34;workable&#34;: true}], &#34;iterative&#34;: false, &#34;name&#34;: &#34;point_placements&#34;, &#34;symmetries&#34;: [], &#34;ver_strats&#34;: [{&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;strategy_class&#34;: &#34;BasicVerificationStrategy&#34;}, {&#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;InsertionEncodingVerificationStrategy&#34;}, {&#34;basis&#34;: [], &#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;OneByOneVerificationStrategy&#34;, &#34;symmetry&#34;: false}, {&#34;basis&#34;: [], &#34;class_module&#34;: &#34;tilings.strategies.verification&#34;, &#34;ignore_parent&#34;: false, &#34;strategy_class&#34;: &#34;LocallyFactorableVerificationStrategy&#34;, &#34;symmetry&#34;: false}]}<br />
  Specification JSON:<br />{&#34;root&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, &#34;rules&#34;: [{&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_insertion&#34;, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: []}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], 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2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 1], [1, 0], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 1], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;direction&#34;: 2, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0], &#34;own_col&#34;: true, &#34;own_row&#34;: true, &#34;strategy_class&#34;: &#34;RequirementPlacementStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 2], [0, 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&#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 0], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 2], [1, 2], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 3], [1, 2], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 2], [1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 2], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 2], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 2]]}, {&#34;patt&#34;: [2, 1, 0], 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3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 4]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 4], [1, 3], [1, 4]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 3], [1, 4], [1, 3]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 3]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 1], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 1], [1, 4]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 2], [1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 1], [1, 0], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 1], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, 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&#34;pos&#34;: [[0, 2]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;direction&#34;: 2, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0, 0], &#34;own_col&#34;: true, &#34;own_row&#34;: true, &#34;strategy_class&#34;: &#34;RequirementPlacementStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 3]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 3], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 0], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 2], [0, 2], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 3], [0, 2], [0, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 3], [0, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 3], [0, 3], [0, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[0, 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[1, 4]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 1], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 3], [1, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 4], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 1], [1, 0], [1, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 3], [1, 3], [1, 4]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 4], [1, 3], [1, 4]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 3], [1, 4], [1, 3]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 3]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 4], [1, 4]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 1], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 1], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 1], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.factor&#34;, &#34;ignore_parent&#34;: true, &#34;partition&#34;: [[[0, 2]], [[1, 0], [1, 1], [1, 3], [1, 4]]], &#34;strategy_class&#34;: &#34;FactorStrategy&#34;, &#34;workable&#34;: true}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 3]]}, {&#34;patt&#34;: [0, 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[[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 1], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], 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[1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 2], [1, 2], [1, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 3]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[1, 2], [1, 2]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], 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[[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}]]}, &#34;rule_class&#34;: &#34;Rule&#34;, &#34;strategy&#34;: {&#34;class_module&#34;: &#34;tilings.strategies.requirement_placement&#34;, &#34;direction&#34;: 2, &#34;gps&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], &#34;ignore_parent&#34;: false, &#34;include_empty&#34;: true, &#34;indices&#34;: [0, 0], &#34;own_col&#34;: true, &#34;own_row&#34;: true, &#34;strategy_class&#34;: &#34;RequirementPlacementStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: 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{&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 0], [0, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 1], [0, 1], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: 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[[0, 1]]}], &#34;ignore_parent&#34;: true, &#34;strategy_class&#34;: &#34;RequirementInsertionStrategy&#34;}}, {&#34;children&#34;: [{&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [], &#34;pos&#34;: []}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [], &#34;pos&#34;: []}], &#34;requirements&#34;: []}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 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[1, 4], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 3], [1, 3], [1, 3]]}, {&#34;patt&#34;: [2, 1, 0], &#34;pos&#34;: [[1, 4], [1, 3], [1, 3]]}, {&#34;patt&#34;: [0, 2, 1, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 2, 3, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[1, 0], [1, 0], [1, 0], [1, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 4]]}]]}, {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: 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[0], &#34;pos&#34;: [[0, 2]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 1]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 1]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 0], [0, 2]]}, {&#34;patt&#34;: [1, 0], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 1], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 0, 2], &#34;pos&#34;: [[0, 2], [0, 1], [0, 2]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 1], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 1], [0, 2], [0, 1]]}, {&#34;patt&#34;: [1, 2, 0], &#34;pos&#34;: [[0, 2], [0, 2], [0, 1]]}, {&#34;patt&#34;: [2, 1, 0], 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{&#34;patt&#34;: [0, 3, 2, 1], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [1, 2, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}, {&#34;patt&#34;: [2, 1, 0, 3], &#34;pos&#34;: [[0, 0], [0, 0], [0, 0], [0, 0]]}], &#34;requirements&#34;: [[{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}], [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}]]}], &#34;class_module&#34;: &#34;comb_spec_searcher.strategies.rule&#34;, &#34;comb_class&#34;: {&#34;assumptions&#34;: [], &#34;class_module&#34;: &#34;tilings.tiling&#34;, &#34;comb_class&#34;: &#34;Tiling&#34;, &#34;obstructions&#34;: [{&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 0]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 1]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 3]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[0, 4]]}, {&#34;patt&#34;: [0], &#34;pos&#34;: [[1, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[0, 2], [0, 2]]}, {&#34;patt&#34;: [0, 1], &#34;pos&#34;: [[1, 0], [1, 1]]}, {&#34;patt&#34;: [0, 1], 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