01342_01423_01432_02341_02431_03241_10342_10423_10432
Counting sequence:
1, 1, 2, 6, 24, 111, 549, 2827, 14977, 81094, 446792, 2496848, 14119216, 80642088, 464534988, 2695750718, 15744889634, 92483547305, 545980210521, 3237753444070, 19278237886512, 115206870514449, 690766103394039, 4154306963585431, 25053614927602931, 151477870581133357, 918013398802048225, 5575625230010963146, 33932416757452425082, 206895816779222324924, 1263716072022760562564, 7731410240745679392197, 47373398248542570655565, 290694139165800450977467, 1786186688482903961183923, 10989359421698539233589080, 67692698434838509708942922, 417452139467986867230046650, 2577156140910259173096056088, 15926477775940240402698878044, 98519303728942312226700535842, 609992898579701510377904669143, 3780165642864013564357482139319, 23445613083341863065004971400566, 145532637567201493255101792641966, 904048437483443773546434551736558, 5620060114347682948919131233575690, 34961864440178977362424036577656928, 217640555565052697044629504931812198, 1355703521497621228964274562855250155, 8450025895694253547331149020989632347, 52699827990569526103121762305658441958, 328857866722060184198601779012522484726, 2053268556754878433985807357637252163627, 12826639534349426301127263750633334888985, 80168037078575848649173257413707688149806, 501305999425631912275355034471222158284212, 3136247522355058073830835680111013568500363, 19629824308821019222522563828978334774580519, 122917688644323604514854882570147434678136974, 770012592059697508592308255518788000265580912, 4825703498175442664392150076131436010413768980, 30254988934268597271573252851652822671310776810, 189758565655217101701974834549211774052963916890, 1190607285530465139437783463433025834045565218232, 7472972992298113449033977459682324972983189382988, 46921428226127373257540294151258990697256768935244, 294711705269605955999491709265618042318079710615904, 1851686760440758838557041883616224963390469150619358, 11637975633999894664410297484584247305959152239357043, 73168330319064753833211283457824764846098142253182819, 460151441793917844960329971851260511584460083220856953, 2894720881458895383632960458459784944139256989529901017, 18215342420884465997882511027498588627537515497100903324, 114654034730042541558218345900071333027998451259925795862, 721870768022936087319347297999830349241172966539816306060, 4546158377037409403764299927347118097666622942667567424422, 28637932695313258553328705755083707358970566322359707957586, 180446259174847801194947487880489444211944782171660555182576, 1137261790255777565175732394414697687506247156262756629209192, 7169298979746771560420763488371646945810765988559951771325614, 45205788418720316993425209156933817494355377138818495397791476, 285108419548921357961594130717600634293168096490047742656781082, 1798549074957204439947448025819307853419968421769946681645448744, 11348239663137745678543919113463394247484627109259609897738665814, 71618702014586110341506288497337188386672706669700233606610372474, 452078645678447821997388537651767189393555938123133960331011508726, 2854230719890936015760288439896778509299306704153058451621074142227, 18023938615568080087314949837197141794260502532562200250885635784537, 113839750827158082943331598490211763223408351090560276132917185961634, 719150726911513889398645620537144158409046216753634188423940291407594, 4543869606632146071376852628990943912165380009899637219085429545865208, 28715078185728936361028142284237325082169023304917550731061735856889398, 181497508078451743662135327214827780238570515129574095381799062303330812, 1147377207812969508320272744559502778481545683206609448995587186802862980, 7254626840483141532739188535633706162774385523119347288043768061731262981, 45877074410432236702031195457457095950662064619186546264730768894940988165, 290166081704786813053317479803917768268537914994560273813805619544069126569, 1835550894759753669212986217261436158578258676838484467751909421569404306103, 11613247385995184790444656722879829758843683905387792412706727441001005377628, 73486410247297972768444326065721942781569473455722533574242477204553765792926
Implicit equation for the generating function in Maple syntax:
(x-1)*(2*x^3-2*x^2+x-6)*x*F(x)^3-(x^4-5*x^3+4*x^2-9*x+13)*x*F(x)^2+(-2*x^4+2*x^3-2*x^2+11*x-1)*F(x)-x^3-x^2-3*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(2 x^{3}-2 x^{2}+x -6\right) x F \! \left(x \right)^{3}-\left(x^{4}-5 x^{3}+4 x^{2}-9 x +13\right) x F \! \left(x \right)^{2}+\left(-2 x^{4}+2 x^{3}-2 x^{2}+11 x -1\right) F \! \left(x \right)-x^{3}-x^{2}-3 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 111
a(6) = 549
a(7) = 2827
a(8) = 14977
a(9) = 81094
a(10) = 446792
a(11) = 2496848
a(12) = 14119216
a(13) = 80642088
a(14) = 464534988
a(15) = 2695750718
a(16) = 15744889634
a(17) = 92483547305
a(18) = 545980210521
a(19) = 3237753444070
a(20) = 19278237886512
a(21) = 115206870514449
a(22) = 690766103394039
a(23) = 4154306963585431
a(24) = 25053614927602931
a(25) = 151477870581133357
a(26) = 918013398802048225
a(27) = 5575625230010963146
a(n+28) = -1/27*n*(2*n+5)/(2*n+57)/(n+28)*a(n)+1/60*(32746*n^2+1371861*n+14365529)/(2*n+57)/(n+28)*a(n+21)-1/60*(17167*n^2+736274*n+7864279)/(2*n+57)/(n+28)*a(n+22)+1/60*(25759*n^2+1158082*n+12984285)/(2*n+57)/(n+28)*a(n+23)-1/20*(4277*n^2+194540*n+2200569)/(2*n+57)/(n+28)*a(n+24)-3/8*(121*n^2+6155*n+78212)/(2*n+57)/(n+28)*a(n+25)+1/120*(877*n^2+37159*n+368820)/(2*n+57)/(n+28)*a(n+26)+1/60*(803*n^2+44663*n+620940)/(2*n+57)/(n+28)*a(n+27)-1/360*(102161*n^2+4153436*n+42232428)/(2*n+57)/(n+28)*a(n+18)+1/40*(24471*n^2+953004*n+9274420)/(2*n+57)/(n+28)*a(n+19)-1/180*(101027*n^2+4302629*n+45691332)/(2*n+57)/(n+28)*a(n+20)-1/1080*(231008*n^2+7542587*n+62210946)/(2*n+57)/(n+28)*a(n+14)-1/1080*(188500*n^2+5564941*n+41319006)/(2*n+57)/(n+28)*a(n+15)-1/360*(104554*n^2+4046151*n+38701166)/(2*n+57)/(n+28)*a(n+16)+1/1080*(341639*n^2+13505816*n+131406768)/(2*n+57)/(n+28)*a(n+17)-1/360*(12930*n^2-23879*n-1768964)/(2*n+57)/(n+28)*a(n+12)-1/1080*(241910*n^2+5366075*n+29417622)/(2*n+57)/(n+28)*a(n+13)-1/135*(92*n^2+446*n+399)/(2*n+57)/(n+28)*a(n+1)-1/135*(362*n^2+2705*n+4362)/(2*n+57)/(n+28)*a(n+2)-1/270*(1796*n^2+18962*n+44127)/(2*n+57)/(n+28)*a(n+3)-1/540*(5810*n^2+89513*n+288090)/(2*n+57)/(n+28)*a(n+4)-1/270*(1658*n^2+60866*n+294813)/(2*n+57)/(n+28)*a(n+5)+1/540*(7354*n^2-49523*n-690672)/(2*n+57)/(n+28)*a(n+6)+1/90*(5054*n^2+45063*n+30839)/(2*n+57)/(n+28)*a(n+7)+1/90*(9932*n^2+151371*n+526392)/(2*n+57)/(n+28)*a(n+8)+1/90*(11424*n^2+230249*n+1084139)/(2*n+57)/(n+28)*a(n+9)+1/540*(72704*n^2+1879019*n+11067144)/(2*n+57)/(n+28)*a(n+10)-1/360*(2679*n^2-339901*n-3762776)/(2*n+57)/(n+28)*a(n+11), n >= 28
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 24
a \! \left(5\right) = 111
a \! \left(6\right) = 549
a \! \left(7\right) = 2827
a \! \left(8\right) = 14977
a \! \left(9\right) = 81094
a \! \left(10\right) = 446792
a \! \left(11\right) = 2496848
a \! \left(12\right) = 14119216
a \! \left(13\right) = 80642088
a \! \left(14\right) = 464534988
a \! \left(15\right) = 2695750718
a \! \left(16\right) = 15744889634
a \! \left(17\right) = 92483547305
a \! \left(18\right) = 545980210521
a \! \left(19\right) = 3237753444070
a \! \left(20\right) = 19278237886512
a \! \left(21\right) = 115206870514449
a \! \left(22\right) = 690766103394039
a \! \left(23\right) = 4154306963585431
a \! \left(24\right) = 25053614927602931
a \! \left(25\right) = 151477870581133357
a \! \left(26\right) = 918013398802048225
a \! \left(27\right) = 5575625230010963146
a \! \left(n +28\right) = -\frac{n \left(2 n +5\right) a \! \left(n \right)}{27 \left(2 n +57\right) \left(n +28\right)}+\frac{\left(32746 n^{2}+1371861 n +14365529\right) a \! \left(n +21\right)}{60 \left(2 n +57\right) \left(n +28\right)}-\frac{\left(17167 n^{2}+736274 n +7864279\right) a \! \left(n +22\right)}{60 \left(2 n +57\right) \left(n +28\right)}+\frac{\left(25759 n^{2}+1158082 n +12984285\right) a \! \left(n +23\right)}{60 \left(2 n +57\right) \left(n +28\right)}-\frac{\left(4277 n^{2}+194540 n +2200569\right) a \! \left(n +24\right)}{20 \left(2 n +57\right) \left(n +28\right)}-\frac{3 \left(121 n^{2}+6155 n +78212\right) a \! \left(n +25\right)}{8 \left(2 n +57\right) \left(n +28\right)}+\frac{\left(877 n^{2}+37159 n +368820\right) a \! \left(n +26\right)}{120 \left(2 n +57\right) \left(n +28\right)}+\frac{\left(803 n^{2}+44663 n +620940\right) a \! \left(n +27\right)}{60 \left(2 n +57\right) \left(n +28\right)}-\frac{\left(102161 n^{2}+4153436 n +42232428\right) a \! \left(n +18\right)}{360 \left(2 n +57\right) \left(n +28\right)}+\frac{\left(24471 n^{2}+953004 n +9274420\right) a \! \left(n +19\right)}{40 \left(2 n +57\right) \left(n +28\right)}-\frac{\left(101027 n^{2}+4302629 n +45691332\right) a \! \left(n +20\right)}{180 \left(2 n +57\right) \left(n +28\right)}-\frac{\left(231008 n^{2}+7542587 n +62210946\right) a \! \left(n +14\right)}{1080 \left(2 n +57\right) \left(n +28\right)}-\frac{\left(188500 n^{2}+5564941 n +41319006\right) a \! \left(n +15\right)}{1080 \left(2 n +57\right) \left(n +28\right)}-\frac{\left(104554 n^{2}+4046151 n +38701166\right) a \! \left(n +16\right)}{360 \left(2 n +57\right) \left(n +28\right)}+\frac{\left(341639 n^{2}+13505816 n +131406768\right) a \! \left(n +17\right)}{1080 \left(2 n +57\right) \left(n +28\right)}-\frac{\left(12930 n^{2}-23879 n -1768964\right) a \! \left(n +12\right)}{360 \left(2 n +57\right) \left(n +28\right)}-\frac{\left(241910 n^{2}+5366075 n +29417622\right) a \! \left(n +13\right)}{1080 \left(2 n +57\right) \left(n +28\right)}-\frac{\left(92 n^{2}+446 n +399\right) a \! \left(n +1\right)}{135 \left(2 n +57\right) \left(n +28\right)}-\frac{\left(362 n^{2}+2705 n +4362\right) a \! \left(n +2\right)}{135 \left(2 n +57\right) \left(n +28\right)}-\frac{\left(1796 n^{2}+18962 n +44127\right) a \! \left(n +3\right)}{270 \left(2 n +57\right) \left(n +28\right)}-\frac{\left(5810 n^{2}+89513 n +288090\right) a \! \left(n +4\right)}{540 \left(2 n +57\right) \left(n +28\right)}-\frac{\left(1658 n^{2}+60866 n +294813\right) a \! \left(n +5\right)}{270 \left(2 n +57\right) \left(n +28\right)}+\frac{\left(7354 n^{2}-49523 n -690672\right) a \! \left(n +6\right)}{540 \left(2 n +57\right) \left(n +28\right)}+\frac{\left(5054 n^{2}+45063 n +30839\right) a \! \left(n +7\right)}{90 \left(2 n +57\right) \left(n +28\right)}+\frac{\left(9932 n^{2}+151371 n +526392\right) a \! \left(n +8\right)}{90 \left(2 n +57\right) \left(n +28\right)}+\frac{\left(11424 n^{2}+230249 n +1084139\right) a \! \left(n +9\right)}{90 \left(2 n +57\right) \left(n +28\right)}+\frac{\left(72704 n^{2}+1879019 n +11067144\right) a \! \left(n +10\right)}{540 \left(2 n +57\right) \left(n +28\right)}-\frac{\left(2679 n^{2}-339901 n -3762776\right) a \! \left(n +11\right)}{360 \left(2 n +57\right) \left(n +28\right)}, \quad n \geq 28
Specification 1
Strategy pack name: point_placements_tracked_fusion
Tree: http://www.permpal.com/tree/24192/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[30,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[30,x]*F[7,x]
F[7,x] = F[8,x]+F[9,x]
F[8,x] = F[0,x]*F[4,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[30,x]
F[11,x] = F[102,x]+F[12,x]
F[12,x] = F[13,x]*F[37,x]
F[13,x] = F[14,x]+F[4,x]
F[14,x] = F[15,x]+F[35,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[30,x]
F[17,x] = F[13,x]+F[18,x]
F[18,x] = F[19,x]+F[33,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[30,x]
F[21,x] = F[22,x]+F[4,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[30,x]
F[24,x] = 1/F[30,x]*F[25,x]
F[25,x] = F[26,x]
F[26,x] = -F[27,x]+F[7,x]
F[27,x] = F[28,x]+F[4,x]
F[28,x] = F[29,x]
F[29,x] = F[17,x]*F[30,x]*F[31,x]
F[30,x] = x
F[31,x] = 1/F[30,x]*F[32,x]
F[32,x] = F[2,x]
F[33,x] = F[34,x]
F[34,x] = F[14,x]*F[30,x]
F[35,x] = F[36,x]
F[36,x] = F[28,x]*F[30,x]
F[37,x] = F[101,x]+F[38,x]
F[38,x] = F[39,x]+F[87,x]
F[39,x] = F[0,x]*F[40,x]
F[40,x] = F[1,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[30,x]*F[43,x]
F[43,x] = F[44,x]+F[51,x]
F[44,x] = F[1,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[30,x]*F[47,x]
F[47,x] = F[44,x]+F[48,x]
F[48,x] = F[30,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[30,x]*F[45,x]
F[51,x] = F[52,x]+F[59,x]
F[52,x] = F[53,x]
F[53,x] = F[30,x]*F[54,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[1,x]+F[30,x]
F[56,x] = F[52,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[30,x]*F[52,x]
F[59,x] = F[60,x]+F[61,x]+F[74,x]
F[60,x] = 0
F[61,x] = F[30,x]*F[62,x]
F[62,x] = F[63,x]+F[67,x]
F[63,x] = F[45,x]+F[64,x]
F[64,x] = F[50,x]+F[60,x]+F[65,x]
F[65,x] = F[30,x]*F[66,x]
F[66,x] = F[48,x]
F[67,x] = F[59,x]+F[68,x]
F[68,x] = 2*F[60,x]+F[69,x]+F[70,x]
F[69,x] = F[30,x]*F[59,x]
F[70,x] = F[30,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[57,x]+F[73,x]
F[73,x] = F[69,x]
F[74,x] = F[30,x]*F[75,x]
F[75,x] = F[51,x]+F[76,x]
F[76,x] = F[77,x]+F[82,x]
F[77,x] = F[58,x]+F[60,x]+F[78,x]
F[78,x] = F[30,x]*F[79,x]
F[79,x] = F[80,x]+F[81,x]
F[80,x] = F[30,x]
F[81,x] = F[57,x]
F[82,x] = 2*F[60,x]+F[69,x]+F[83,x]
F[83,x] = F[30,x]*F[84,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[49,x]
F[86,x] = F[73,x]
F[87,x] = F[88,x]
F[88,x] = F[30,x]*F[89,x]
F[89,x] = 1/F[30,x]*F[90,x]
F[90,x] = F[91,x]
F[91,x] = F[92,x]+F[96,x]
F[92,x] = F[0,x]*F[93,x]
F[93,x] = -F[40,x]+F[94,x]
F[94,x] = 1/F[30,x]*F[95,x]
F[95,x] = F[2,x]
F[96,x] = F[100,x]*F[97,x]
F[97,x] = -F[55,x]+F[98,x]
F[98,x] = F[0,x]+F[99,x]
F[99,x] = F[3,x]
F[100,x] = -F[0,x]+F[31,x]
F[101,x] = F[100,x]*F[55,x]
F[102,x] = F[103,x]*F[18,x]
F[103,x] = F[104,x]+F[87,x]
F[104,x] = F[105,x]+F[31,x]
F[105,x] = F[0,x]*F[41,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{30}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)+F_{9}\! \left(x \right)
F_{8}\! \left(x \right) = F_{0}\! \left(x \right) F_{4}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{30}\! \left(x \right)
F_{11}\! \left(x \right) = F_{102}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{37}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{35}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{30}\! \left(x \right)
F_{17}\! \left(x \right) = F_{13}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{33}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{30}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{30}\! \left(x \right)
F_{24}\! \left(x \right) = \frac{F_{25}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = -F_{27}\! \left(x \right)+F_{7}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{17}\! \left(x \right) F_{30}\! \left(x \right) F_{31}\! \left(x \right)
F_{30}\! \left(x \right) = x
F_{31}\! \left(x \right) = \frac{F_{32}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{32}\! \left(x \right) = F_{2}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{14}\! \left(x \right) F_{30}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{28}\! \left(x \right) F_{30}\! \left(x \right)
F_{37}\! \left(x \right) = F_{101}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{87}\! \left(x \right)
F_{39}\! \left(x \right) = F_{0}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{1}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{30}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{51}\! \left(x \right)
F_{44}\! \left(x \right) = F_{1}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{30}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{44}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{30}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{30}\! \left(x \right) F_{45}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{59}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{30}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{1}\! \left(x \right)+F_{30}\! \left(x \right)
F_{56}\! \left(x \right) = F_{52}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{30}\! \left(x \right) F_{52}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{61}\! \left(x \right)+F_{74}\! \left(x \right)
F_{60}\! \left(x \right) = 0
F_{61}\! \left(x \right) = F_{30}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{67}\! \left(x \right)
F_{63}\! \left(x \right) = F_{45}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{50}\! \left(x \right)+F_{60}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{30}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{48}\! \left(x \right)
F_{67}\! \left(x \right) = F_{59}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = 2 F_{60}\! \left(x \right)+F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{30}\! \left(x \right) F_{59}\! \left(x \right)
F_{70}\! \left(x \right) = F_{30}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{57}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{69}\! \left(x \right)
F_{74}\! \left(x \right) = F_{30}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{51}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{82}\! \left(x \right)
F_{77}\! \left(x \right) = F_{58}\! \left(x \right)+F_{60}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{30}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = F_{30}\! \left(x \right)
F_{81}\! \left(x \right) = F_{57}\! \left(x \right)
F_{82}\! \left(x \right) = 2 F_{60}\! \left(x \right)+F_{69}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{30}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{86}\! \left(x \right)
F_{85}\! \left(x \right) = F_{49}\! \left(x \right)
F_{86}\! \left(x \right) = F_{73}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{30}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = \frac{F_{90}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{96}\! \left(x \right)
F_{92}\! \left(x \right) = F_{0}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = -F_{40}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = \frac{F_{95}\! \left(x \right)}{F_{30}\! \left(x \right)}
F_{95}\! \left(x \right) = F_{2}\! \left(x \right)
F_{96}\! \left(x \right) = F_{100}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = -F_{55}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{0}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{3}\! \left(x \right)
F_{100}\! \left(x \right) = -F_{0}\! \left(x \right)+F_{31}\! \left(x \right)
F_{101}\! \left(x \right) = F_{100}\! \left(x \right) F_{55}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{18}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{87}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{31}\! \left(x \right)
F_{105}\! \left(x \right) = F_{0}\! \left(x \right) F_{41}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_30(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_30(x)*F_7(x))
Eq(F_7(x), F_8(x) + F_9(x))
Eq(F_8(x), F_0(x)*F_4(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_30(x))
Eq(F_11(x), F_102(x) + F_12(x))
Eq(F_12(x), F_13(x)*F_37(x))
Eq(F_13(x), F_14(x) + F_4(x))
Eq(F_14(x), F_15(x) + F_35(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_30(x))
Eq(F_17(x), F_13(x) + F_18(x))
Eq(F_18(x), F_19(x) + F_33(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_30(x))
Eq(F_21(x), F_22(x) + F_4(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_30(x))
Eq(F_24(x), F_25(x)/F_30(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), -F_27(x) + F_7(x))
Eq(F_27(x), F_28(x) + F_4(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_17(x)*F_30(x)*F_31(x))
Eq(F_30(x), x)
Eq(F_31(x), F_32(x)/F_30(x))
Eq(F_32(x), F_2(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_14(x)*F_30(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_28(x)*F_30(x))
Eq(F_37(x), F_101(x) + F_38(x))
Eq(F_38(x), F_39(x) + F_87(x))
Eq(F_39(x), F_0(x)*F_40(x))
Eq(F_40(x), F_1(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_30(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_51(x))
Eq(F_44(x), F_1(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_30(x)*F_47(x))
Eq(F_47(x), F_44(x) + F_48(x))
Eq(F_48(x), F_30(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_30(x)*F_45(x))
Eq(F_51(x), F_52(x) + F_59(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_30(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_1(x) + F_30(x))
Eq(F_56(x), F_52(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_30(x)*F_52(x))
Eq(F_59(x), F_60(x) + F_61(x) + F_74(x))
Eq(F_60(x), 0)
Eq(F_61(x), F_30(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_67(x))
Eq(F_63(x), F_45(x) + F_64(x))
Eq(F_64(x), F_50(x) + F_60(x) + F_65(x))
Eq(F_65(x), F_30(x)*F_66(x))
Eq(F_66(x), F_48(x))
Eq(F_67(x), F_59(x) + F_68(x))
Eq(F_68(x), 2*F_60(x) + F_69(x) + F_70(x))
Eq(F_69(x), F_30(x)*F_59(x))
Eq(F_70(x), F_30(x)*F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_57(x) + F_73(x))
Eq(F_73(x), F_69(x))
Eq(F_74(x), F_30(x)*F_75(x))
Eq(F_75(x), F_51(x) + F_76(x))
Eq(F_76(x), F_77(x) + F_82(x))
Eq(F_77(x), F_58(x) + F_60(x) + F_78(x))
Eq(F_78(x), F_30(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_81(x))
Eq(F_80(x), F_30(x))
Eq(F_81(x), F_57(x))
Eq(F_82(x), 2*F_60(x) + F_69(x) + F_83(x))
Eq(F_83(x), F_30(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_49(x))
Eq(F_86(x), F_73(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_30(x)*F_89(x))
Eq(F_89(x), F_90(x)/F_30(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_92(x) + F_96(x))
Eq(F_92(x), F_0(x)*F_93(x))
Eq(F_93(x), -F_40(x) + F_94(x))
Eq(F_94(x), F_95(x)/F_30(x))
Eq(F_95(x), F_2(x))
Eq(F_96(x), F_100(x)*F_97(x))
Eq(F_97(x), -F_55(x) + F_98(x))
Eq(F_98(x), F_0(x) + F_99(x))
Eq(F_99(x), F_3(x))
Eq(F_100(x), -F_0(x) + F_31(x))
Eq(F_101(x), F_100(x)*F_55(x))
Eq(F_102(x), F_103(x)*F_18(x))
Eq(F_103(x), F_104(x) + F_87(x))
Eq(F_104(x), F_105(x) + F_31(x))
Eq(F_105(x), F_0(x)*F_41(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "idx": 1, "original_rule": {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": 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