0123_0132_0231_1023_1203_3012
Counting sequence:
1, 1, 2, 6, 18, 53, 159, 495, 1600, 5333, 18194, 63167, 222294, 790797, 2838452, 10265484, 37368348, 136803359, 503347857, 1860283302, 6902856644, 25706763213, 96048126849, 359937671342, 1352548393986, 5095293095211, 19239398084785, 72802194266612, 276033039859496, 1048530949011737, 3989799629112615, 15206242263066231, 58042975116516968, 221867842088244069, 849218688722393562, 3254557274713803747, 12487657627650216622, 47968785399293917861, 184458785560367742248, 710033854453692613065, 2735746507526853342162, 10550410324778199138269, 40723080570027955885026, 157315702487561837767473, 608201247790833814769270, 2353157649393357935862117, 9111060415375553450595294, 35301050730560691295020491, 136865691700144516457980098, 530979855048809211219395457, 2061232157720372111473191008, 8006280032499519055742685255, 31115718386884408799349170610, 120994274850882546898111688885, 470735553922417979898405464400, 1832348632493796467201543382495, 7135925742667295307722572807838, 27803292807509602526035178888073, 108377422329353086935550993090224, 422640787138732377879154165083155, 1648874747316403472952182100240666, 6435489353041592851773327638763741, 25127391365393720516653125122393372, 98147601989762452729853826400338756, 383506952654785390083712694985826404, 1499074058560248162377498651821221191, 5861712294441154476424684848164713017, 22928357648025842597219546463257412582, 89714803806085984065853813436177013836, 351150956347826249650630015073049665829, 1374859188159761840349695870190032364561, 5384599606157799430782516421576678066682, 21094819151373869017091096187073119282642, 82665045793695465529953497676249898968891, 324032360918121976172068295215632267576269, 1270492252116954382883212049153802760467576, 4982757321395670124918097676418166848375992, 19546930467765378478989209996935562733851057, 76700053913418795913137775653275277459551811, 301035906179453100228211268948248726151613804, 1181799552522007240372061484361993051402481086, 4640552552613187581375882626475111368502143267, 18226088505946818326379989951698862133350712227, 71599963648417725126456737833473325130243655446, 281336060667930772390789855010708092260085337904, 1105679052766915026130152765763379864412920941101, 4346320257853259067026058713999472423110205407117, 17088395398689636996522675150099578912602585401492, 67199460777712256997453292162433944740755078943366, 264309837445629452873488872953694331036173223461159, 1039781433048082360093658258182336205289720598608871, 4091195153680013707859477591338608425447687730637702, 16100375923482363192833910869520431287289293977164252, 63372063511071892401348101500512472516064569902191121, 249479047295980027469315116256637538138186949655140709, 982297718307425207996981186464894002647953895728542266, 3868329923573308211497146572010139904262022313261066742, 15236096799937625941852895106776486816076519335721098487, 60019497961830873026892905482973432766101831827302066101, 236471078063067052092924249812132360993456312367974449224, 931814366019893684188221478805415911052914629566130848156
Generating function in Maple syntax:
1/2/x*(-1+(1-4*x)^(1/2))*(3*x^2-3*x+1)/(x-1)^3
Generating function in latex syntax:
\frac{\left(-1+\sqrt{1-4 x}\right) \left(3 x^{2}-3 x +1\right)}{2 x \left(x -1\right)^{3}}
Generating function in sympy syntax:
(sqrt(1 - 4*x) - 1)*(3*x**2 - 3*x + 1)/(2*x*(x - 1)**3)
Implicit equation for the generating function in Maple syntax:
x*(x-1)^6*F(x)^2+(3*x^2-3*x+1)*(x-1)^3*F(x)+(3*x^2-3*x+1)^2 = 0
Implicit equation for the generating function in latex syntax:
x \left(x -1\right)^{6} F \! \left(x \right)^{2}+\left(3 x^{2}-3 x +1\right) \left(x -1\right)^{3} F \! \left(x \right)+\left(3 x^{2}-3 x +1\right)^{2} = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 18
a(n+4) = -6*(3+2*n)/(5+n)*a(n)+9*(5+3*n)/(5+n)*a(1+n)-2*(29+11*n)/(5+n)*a(n+2)+2*(15+4*n)/(5+n)*a(n+3)+(n-1)/(5+n), n >= 5
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) = 18
a \! \left(n +4\right) = -\frac{6 \left(3+2 n \right) a \! \left(n \right)}{5+n}+\frac{9 \left(5+3 n \right) a \! \left(1+n \right)}{5+n}-\frac{2 \left(29+11 n \right) a \! \left(n +2\right)}{5+n}+\frac{2 \left(15+4 n \right) a \! \left(n +3\right)}{5+n}+\frac{n -1}{5+n}, \quad n \geq 5
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://www.permpal.com/tree/22078/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[13,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[46,x]
F[4,x] = F[5,x]
F[5,x] = F[13,x]*F[6,x]
F[6,x] = F[45,x]+F[7,x]
F[7,x] = F[24,x]+F[8,x]
F[8,x] = F[1,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[13,x]
F[11,x] = F[12,x]+F[15,x]
F[12,x] = F[1,x]+F[13,x]
F[13,x] = F[14,x,1]
F[14,x,k[0]] = k[0]*x
F[15,x] = F[16,x]+F[19,x]
F[16,x] = F[17,x]
F[17,x] = F[13,x]*F[18,x]
F[18,x] = F[1,x]+F[16,x]
F[19,x] = F[20,x]+F[21,x]+F[23,x]
F[20,x] = 0
F[21,x] = F[13,x]*F[22,x]
F[22,x] = F[13,x]+F[19,x]
F[23,x] = F[13,x]*F[16,x]
F[24,x] = F[16,x]+F[25,x]
F[25,x] = F[20,x]+F[26,x]+F[31,x]
F[26,x] = F[13,x]*F[27,x]
F[27,x] = F[16,x]+F[28,x]
F[28,x] = F[20,x]+F[26,x]+F[29,x]
F[29,x] = F[13,x]*F[30,x]
F[30,x] = F[16,x]+F[28,x]
F[31,x] = F[13,x]*F[32,x]
F[32,x] = F[33,x]+F[37,x]
F[33,x] = F[16,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[13,x]*F[36,x]
F[36,x] = F[13,x]+F[34,x]
F[37,x] = F[28,x]+F[38,x]
F[38,x] = 2*F[20,x]+F[39,x]+F[43,x]
F[39,x] = F[13,x]*F[40,x]
F[40,x] = F[41,x]+F[42,x]
F[41,x] = F[23,x]
F[42,x] = F[39,x]
F[43,x] = F[13,x]*F[44,x]
F[44,x] = F[34,x]+F[38,x]
F[45,x] = F[18,x]^2*F[13,x]
F[46,x] = F[13,x]*F[47,x]
F[47,x] = F[48,x,1]
F[48,x,k[0]] = F[1,x]+F[49,x,k[0]]+F[75,x,k[0]]+F[83,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[13,x]*F[51,x,k[0]]
F[51,x,k[0]] = F[45,x]+F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]+F[62,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]+F[57,x,k[0]]
F[54,x,k[0]] = F[1,x]+F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]
F[56,x,k[0]] = F[14,x,k[0]]*F[54,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]+F[9,x]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[14,x,k[0]]*F[60,x,k[0]]
F[60,x,k[0]] = F[16,x]+F[61,x,k[0]]
F[61,x,k[0]] = F[59,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]+F[68,x,k[0]]
F[63,x,k[0]] = F[16,x]+F[64,x,k[0]]
F[64,x,k[0]] = F[20,x]+F[65,x,k[0]]+F[67,x,k[0]]
F[65,x,k[0]] = F[13,x]*F[66,x,k[0]]
F[66,x,k[0]] = F[55,x,k[0]]+F[64,x,k[0]]
F[67,x,k[0]] = F[14,x,k[0]]*F[63,x,k[0]]
F[68,x,k[0]] = F[25,x]+F[69,x,k[0]]
F[69,x,k[0]] = 2*F[20,x]+F[70,x,k[0]]+F[73,x,k[0]]
F[70,x,k[0]] = F[13,x]*F[71,x,k[0]]
F[71,x,k[0]] = F[61,x,k[0]]+F[72,x,k[0]]
F[72,x,k[0]] = 2*F[20,x]+F[70,x,k[0]]+F[73,x,k[0]]
F[73,x,k[0]] = F[14,x,k[0]]*F[74,x,k[0]]
F[74,x,k[0]] = F[28,x]+F[72,x,k[0]]
F[75,x,k[0]] = F[13,x]*F[76,x,k[0]]
F[76,x,k[0]] = F[1,x]+F[77,x,k[0]]+F[80,x,k[0]]+F[82,x]+F[84,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[13,x]*F[79,x,k[0]]
F[79,x,k[0]] = 1/(-1+k[0])*(F[51,x,k[0]]*k[0]-F[51,x,1])
F[80,x,k[0]] = F[13,x]*F[81,x,k[0]]
F[81,x,k[0]] = 1/(-1+k[0])*(F[76,x,k[0]]*k[0]-F[76,x,1])
F[82,x] = F[83,x,1]
F[83,x,k[0]] = F[14,x,k[0]]*F[48,x,k[0]]
F[84,x,k[0]] = F[14,x,k[0]]*F[76,x,k[0]]
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_{13}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{46}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{13}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{45}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{24}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{1}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{13}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{15}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x , 1\right)
F_{14}\! \left(x , y\right) = y x
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{13}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{13}\! \left(x \right)+F_{19}\! \left(x \right)
F_{23}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{24}\! \left(x \right) = F_{16}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{20}\! \left(x \right)+F_{26}\! \left(x \right)+F_{31}\! \left(x \right)
F_{26}\! \left(x \right) = F_{13}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{16}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{20}\! \left(x \right)+F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{13}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{16}\! \left(x \right)+F_{28}\! \left(x \right)
F_{31}\! \left(x \right) = F_{13}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{37}\! \left(x \right)
F_{33}\! \left(x \right) = F_{16}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{13}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{13}\! \left(x \right)+F_{34}\! \left(x \right)
F_{37}\! \left(x \right) = F_{28}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{39}\! \left(x \right)+F_{43}\! \left(x \right)
F_{39}\! \left(x \right) = F_{13}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = F_{23}\! \left(x \right)
F_{42}\! \left(x \right) = F_{39}\! \left(x \right)
F_{43}\! \left(x \right) = F_{13}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{45}\! \left(x \right) = F_{18} \left(x \right)^{2} F_{13}\! \left(x \right)
F_{46}\! \left(x \right) = F_{13}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x , 1\right)
F_{48}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{49}\! \left(x , y\right)+F_{75}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{51}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{45}\! \left(x \right)+F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{54}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{9}\! \left(x \right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{16}\! \left(x \right)+F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{16}\! \left(x \right)+F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{20}\! \left(x \right)+F_{65}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{63}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{25}\! \left(x \right)+F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = 2 F_{20}\! \left(x \right)+F_{70}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = 2 F_{20}\! \left(x \right)+F_{70}\! \left(x , y\right)+F_{73}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{28}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{77}\! \left(x , y\right)+F_{80}\! \left(x , y\right)+F_{82}\! \left(x \right)+F_{84}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = -\frac{-y F_{51}\! \left(x , y\right)+F_{51}\! \left(x , 1\right)}{-1+y}
F_{80}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = -\frac{-y F_{76}\! \left(x , y\right)+F_{76}\! \left(x , 1\right)}{-1+y}
F_{82}\! \left(x \right) = F_{83}\! \left(x , 1\right)
F_{83}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{48}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{76}\! \left(x , y\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_13(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_46(x))
Eq(F_4(x), F_5(x))
Eq(F_5(x), F_13(x)*F_6(x))
Eq(F_6(x), F_45(x) + F_7(x))
Eq(F_7(x), F_24(x) + F_8(x))
Eq(F_8(x), F_1(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_13(x))
Eq(F_11(x), F_12(x) + F_15(x))
Eq(F_12(x), F_1(x) + F_13(x))
Eq(F_13(x), F_14(x, 1))
Eq(F_14(x, k_0), k_0*x)
Eq(F_15(x), F_16(x) + F_19(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_13(x)*F_18(x))
Eq(F_18(x), F_1(x) + F_16(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_23(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_13(x)*F_22(x))
Eq(F_22(x), F_13(x) + F_19(x))
Eq(F_23(x), F_13(x)*F_16(x))
Eq(F_24(x), F_16(x) + F_25(x))
Eq(F_25(x), F_20(x) + F_26(x) + F_31(x))
Eq(F_26(x), F_13(x)*F_27(x))
Eq(F_27(x), F_16(x) + F_28(x))
Eq(F_28(x), F_20(x) + F_26(x) + F_29(x))
Eq(F_29(x), F_13(x)*F_30(x))
Eq(F_30(x), F_16(x) + F_28(x))
Eq(F_31(x), F_13(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_37(x))
Eq(F_33(x), F_16(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_13(x)*F_36(x))
Eq(F_36(x), F_13(x) + F_34(x))
Eq(F_37(x), F_28(x) + F_38(x))
Eq(F_38(x), 2*F_20(x) + F_39(x) + F_43(x))
Eq(F_39(x), F_13(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_42(x))
Eq(F_41(x), F_23(x))
Eq(F_42(x), F_39(x))
Eq(F_43(x), F_13(x)*F_44(x))
Eq(F_44(x), F_34(x) + F_38(x))
Eq(F_45(x), F_13(x)*F_18(x)**2)
Eq(F_46(x), F_13(x)*F_47(x))
Eq(F_47(x), F_48(x, 1))
Eq(F_48(x, k_0), F_1(x) + F_49(x, k_0) + F_75(x, k_0) + F_83(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_13(x)*F_51(x, k_0))
Eq(F_51(x, k_0), F_45(x) + F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0) + F_62(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0) + F_57(x, k_0))
Eq(F_54(x, k_0), F_1(x) + F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0))
Eq(F_56(x, k_0), F_14(x, k_0)*F_54(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0) + F_9(x))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_14(x, k_0)*F_60(x, k_0))
Eq(F_60(x, k_0), F_16(x) + F_61(x, k_0))
Eq(F_61(x, k_0), F_59(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0) + F_68(x, k_0))
Eq(F_63(x, k_0), F_16(x) + F_64(x, k_0))
Eq(F_64(x, k_0), F_20(x) + F_65(x, k_0) + F_67(x, k_0))
Eq(F_65(x, k_0), F_13(x)*F_66(x, k_0))
Eq(F_66(x, k_0), F_55(x, k_0) + F_64(x, k_0))
Eq(F_67(x, k_0), F_14(x, k_0)*F_63(x, k_0))
Eq(F_68(x, k_0), F_25(x) + F_69(x, k_0))
Eq(F_69(x, k_0), 2*F_20(x) + F_70(x, k_0) + F_73(x, k_0))
Eq(F_70(x, k_0), F_13(x)*F_71(x, k_0))
Eq(F_71(x, k_0), F_61(x, k_0) + F_72(x, k_0))
Eq(F_72(x, k_0), 2*F_20(x) + F_70(x, k_0) + F_73(x, k_0))
Eq(F_73(x, k_0), F_14(x, k_0)*F_74(x, k_0))
Eq(F_74(x, k_0), F_28(x) + F_72(x, k_0))
Eq(F_75(x, k_0), F_13(x)*F_76(x, k_0))
Eq(F_76(x, k_0), F_1(x) + F_77(x, k_0) + F_80(x, k_0) + F_82(x) + F_84(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_13(x)*F_79(x, k_0))
Eq(F_79(x, k_0), (k_0*F_51(x, k_0) - F_51(x, 1))/(k_0 - 1))
Eq(F_80(x, k_0), F_13(x)*F_81(x, k_0))
Eq(F_81(x, k_0), (k_0*F_76(x, k_0) - F_76(x, 1))/(k_0 - 1))
Eq(F_82(x), F_83(x, 1))
Eq(F_83(x, k_0), F_14(x, k_0)*F_48(x, k_0))
Eq(F_84(x, k_0), F_14(x, k_0)*F_76(x, k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "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": "row_placements_tracked_fusion", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": []}, {"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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [1, 1], [1, 1], [3, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [1, 1], [1, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [1, 1], [1, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], 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