0123_0213_0231_0312_2130
Counting sequence:
1, 1, 2, 6, 19, 56, 155, 406, 1017, 2463, 5818, 13493, 30874, 69951, 157348, 352076, 784757, 1744246, 3868861, 8568444, 18955715, 41901197, 92566724, 204406395, 451227588, 995853261, 2197458454, 4848322018, 10696021031, 23595202500, 52047953519, 114806857394, 253233074013, 558553188555, 1231976479262, 2717288365393, 5993295498110, 13218835388331, 29155392634968, 64304782175176, 141829534640169, 312816298225442, 689940349839281, 1521715041843768, 3356254160652999, 7402461257412185, 16326657921677000, 36009602955284791, 79421720484270536, 175170185157786841, 386350112854718314, 852122172045138174, 1879414894683356539, 4145180493508158352, 9142484115783477891, 20164384674259065102, 44473952346757067265, 98090392862037146935, 216345176955803675330, 477164316868574272045, 1052419043766865864866, 2321183292267425436503, 5119530946348995353932, 11291481009188316816772, 24904145428313089526813, 54927821993367665112334, 121147125303985168207077, 267198396534737437815604, 589324615869358073788171, 1299796358347670860707173, 2866791115341564237202956, 6322906849968941171095603, 13945610063813492903777804, 30758011251912944368544549, 67838929368267163932855294, 149623468823764549117950298, 330004948937331104977583119, 727848827304235164609627036, 1605321123531429731431953623, 3540647196160691211657851050, 7809143219885313084836445157, 17223607563722252041832326883, 37987862324285086932961110182, 83784867869555574729124760393, 184793343304613380916086554630, 407574548936391915959505028163, 898933965746999453258510339456, 1982661274806152401237853572224, 4372897098560896878850334041425, 9644728162888533485179046637370, 21272117600615159806230936938585, 46917132299842897200167066233200, 103478992762657949029003027518095, 228230103126066359716581698711985, 503377338552194539629165018817168, 1110233669867401253135512327058287, 2448697442861442013831620169903248, 5400772224276005939984598437613233, 11911778118420913653640916098358226, 26272253679705697214341852341692150, 57945279583691328782432909992153059
Generating function in Maple syntax:
(x^8-x^7-x^6-x^4+5*x^3-9*x^2+5*x-1)/(x^2+x-1)/(x^3+2*x-1)/(x-1)^3
Generating function in latex syntax:
\frac{x^{8}-x^{7}-x^{6}-x^{4}+5 x^{3}-9 x^{2}+5 x -1}{\left(x^{2}+x -1\right) \left(x^{3}+2 x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(x**8 - x**7 - x**6 - x**4 + 5*x**3 - 9*x**2 + 5*x - 1)/((x - 1)**3*(x**2 + x - 1)*(x**3 + 2*x - 1))
Implicit equation for the generating function in Maple syntax:
(x^2+x-1)*(x^3+2*x-1)*(x-1)^3*F(x)-x^8+x^7+x^6+x^4-5*x^3+9*x^2-5*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}+x -1\right) \left(x^{3}+2 x -1\right) \left(x -1\right)^{3} F \! \left(x \right)-x^{8}+x^{7}+x^{6}+x^{4}-5 x^{3}+9 x^{2}-5 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,35/5664*((3*I*59^(1/2)-9)*(108+12*59^(1/2)*3^(1/2))^(1/3)-9*(I-1/9*59^(1/2))*3^(5/6)*(36+4*59^(1/2)*3^(1/2))^(1/3)+48*I*3^(1/2)-48)^(-n)*(-(-2832/35*(108+12*59^(1/2)*3^(1/2))^(-2/3*n)*576^n*((47/10*5^(1/2)-21/2)*(-1/2*5^(1/2)-1/2)^(-n)+n^2+7*n+16)*(-1/12*(108+12*59^(1/2)*3^(1/2))^(1/3)-1/12*I*(36+4*59^(1/2)*3^(1/2))^(1/3)*3^(5/6)+1/96*((-I*59^(1/2)-3)*18^(1/3)+9*I*3^(1/6)*2^(1/3)+59^(1/2)*3^(1/6)*2^(1/3))*(9+59^(1/2)*3^(1/2))^(2/3))^n+66552/175*(5^(1/2)+105/47)*(108+12*59^(1/2)*3^(1/2))^(-2/3*n)*(5^(1/2)-1)^(-n)*576^n*(-1/6*(108+12*59^(1/2)*3^(1/2))^(1/3)-1/6*I*(36+4*59^(1/2)*3^(1/2))^(1/3)*3^(5/6)+1/48*((-I*59^(1/2)-3)*18^(1/3)+9*I*3^(1/6)*2^(1/3)+59^(1/2)*3^(1/6)*2^(1/3))*(9+59^(1/2)*3^(1/2))^(2/3))^n-59/35*(I-113/177*59^(1/2))*3^(2*n+1/2)*64^n*(108+12*59^(1/2)*3^(1/2))^(-2/3*n+1/3)-767/210*(I+35/767*59^(1/2))*3^(2*n+1/2)*64^n*(108+12*59^(1/2)*3^(1/2))^(-2/3*n+2/3)+(3^(2*n+2/3)*(9+59^(1/2)*3^(1/2))^(2/3)*(I*59^(1/2)+767/105)*2^(6*n+1/3)+113/35*(I*59^(1/2)-59/113)*(9+59^(1/2)*3^(1/2))^(1/3)*3^(2*n+1/3)*2^(6*n+2/3)-944/7*576^n)*(108+12*59^(1/2)*3^(1/2))^(-2/3*n))*(1/576*(-3*I*59^(1/2)-9)*(108+12*59^(1/2)*3^(1/2))^(1/3)+1/64*(I+1/9*59^(1/2))*3^(5/6)*(36+4*59^(1/2)*3^(1/2))^(1/3)-1/12*I*3^(1/2)-1/12)^(-n)*(-1/12*(108+12*59^(1/2)*3^(1/2))^(1/3)+1/12*I*(36+4*59^(1/2)*3^(1/2))^(1/3)*3^(5/6)+1/96*((I*59^(1/2)-3)*18^(1/3)-9*I*2^(1/3)*3^(1/6)+59^(1/2)*3^(1/6)*2^(1/3))*(9+59^(1/2)*3^(1/2))^(2/3))^n+(-1/12*(108+12*59^(1/2)*3^(1/2))^(1/3)-1/12*I*(36+4*59^(1/2)*3^(1/2))^(1/3)*3^(5/6)+1/96*((-I*59^(1/2)-3)*18^(1/3)+9*I*3^(1/6)*2^(1/3)+59^(1/2)*3^(1/6)*2^(1/3))*(9+59^(1/2)*3^(1/2))^(2/3))^n*(226/105*(1/48*(-3*I*59^(1/2)-9)*(108+12*59^(1/2)*3^(1/2))^(1/3)+3/16*(I+1/9*59^(1/2))*3^(5/6)*(36+4*59^(1/2)*3^(1/2))^(1/3)-I*3^(1/2)-1)^(-n)*(8*(108+12*59^(1/2)*3^(1/2))^(1/3)+(-59^(1/2)*3^(1/6)*2^(1/3)+3*18^(1/3))*(9+59^(1/2)*3^(1/2))^(2/3))^(-n)*(64^n*59^(1/2)*3^(2*n+1/2)*(108+12*59^(1/2)*3^(1/2))^(-2/3*n+1/3)-35/226*64^n*59^(1/2)*3^(2*n+1/2)*(108+12*59^(1/2)*3^(1/2))^(-2/3*n+2/3)+767/113*(108+12*59^(1/2)*3^(1/2))^(-2/3*n)*(3^(2*n+2/3)*2^(6*n+1/3)*(9+59^(1/2)*3^(1/2))^(2/3)-3/13*3^(2*n+1/3)*2^(6*n+2/3)*(9+59^(1/2)*3^(1/2))^(1/3)))*(-48*(108+12*59^(1/2)*3^(1/2))^(1/3)+48*I*(36+4*59^(1/2)*3^(1/2))^(1/3)*3^(5/6)+((6*I*59^(1/2)-18)*18^(1/3)-54*I*2^(1/3)*3^(1/6)+6*59^(1/2)*3^(1/6)*2^(1/3))*(9+59^(1/2)*3^(1/2))^(2/3))^n+(944/7*9^n*32^n*(108+12*59^(1/2)*3^(1/2))^(-2/3*n)*(8*(108+12*59^(1/2)*3^(1/2))^(1/3)+(-59^(1/2)*3^(1/6)*2^(1/3)+3*18^(1/3))*(9+59^(1/2)*3^(1/2))^(2/3))^(-n)*(-8*(108+12*59^(1/2)*3^(1/2))^(1/3)+8*I*(36+4*59^(1/2)*3^(1/2))^(1/3)*3^(5/6)+((I*59^(1/2)-3)*18^(1/3)-9*I*2^(1/3)*3^(1/6)+59^(1/2)*3^(1/6)*2^(1/3))*(9+59^(1/2)*3^(1/2))^(2/3))^n-59/35*(113/177*59^(1/2)+I)*3^(2*n+1/2)*64^n*(108+12*59^(1/2)*3^(1/2))^(-2/3*n+1/3)-767/210*(-35/767*59^(1/2)+I)*3^(2*n+1/2)*64^n*(108+12*59^(1/2)*3^(1/2))^(-2/3*n+2/3)+(108+12*59^(1/2)*3^(1/2))^(-2/3*n)*(3^(2*n+2/3)*(9+59^(1/2)*3^(1/2))^(2/3)*(I*59^(1/2)-767/105)*2^(6*n+1/3)+113/35*(I*59^(1/2)+59/113)*(9+59^(1/2)*3^(1/2))^(1/3)*3^(2*n+1/3)*2^(6*n+2/3)+944/7*576^n))*(1/576*(-3*I*59^(1/2)-9)*(108+12*59^(1/2)*3^(1/2))^(1/3)+1/64*(I+1/9*59^(1/2))*3^(5/6)*(36+4*59^(1/2)*3^(1/2))^(1/3)-1/12*I*3^(1/2)-1/12)^(-n))))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{35 \left(\left(3 \,\mathrm{I} \sqrt{59}-9\right) \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}-9 \left(\mathrm{I}-\frac{\sqrt{59}}{9}\right) 3^{\frac{5}{6}} \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}+48 \,\mathrm{I} \sqrt{3}-48\right)^{-n} \left(-\left(-\frac{2832 \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{-\frac{2 n}{3}} 576^{n} \left(\left(\frac{47 \sqrt{5}}{10}-\frac{21}{2}\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}+n^{2}+7 n +16\right) \left(-\frac{\left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}-\frac{\mathrm{I} \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} 3^{\frac{5}{6}}}{12}+\frac{\left(\left(-\mathrm{I} \sqrt{59}-3\right) 18^{\frac{1}{3}}+9 \,\mathrm{I} \,3^{\frac{1}{6}} 2^{\frac{1}{3}}+\sqrt{59}\, 3^{\frac{1}{6}} 2^{\frac{1}{3}}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}}{96}\right)^{n}}{35}+\frac{66552 \left(\sqrt{5}+\frac{105}{47}\right) \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{-\frac{2 n}{3}} \left(\sqrt{5}-1\right)^{-n} 576^{n} \left(-\frac{\left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\mathrm{I} \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} 3^{\frac{5}{6}}}{6}+\frac{\left(\left(-\mathrm{I} \sqrt{59}-3\right) 18^{\frac{1}{3}}+9 \,\mathrm{I} \,3^{\frac{1}{6}} 2^{\frac{1}{3}}+\sqrt{59}\, 3^{\frac{1}{6}} 2^{\frac{1}{3}}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}}{48}\right)^{n}}{175}-\frac{59 \left(\mathrm{I}-\frac{113 \sqrt{59}}{177}\right) 3^{2 n +\frac{1}{2}} 64^{n} \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{-\frac{2 n}{3}+\frac{1}{3}}}{35}-\frac{767 \left(\mathrm{I}+\frac{35 \sqrt{59}}{767}\right) 3^{2 n +\frac{1}{2}} 64^{n} \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{-\frac{2 n}{3}+\frac{2}{3}}}{210}+\left(3^{2 n +\frac{2}{3}} \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}} \left(\mathrm{I} \sqrt{59}+\frac{767}{105}\right) 2^{6 n +\frac{1}{3}}+\frac{113 \left(\mathrm{I} \sqrt{59}-\frac{59}{113}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} 3^{2 n +\frac{1}{3}} 2^{6 n +\frac{2}{3}}}{35}-\frac{944 \,576^{n}}{7}\right) \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{-\frac{2 n}{3}}\right) \left(\frac{\left(-3 \,\mathrm{I} \sqrt{59}-9\right) \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{576}+\frac{\left(\mathrm{I}+\frac{\sqrt{59}}{9}\right) 3^{\frac{5}{6}} \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{64}-\frac{\mathrm{I} \sqrt{3}}{12}-\frac{1}{12}\right)^{-n} \left(-\frac{\left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}+\frac{\mathrm{I} \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} 3^{\frac{5}{6}}}{12}+\frac{\left(\left(\mathrm{I} \sqrt{59}-3\right) 18^{\frac{1}{3}}-9 \,\mathrm{I} \,2^{\frac{1}{3}} 3^{\frac{1}{6}}+\sqrt{59}\, 3^{\frac{1}{6}} 2^{\frac{1}{3}}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}}{96}\right)^{n}+\left(-\frac{\left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{12}-\frac{\mathrm{I} \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} 3^{\frac{5}{6}}}{12}+\frac{\left(\left(-\mathrm{I} \sqrt{59}-3\right) 18^{\frac{1}{3}}+9 \,\mathrm{I} \,3^{\frac{1}{6}} 2^{\frac{1}{3}}+\sqrt{59}\, 3^{\frac{1}{6}} 2^{\frac{1}{3}}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}}{96}\right)^{n} \left(\frac{226 \left(\frac{\left(-3 \,\mathrm{I} \sqrt{59}-9\right) \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{48}+\frac{3 \left(\mathrm{I}+\frac{\sqrt{59}}{9}\right) 3^{\frac{5}{6}} \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{16}-\mathrm{I} \sqrt{3}-1\right)^{-n} \left(8 \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}+\left(-\sqrt{59}\, 3^{\frac{1}{6}} 2^{\frac{1}{3}}+3 \,18^{\frac{1}{3}}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}\right)^{-n} \left(64^{n} \sqrt{59}\, 3^{2 n +\frac{1}{2}} \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{-\frac{2 n}{3}+\frac{1}{3}}-\frac{35 \,64^{n} \sqrt{59}\, 3^{2 n +\frac{1}{2}} \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{-\frac{2 n}{3}+\frac{2}{3}}}{226}+\frac{767 \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{-\frac{2 n}{3}} \left(3^{2 n +\frac{2}{3}} 2^{6 n +\frac{1}{3}} \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}-\frac{3 \,3^{2 n +\frac{1}{3}} 2^{6 n +\frac{2}{3}} \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{13}\right)}{113}\right) \left(-48 \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}+48 \,\mathrm{I} \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} 3^{\frac{5}{6}}+\left(\left(6 \,\mathrm{I} \sqrt{59}-18\right) 18^{\frac{1}{3}}-54 \,\mathrm{I} \,2^{\frac{1}{3}} 3^{\frac{1}{6}}+6 \sqrt{59}\, 3^{\frac{1}{6}} 2^{\frac{1}{3}}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}\right)^{n}}{105}+\left(\frac{944 \,9^{n} 32^{n} \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{-\frac{2 n}{3}} \left(8 \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}+\left(-\sqrt{59}\, 3^{\frac{1}{6}} 2^{\frac{1}{3}}+3 \,18^{\frac{1}{3}}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}\right)^{-n} \left(-8 \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}+8 \,\mathrm{I} \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} 3^{\frac{5}{6}}+\left(\left(\mathrm{I} \sqrt{59}-3\right) 18^{\frac{1}{3}}-9 \,\mathrm{I} \,2^{\frac{1}{3}} 3^{\frac{1}{6}}+\sqrt{59}\, 3^{\frac{1}{6}} 2^{\frac{1}{3}}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}}\right)^{n}}{7}-\frac{59 \left(\frac{113 \sqrt{59}}{177}+\mathrm{I}\right) 3^{2 n +\frac{1}{2}} 64^{n} \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{-\frac{2 n}{3}+\frac{1}{3}}}{35}-\frac{767 \left(-\frac{35 \sqrt{59}}{767}+\mathrm{I}\right) 3^{2 n +\frac{1}{2}} 64^{n} \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{-\frac{2 n}{3}+\frac{2}{3}}}{210}+\left(108+12 \sqrt{59}\, \sqrt{3}\right)^{-\frac{2 n}{3}} \left(3^{2 n +\frac{2}{3}} \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{2}{3}} \left(\mathrm{I} \sqrt{59}-\frac{767}{105}\right) 2^{6 n +\frac{1}{3}}+\frac{113 \left(\mathrm{I} \sqrt{59}+\frac{59}{113}\right) \left(9+\sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}} 3^{2 n +\frac{1}{3}} 2^{6 n +\frac{2}{3}}}{35}+\frac{944 \,576^{n}}{7}\right)\right) \left(\frac{\left(-3 \,\mathrm{I} \sqrt{59}-9\right) \left(108+12 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{576}+\frac{\left(\mathrm{I}+\frac{\sqrt{59}}{9}\right) 3^{\frac{5}{6}} \left(36+4 \sqrt{59}\, \sqrt{3}\right)^{\frac{1}{3}}}{64}-\frac{\mathrm{I} \sqrt{3}}{12}-\frac{1}{12}\right)^{-n}\right)\right)}{5664} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 56
a(6) = 155
a(7) = 406
a(8) = 1017
a(n+5) = -a(n)-a(n+1)-a(n+2)-a(n+3)+3*a(n+4)+(n+4)*(n+2), n >= 9
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) = 19
a \! \left(5\right) = 56
a \! \left(6\right) = 155
a \! \left(7\right) = 406
a \! \left(8\right) = 1017
a \! \left(n +5\right) = -a \! \left(n \right)-a \! \left(n +1\right)-a \! \left(n +2\right)-a \! \left(n +3\right)+3 a \! \left(n +4\right)+\left(n +4\right) \left(n +2\right), \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16682/
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[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[14,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[11,x]
F[14,x] = F[15,x]+F[2,x]
F[15,x] = F[136,x]+F[16,x]+F[17,x]
F[16,x] = 0
F[17,x] = F[18,x]*F[4,x]
F[18,x] = F[19,x]+F[30,x]
F[19,x] = F[20,x]+F[7,x]
F[20,x] = F[16,x]+F[21,x]+F[27,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]
F[23,x] = F[11,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[11,x]+F[24,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[13,x]+F[29,x]
F[29,x] = F[24,x]
F[30,x] = F[31,x]+F[65,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[38,x]
F[34,x] = F[35,x]+F[7,x]
F[35,x] = F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[11,x]
F[38,x] = F[31,x]+F[39,x]
F[39,x] = 2*F[16,x]+F[40,x]+F[48,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[35,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[47,x]
F[46,x] = F[35,x]
F[47,x] = F[44,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[53,x]+F[55,x]
F[53,x] = F[11,x]+F[54,x]
F[54,x] = F[36,x]
F[55,x] = F[50,x]+F[56,x]
F[56,x] = 2*F[16,x]+F[48,x]+F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[59,x]+F[60,x]
F[59,x] = F[54,x]
F[60,x] = F[61,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = F[54,x]
F[64,x] = F[61,x]
F[65,x] = 2*F[16,x]+F[118,x]+F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[72,x]
F[68,x] = F[20,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[24,x]
F[72,x] = F[107,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]+F[80,x]
F[76,x] = F[20,x]+F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[24,x]
F[80,x] = F[73,x]+F[81,x]
F[81,x] = 3*F[16,x]+F[82,x]+F[90,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[77,x]
F[85,x] = F[86,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[77,x]
F[89,x] = F[86,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[93,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[95,x]+F[97,x]
F[95,x] = F[24,x]+F[96,x]
F[96,x] = F[78,x]
F[97,x] = F[92,x]+F[98,x]
F[98,x] = 3*F[16,x]+F[90,x]+F[99,x]
F[99,x] = F[100,x]*F[4,x]
F[100,x] = F[101,x]+F[102,x]
F[101,x] = F[96,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[4,x]
F[104,x] = F[105,x]+F[106,x]
F[105,x] = F[96,x]
F[106,x] = F[103,x]
F[107,x] = 3*F[16,x]+F[108,x]+F[116,x]
F[108,x] = F[109,x]*F[4,x]
F[109,x] = F[110,x]+F[111,x]
F[110,x] = F[69,x]
F[111,x] = F[112,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[114,x]+F[115,x]
F[114,x] = F[69,x]
F[115,x] = F[112,x]
F[116,x] = F[117,x]*F[4,x]
F[117,x] = F[92,x]
F[118,x] = F[119,x]*F[4,x]
F[119,x] = F[120,x]
F[120,x] = F[121,x]+F[50,x]
F[121,x] = F[122,x]
F[122,x] = F[123,x]*F[4,x]
F[123,x] = F[124,x]+F[126,x]
F[124,x] = F[125,x]+F[24,x]
F[125,x] = F[70,x]
F[126,x] = F[127,x]+F[92,x]
F[127,x] = 3*F[16,x]+F[116,x]+F[128,x]
F[128,x] = F[129,x]*F[4,x]
F[129,x] = F[130,x]+F[131,x]
F[130,x] = F[125,x]
F[131,x] = F[132,x]
F[132,x] = F[133,x]*F[4,x]
F[133,x] = F[134,x]+F[135,x]
F[134,x] = F[125,x]
F[135,x] = F[132,x]
F[136,x] = F[137,x]*F[4,x]
F[137,x] = F[138,x]+F[176,x]
F[138,x] = F[139,x]+F[2,x]
F[139,x] = F[140,x]+F[16,x]+F[175,x]
F[140,x] = F[141,x]*F[4,x]
F[141,x] = F[142,x]+F[144,x]
F[142,x] = F[11,x]+F[143,x]
F[143,x] = F[16,x]+F[21,x]+F[25,x]
F[144,x] = F[145,x]+F[50,x]
F[145,x] = 2*F[16,x]+F[118,x]+F[146,x]
F[146,x] = F[147,x]*F[4,x]
F[147,x] = F[148,x]+F[150,x]
F[148,x] = F[143,x]+F[149,x]
F[149,x] = F[70,x]
F[150,x] = F[151,x]+F[166,x]
F[151,x] = F[152,x]
F[152,x] = F[153,x]*F[4,x]
F[153,x] = F[154,x]+F[156,x]
F[154,x] = F[143,x]+F[155,x]
F[155,x] = F[78,x]
F[156,x] = F[151,x]+F[157,x]
F[157,x] = 3*F[16,x]+F[158,x]+F[90,x]
F[158,x] = F[159,x]*F[4,x]
F[159,x] = F[160,x]+F[161,x]
F[160,x] = F[155,x]
F[161,x] = F[162,x]
F[162,x] = F[163,x]*F[4,x]
F[163,x] = F[164,x]+F[165,x]
F[164,x] = F[155,x]
F[165,x] = F[162,x]
F[166,x] = 3*F[16,x]+F[116,x]+F[167,x]
F[167,x] = F[168,x]*F[4,x]
F[168,x] = F[169,x]+F[170,x]
F[169,x] = F[149,x]
F[170,x] = F[171,x]
F[171,x] = F[172,x]*F[4,x]
F[172,x] = F[173,x]+F[174,x]
F[173,x] = F[149,x]
F[174,x] = F[171,x]
F[175,x] = F[138,x]*F[4,x]
F[176,x] = F[139,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_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{14}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = F_{136}\! \left(x \right)+F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = 0
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{30}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{7}\! \left(x \right)
F_{20}\! \left(x \right) = F_{16}\! \left(x \right)+F_{21}\! \left(x \right)+F_{27}\! \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_{11}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right)+F_{24}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{13}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{24}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{65}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{7}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{11}\! \left(x \right)
F_{38}\! \left(x \right) = F_{31}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{40}\! \left(x \right)+F_{48}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{35}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{47}\! \left(x \right)
F_{46}\! \left(x \right) = F_{35}\! \left(x \right)
F_{47}\! \left(x \right) = F_{44}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{55}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{36}\! \left(x \right)
F_{55}\! \left(x \right) = F_{50}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{48}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{60}\! \left(x \right)
F_{59}\! \left(x \right) = F_{54}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = F_{54}\! \left(x \right)
F_{64}\! \left(x \right) = F_{61}\! \left(x \right)
F_{65}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{118}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{72}\! \left(x \right)
F_{68}\! \left(x \right) = F_{20}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{24}\! \left(x \right)
F_{72}\! \left(x \right) = F_{107}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{80}\! \left(x \right)
F_{76}\! \left(x \right) = F_{20}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{24}\! \left(x \right)
F_{80}\! \left(x \right) = F_{73}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = 3 F_{16}\! \left(x \right)+F_{82}\! \left(x \right)+F_{90}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{77}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{77}\! \left(x \right)
F_{89}\! \left(x \right) = F_{86}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{97}\! \left(x \right)
F_{95}\! \left(x \right) = F_{24}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{78}\! \left(x \right)
F_{97}\! \left(x \right) = F_{92}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = 3 F_{16}\! \left(x \right)+F_{90}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{4}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{102}\! \left(x \right)
F_{101}\! \left(x \right) = F_{96}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{106}\! \left(x \right)
F_{105}\! \left(x \right) = F_{96}\! \left(x \right)
F_{106}\! \left(x \right) = F_{103}\! \left(x \right)
F_{107}\! \left(x \right) = 3 F_{16}\! \left(x \right)+F_{108}\! \left(x \right)+F_{116}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{111}\! \left(x \right)
F_{110}\! \left(x \right) = F_{69}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{115}\! \left(x \right)
F_{114}\! \left(x \right) = F_{69}\! \left(x \right)
F_{115}\! \left(x \right) = F_{112}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{4}\! \left(x \right)
F_{117}\! \left(x \right) = F_{92}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{4}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{50}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{4}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{126}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{24}\! \left(x \right)
F_{125}\! \left(x \right) = F_{70}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{92}\! \left(x \right)
F_{127}\! \left(x \right) = 3 F_{16}\! \left(x \right)+F_{116}\! \left(x \right)+F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{4}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{131}\! \left(x \right)
F_{130}\! \left(x \right) = F_{125}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right) F_{4}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{135}\! \left(x \right)
F_{134}\! \left(x \right) = F_{125}\! \left(x \right)
F_{135}\! \left(x \right) = F_{132}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{4}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{176}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{2}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{16}\! \left(x \right)+F_{175}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{4}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{144}\! \left(x \right)
F_{142}\! \left(x \right) = F_{11}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{16}\! \left(x \right)+F_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{50}\! \left(x \right)
F_{145}\! \left(x \right) = 2 F_{16}\! \left(x \right)+F_{118}\! \left(x \right)+F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right) F_{4}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{150}\! \left(x \right)
F_{148}\! \left(x \right) = F_{143}\! \left(x \right)+F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{70}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{166}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right) F_{4}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right)+F_{156}\! \left(x \right)
F_{154}\! \left(x \right) = F_{143}\! \left(x \right)+F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{78}\! \left(x \right)
F_{156}\! \left(x \right) = F_{151}\! \left(x \right)+F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = 3 F_{16}\! \left(x \right)+F_{158}\! \left(x \right)+F_{90}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right) F_{4}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{161}\! \left(x \right)
F_{160}\! \left(x \right) = F_{155}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right) F_{4}\! \left(x \right)
F_{163}\! \left(x \right) = F_{164}\! \left(x \right)+F_{165}\! \left(x \right)
F_{164}\! \left(x \right) = F_{155}\! \left(x \right)
F_{165}\! \left(x \right) = F_{162}\! \left(x \right)
F_{166}\! \left(x \right) = 3 F_{16}\! \left(x \right)+F_{116}\! \left(x \right)+F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right) F_{4}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{170}\! \left(x \right)
F_{169}\! \left(x \right) = F_{149}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right) F_{4}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)+F_{174}\! \left(x \right)
F_{173}\! \left(x \right) = F_{149}\! \left(x \right)
F_{174}\! \left(x \right) = F_{171}\! \left(x \right)
F_{175}\! \left(x \right) = F_{138}\! \left(x \right) F_{4}\! \left(x \right)
F_{176}\! \left(x \right) = F_{139}\! \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_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_14(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_11(x))
Eq(F_14(x), F_15(x) + F_2(x))
Eq(F_15(x), F_136(x) + F_16(x) + F_17(x))
Eq(F_16(x), 0)
Eq(F_17(x), F_18(x)*F_4(x))
Eq(F_18(x), F_19(x) + F_30(x))
Eq(F_19(x), F_20(x) + F_7(x))
Eq(F_20(x), F_16(x) + F_21(x) + F_27(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_11(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_11(x) + F_24(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_13(x) + F_29(x))
Eq(F_29(x), F_24(x))
Eq(F_30(x), F_31(x) + F_65(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_38(x))
Eq(F_34(x), F_35(x) + F_7(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_11(x))
Eq(F_38(x), F_31(x) + F_39(x))
Eq(F_39(x), 2*F_16(x) + F_40(x) + F_48(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_35(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_47(x))
Eq(F_46(x), F_35(x))
Eq(F_47(x), F_44(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_55(x))
Eq(F_53(x), F_11(x) + F_54(x))
Eq(F_54(x), F_36(x))
Eq(F_55(x), F_50(x) + F_56(x))
Eq(F_56(x), 2*F_16(x) + F_48(x) + F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_60(x))
Eq(F_59(x), F_54(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), F_54(x))
Eq(F_64(x), F_61(x))
Eq(F_65(x), F_118(x) + 2*F_16(x) + F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_72(x))
Eq(F_68(x), F_20(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_24(x))
Eq(F_72(x), F_107(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_80(x))
Eq(F_76(x), F_20(x) + F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_24(x))
Eq(F_80(x), F_73(x) + F_81(x))
Eq(F_81(x), 3*F_16(x) + F_82(x) + F_90(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_77(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_77(x))
Eq(F_89(x), F_86(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_95(x) + F_97(x))
Eq(F_95(x), F_24(x) + F_96(x))
Eq(F_96(x), F_78(x))
Eq(F_97(x), F_92(x) + F_98(x))
Eq(F_98(x), 3*F_16(x) + F_90(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_4(x))
Eq(F_100(x), F_101(x) + F_102(x))
Eq(F_101(x), F_96(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_4(x))
Eq(F_104(x), F_105(x) + F_106(x))
Eq(F_105(x), F_96(x))
Eq(F_106(x), F_103(x))
Eq(F_107(x), F_108(x) + F_116(x) + 3*F_16(x))
Eq(F_108(x), F_109(x)*F_4(x))
Eq(F_109(x), F_110(x) + F_111(x))
Eq(F_110(x), F_69(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_114(x) + F_115(x))
Eq(F_114(x), F_69(x))
Eq(F_115(x), F_112(x))
Eq(F_116(x), F_117(x)*F_4(x))
Eq(F_117(x), F_92(x))
Eq(F_118(x), F_119(x)*F_4(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_121(x) + F_50(x))
Eq(F_121(x), F_122(x))
Eq(F_122(x), F_123(x)*F_4(x))
Eq(F_123(x), F_124(x) + F_126(x))
Eq(F_124(x), F_125(x) + F_24(x))
Eq(F_125(x), F_70(x))
Eq(F_126(x), F_127(x) + F_92(x))
Eq(F_127(x), F_116(x) + F_128(x) + 3*F_16(x))
Eq(F_128(x), F_129(x)*F_4(x))
Eq(F_129(x), F_130(x) + F_131(x))
Eq(F_130(x), F_125(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_133(x)*F_4(x))
Eq(F_133(x), F_134(x) + F_135(x))
Eq(F_134(x), F_125(x))
Eq(F_135(x), F_132(x))
Eq(F_136(x), F_137(x)*F_4(x))
Eq(F_137(x), F_138(x) + F_176(x))
Eq(F_138(x), F_139(x) + F_2(x))
Eq(F_139(x), F_140(x) + F_16(x) + F_175(x))
Eq(F_140(x), F_141(x)*F_4(x))
Eq(F_141(x), F_142(x) + F_144(x))
Eq(F_142(x), F_11(x) + F_143(x))
Eq(F_143(x), F_16(x) + F_21(x) + F_25(x))
Eq(F_144(x), F_145(x) + F_50(x))
Eq(F_145(x), F_118(x) + F_146(x) + 2*F_16(x))
Eq(F_146(x), F_147(x)*F_4(x))
Eq(F_147(x), F_148(x) + F_150(x))
Eq(F_148(x), F_143(x) + F_149(x))
Eq(F_149(x), F_70(x))
Eq(F_150(x), F_151(x) + F_166(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_153(x)*F_4(x))
Eq(F_153(x), F_154(x) + F_156(x))
Eq(F_154(x), F_143(x) + F_155(x))
Eq(F_155(x), F_78(x))
Eq(F_156(x), F_151(x) + F_157(x))
Eq(F_157(x), F_158(x) + 3*F_16(x) + F_90(x))
Eq(F_158(x), F_159(x)*F_4(x))
Eq(F_159(x), F_160(x) + F_161(x))
Eq(F_160(x), F_155(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_163(x)*F_4(x))
Eq(F_163(x), F_164(x) + F_165(x))
Eq(F_164(x), F_155(x))
Eq(F_165(x), F_162(x))
Eq(F_166(x), F_116(x) + 3*F_16(x) + F_167(x))
Eq(F_167(x), F_168(x)*F_4(x))
Eq(F_168(x), F_169(x) + F_170(x))
Eq(F_169(x), F_149(x))
Eq(F_170(x), F_171(x))
Eq(F_171(x), F_172(x)*F_4(x))
Eq(F_172(x), F_173(x) + F_174(x))
Eq(F_173(x), F_149(x))
Eq(F_174(x), F_171(x))
Eq(F_175(x), F_138(x)*F_4(x))
Eq(F_176(x), F_139(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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [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, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"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, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, 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