0123_0231_0321_1203_2130
Counting sequence:
1, 1, 2, 6, 19, 50, 114, 253, 554, 1194, 2551, 5438, 11574, 24601, 52262, 111006, 235747, 500618, 1063050, 2257333, 4793282, 10178130, 21612367, 45891926, 97447326, 206920465, 439376606, 932975814, 1981088251, 4206658466, 8932451826, 18967238701, 40275184250, 85520643834, 181595209447, 385600699502, 818787565446, 1738619971849, 3691799355542, 7839195857646, 16645810288147, 35345844800954, 75053645515866, 159369502608805, 338406458303282, 718574941546146, 1525827696099199, 3239954559469958, 6879745055268462, 14608504890029569, 31019814456436814, 65867718575943702, 139864032922977067, 296988390191854034, 630627489179592642, 1339079382369288733, 2843411717778544106, 6037722858890726730, 12820548319767034135, 27223253378953427102, 57806070852059003478, 122745866588327952889, 260639540837827879430, 553444055888180694078, 1175187471606782486851, 2495402342347274846186, 5298757007406074480682, 11251422404743275689365, 23891359040057464836770, 50731100144307439180530, 107722818008663604358063, 228739481042572524591542, 485707217419965936984894, 1031354534768480548654321, 2189986350290918743539134, 4650234281984476215347046, 9874344136652287930165339, 20967260188755562729900034, 44522045589958640577838482, 94538462615987731598764045, 200743716856762073496734042, 426260791030178211710975898, 905125524298833029560915783, 1921950674274510851462888654, 4081085214347224451439225126, 8665808519279757785445897961, 18401046130773669998932732790, 39072926427296898390182859150, 82967760025324532862885838963, 176174395752728286821825960474, 374090100894193956462942984186, 794345869552165105790906341765, 1686720282002464701623272925714, 3581595144848474293983717157698, 7605187367743657120114688736223, 16148914815701391028926764429798, 34290733037146926140255433333774, 72813212878032579997379009552353, 154612150282069602435717349219118, 328304658865798816771460754299574, 697124700978227431482446989291915
Generating function in Maple syntax:
(x+1)*(2*x^5-8*x^4+3*x^3-4*x^2+3*x-1)/(2*x^4+2*x^3+x^2+x-1)/(x-1)^2
Generating function in latex syntax:
\frac{\left(x +1\right) \left(2 x^{5}-8 x^{4}+3 x^{3}-4 x^{2}+3 x -1\right)}{\left(2 x^{4}+2 x^{3}+x^{2}+x -1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(x + 1)*(2*x**5 - 8*x**4 + 3*x**3 - 4*x**2 + 3*x - 1)/((x - 1)**2*(2*x**4 + 2*x**3 + x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x^4+2*x^3+x^2+x-1)*(x-1)^2*F(x)-(x+1)*(2*x^5-8*x^4+3*x^3-4*x^2+3*x-1) = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{4}+2 x^{3}+x^{2}+x -1\right) \left(x -1\right)^{2} F \! \left(x \right)-\left(x +1\right) \left(2 x^{5}-8 x^{4}+3 x^{3}-4 x^{2}+3 x -1\right) = 0
Explicit closed form in Maple syntax:
piecewise(n = 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1/2))^(2/3)+841*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)+841)^(1/2)*3^(1/2)*53^(1/2)-116335530)*((116*53^(1/2)*3^(1/2)*2^(1/2)-290)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-2*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+382*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+10933)^(1/2)+2523*(-9*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+87*((116*53^(1/2)*3^(1/2)*2^(1/2)-290)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-2*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+382*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+10933)^(1/2)+37*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+841*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)+841)^(1/2)*(-73*53^(1/2)*3^(1/2)+954*2^(1/2))*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)-2523*(-9*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+87*((116*53^(1/2)*3^(1/2)*2^(1/2)-290)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-2*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+382*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+10933)^(1/2)+37*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+841*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)+841)^(1/2)*(499*53^(1/2)*3^(1/2)+2385*2^(1/2))*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)+1390173*(-9*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+87*((116*53^(1/2)*3^(1/2)*2^(1/2)-290)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-2*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+382*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+10933)^(1/2)+37*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+841*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)+841)^(1/2)*3^(1/2)*53^(1/2)+6072714666)*(-1/348*(522*((116*53^(1/2)*3^(1/2)*2^(1/2)-290)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-2*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+382*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+10933)^(1/2)+(54*53^(1/2)*3^(1/2)*2^(1/2)-222)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)-5046*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-5046)^(1/2)+1/878004*(-1682*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-74*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+841)*((116*53^(1/2)*3^(1/2)*2^(1/2)-290)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-2*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+382*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+10933)^(1/2)+1/48778*((36888*53^(1/2)*3^(1/2)*2^(1/2)-92220)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-636*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+121476*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+3476694)^(1/2)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)-1/4)^(-n)+1/40484764440*(((-53^(1/2)*(3743*(-9*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+87*((116*53^(1/2)*3^(1/2)*2^(1/2)-290)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-2*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+382*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+10933)^(1/2)+37*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+841*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)+841)^(1/2)-440046*2^(1/2))*3^(1/2)+3816*(-9*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+87*((116*53^(1/2)*3^(1/2)*2^(1/2)-290)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-2*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+382*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+10933)^(1/2)+37*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+841*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)+841)^(1/2)*2^(1/2)+2434608)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+(29*53^(1/2)*(83*(-9*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+87*((116*53^(1/2)*3^(1/2)*2^(1/2)-290)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-2*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+382*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+10933)^(1/2)+37*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+841*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)+841)^(1/2)+45414*2^(1/2))*3^(1/2)-179829*(-9*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+87*((116*53^(1/2)*3^(1/2)*2^(1/2)-290)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-2*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+382*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+10933)^(1/2)+37*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+841*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)+841)^(1/2)*2^(1/2)-46534212)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)+283417*(-9*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+87*((116*53^(1/2)*3^(1/2)*2^(1/2)-290)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-2*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+382*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+10933)^(1/2)+37*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+841*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)+841)^(1/2)*3^(1/2)*53^(1/2)-116335530)*((116*53^(1/2)*3^(1/2)*2^(1/2)-290)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-2*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+382*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+10933)^(1/2)-2523*(-9*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+87*((116*53^(1/2)*3^(1/2)*2^(1/2)-290)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-2*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+382*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+10933)^(1/2)+37*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+841*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)+841)^(1/2)*(-73*53^(1/2)*3^(1/2)+954*2^(1/2))*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+2523*(-9*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+87*((116*53^(1/2)*3^(1/2)*2^(1/2)-290)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-2*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+382*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+10933)^(1/2)+37*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+841*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)+841)^(1/2)*(499*53^(1/2)*3^(1/2)+2385*2^(1/2))*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-1390173*(-9*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+87*((116*53^(1/2)*3^(1/2)*2^(1/2)-290)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-2*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+382*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+10933)^(1/2)+37*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+841*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)+841)^(1/2)*3^(1/2)*53^(1/2)+6072714666)*(1/348*(522*((116*53^(1/2)*3^(1/2)*2^(1/2)-290)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-2*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+382*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+10933)^(1/2)+(54*53^(1/2)*3^(1/2)*2^(1/2)-222)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)-5046*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-5046)^(1/2)+1/878004*(-1682*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-74*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+841)*((116*53^(1/2)*3^(1/2)*2^(1/2)-290)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-2*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+382*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+10933)^(1/2)+1/48778*((36888*53^(1/2)*3^(1/2)*2^(1/2)-92220)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(1/3)-636*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)*53^(1/2)*3^(1/2)*2^(1/2)+121476*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)+3476694)^(1/2)*(37+9*53^(1/2)*3^(1/2)*2^(1/2))^(2/3)-1/4)^(-n)-2*n-3/5)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(\left(\left(-\sqrt{2}\, \left(12395 \,\mathrm{I} \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}+440046 \sqrt{53}\right) \sqrt{3}+18090 \,\mathrm{I} \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \sqrt{53}-2434608\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+\left(46534212-841 \sqrt{2}\, \left(335 \,\mathrm{I} \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}+1566 \sqrt{53}\right) \sqrt{3}\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+470119 \,\mathrm{I} \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \sqrt{2}\, \sqrt{3}+116335530\right) \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}-7569 \,\mathrm{I} \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \left(37 \sqrt{2}\, \sqrt{3}-54 \sqrt{53}\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}-6365529 \,\mathrm{I} \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \sqrt{2}\, \sqrt{3}\, \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-61679781 \,\mathrm{I} \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \sqrt{2}\, \sqrt{3}+6072714666\right) \left(-\frac{\mathrm{I} \sqrt{522 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+\left(-54 \sqrt{53}\, \sqrt{3}\, \sqrt{2}+222\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+5046 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+5046}}{348}+\frac{\left(1682 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+74 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}-841\right) \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}}{878004}-\frac{\sqrt{\left(36888 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-92220\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-636 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+121476 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+3476694}\, \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}}{48778}-\frac{1}{4}\right)^{-n}}{40484764440}\\+\\\frac{\left(\left(\left(\sqrt{2}\, \left(12395 \,\mathrm{I} \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}-440046 \sqrt{53}\right) \sqrt{3}-18090 \,\mathrm{I} \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \sqrt{53}-2434608\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+\left(46534212+841 \sqrt{2}\, \left(335 \,\mathrm{I} \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}-1566 \sqrt{53}\right) \sqrt{3}\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-470119 \,\mathrm{I} \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \sqrt{2}\, \sqrt{3}+116335530\right) \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+6365529 \,\mathrm{I} \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \sqrt{2}\, \sqrt{3}\, \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+7569 \,\mathrm{I} \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \left(37 \sqrt{2}\, \sqrt{3}-54 \sqrt{53}\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+61679781 \,\mathrm{I} \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \sqrt{2}\, \sqrt{3}+6072714666\right) \left(\frac{\mathrm{I} \sqrt{522 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+\left(-54 \sqrt{53}\, \sqrt{3}\, \sqrt{2}+222\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+5046 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+5046}}{348}+\frac{\left(1682 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+74 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}-841\right) \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}}{878004}-\frac{\sqrt{\left(36888 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-92220\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-636 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+121476 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+3476694}\, \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}}{48778}-\frac{1}{4}\right)^{-n}}{40484764440}\\+\\\frac{\left(\left(\left(\sqrt{53}\, \left(3743 \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}+440046 \sqrt{2}\right) \sqrt{3}-3816 \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \sqrt{2}+2434608\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+\left(-29 \sqrt{53}\, \left(83 \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}-45414 \sqrt{2}\right) \sqrt{3}+179829 \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \sqrt{2}-46534212\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-283417 \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \sqrt{3}\, \sqrt{53}-116335530\right) \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+2523 \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \left(-73 \sqrt{53}\, \sqrt{3}+954 \sqrt{2}\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}-2523 \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \left(499 \sqrt{53}\, \sqrt{3}+2385 \sqrt{2}\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+1390173 \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \sqrt{3}\, \sqrt{53}+6072714666\right) \left(-\frac{\sqrt{522 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+\left(54 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-222\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}-5046 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-5046}}{348}+\frac{\left(-1682 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-74 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841\right) \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}}{878004}+\frac{\sqrt{\left(36888 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-92220\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-636 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+121476 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+3476694}\, \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}}{48778}-\frac{1}{4}\right)^{-n}}{40484764440}\\+\\\frac{\left(\left(\left(-\sqrt{53}\, \left(3743 \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}-440046 \sqrt{2}\right) \sqrt{3}+3816 \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \sqrt{2}+2434608\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+\left(29 \sqrt{53}\, \left(83 \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}+45414 \sqrt{2}\right) \sqrt{3}-179829 \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \sqrt{2}-46534212\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+283417 \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \sqrt{3}\, \sqrt{53}-116335530\right) \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}-2523 \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \left(-73 \sqrt{53}\, \sqrt{3}+954 \sqrt{2}\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+2523 \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \left(499 \sqrt{53}\, \sqrt{3}+2385 \sqrt{2}\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-1390173 \sqrt{-9 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+87 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+37 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}+841}\, \sqrt{3}\, \sqrt{53}+6072714666\right) \left(\frac{\sqrt{522 \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}+\left(54 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-222\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}-5046 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-5046}}{348}+\frac{\left(-1682 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-74 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+841\right) \sqrt{\left(116 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-290\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-2 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+382 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+10933}}{878004}+\frac{\sqrt{\left(36888 \sqrt{53}\, \sqrt{3}\, \sqrt{2}-92220\right) \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{1}{3}}-636 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}} \sqrt{53}\, \sqrt{3}\, \sqrt{2}+121476 \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}+3476694}\, \left(37+9 \sqrt{53}\, \sqrt{3}\, \sqrt{2}\right)^{\frac{2}{3}}}{48778}-\frac{1}{4}\right)^{-n}}{40484764440}\\-2 n -\frac{3}{5} & \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) = 50
a(6) = 114
a(n+4) = 2*a(n)+2*a(n+1)+a(n+2)+a(n+3)+10*n+9, n >= 7
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) = 50
a \! \left(6\right) = 114
a \! \left(n +4\right) = 2 a \! \left(n \right)+2 a \! \left(n +1\right)+a \! \left(n +2\right)+a \! \left(n +3\right)+10 n +9, \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/17092/
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[20,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[14,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[4,x]
F[14,x] = F[15,x]+F[17,x]
F[15,x] = F[16,x]
F[16,x] = F[13,x]*F[4,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[11,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[101,x]+F[22,x]+F[23,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[43,x]
F[25,x] = F[26,x]+F[7,x]
F[26,x] = F[22,x]+F[27,x]+F[37,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[33,x]
F[29,x] = F[11,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[4,x]
F[33,x] = F[17,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[30,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[15,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[4,x]
F[43,x] = F[44,x]+F[63,x]
F[44,x] = F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]+F[53,x]
F[47,x] = F[48,x]+F[7,x]
F[48,x] = F[49,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[11,x]
F[52,x] = F[17,x]
F[53,x] = F[44,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[57,x]+F[58,x]
F[57,x] = F[48,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[48,x]
F[62,x] = F[59,x]
F[63,x] = F[64,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]+F[72,x]
F[66,x] = F[26,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[30,x]
F[71,x] = F[34,x]
F[72,x] = F[73,x]+F[92,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]+F[82,x]
F[76,x] = F[26,x]+F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[81,x]
F[80,x] = F[30,x]
F[81,x] = F[34,x]
F[82,x] = F[73,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[77,x]
F[87,x] = F[88,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[90,x]+F[91,x]
F[90,x] = F[77,x]
F[91,x] = F[88,x]
F[92,x] = F[93,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[95,x]+F[96,x]
F[95,x] = F[67,x]
F[96,x] = F[97,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[100,x]+F[99,x]
F[99,x] = F[67,x]
F[100,x] = F[97,x]
F[101,x] = F[102,x]*F[4,x]
F[102,x] = F[103,x]+F[109,x]
F[103,x] = F[104,x]+F[2,x]
F[104,x] = F[105,x]
F[105,x] = F[106,x]*F[4,x]
F[106,x] = F[107,x]+F[2,x]
F[107,x] = F[108,x]
F[108,x] = F[2,x]*F[4,x]
F[109,x] = F[110,x]
F[110,x] = F[111,x]+F[185,x]+F[22,x]
F[111,x] = F[112,x]*F[4,x]
F[112,x] = F[113,x]+F[127,x]
F[113,x] = F[114,x]+F[15,x]
F[114,x] = F[115,x]+F[125,x]+F[22,x]
F[115,x] = F[116,x]*F[4,x]
F[116,x] = F[117,x]+F[120,x]
F[117,x] = F[118,x]+F[4,x]
F[118,x] = F[119,x]
F[119,x] = x^2
F[120,x] = F[121,x]+F[122,x]
F[121,x] = F[41,x]
F[122,x] = F[123,x]
F[123,x] = F[124,x]*F[4,x]
F[124,x] = F[118,x]
F[125,x] = F[126,x]*F[4,x]
F[126,x] = F[15,x]
F[127,x] = F[128,x]+F[147,x]
F[128,x] = F[129,x]
F[129,x] = F[130,x]*F[4,x]
F[130,x] = F[131,x]+F[137,x]
F[131,x] = F[132,x]+F[15,x]
F[132,x] = F[133,x]
F[133,x] = F[134,x]*F[4,x]
F[134,x] = F[135,x]+F[136,x]
F[135,x] = F[4,x]
F[136,x] = F[121,x]
F[137,x] = F[128,x]+F[138,x]
F[138,x] = F[139,x]
F[139,x] = F[140,x]*F[4,x]
F[140,x] = F[141,x]+F[142,x]
F[141,x] = F[132,x]
F[142,x] = F[143,x]
F[143,x] = F[144,x]*F[4,x]
F[144,x] = F[145,x]+F[146,x]
F[145,x] = F[132,x]
F[146,x] = F[143,x]
F[147,x] = F[148,x]
F[148,x] = F[149,x]*F[4,x]
F[149,x] = F[150,x]+F[156,x]
F[150,x] = F[114,x]+F[151,x]
F[151,x] = F[152,x]
F[152,x] = F[153,x]*F[4,x]
F[153,x] = F[154,x]+F[155,x]
F[154,x] = F[118,x]
F[155,x] = F[122,x]
F[156,x] = F[157,x]+F[176,x]
F[157,x] = F[158,x]
F[158,x] = F[159,x]*F[4,x]
F[159,x] = F[160,x]+F[166,x]
F[160,x] = F[114,x]+F[161,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[118,x]
F[165,x] = F[122,x]
F[166,x] = F[157,x]+F[167,x]
F[167,x] = F[168,x]
F[168,x] = F[169,x]*F[4,x]
F[169,x] = F[170,x]+F[171,x]
F[170,x] = F[161,x]
F[171,x] = F[172,x]
F[172,x] = F[173,x]*F[4,x]
F[173,x] = F[174,x]+F[175,x]
F[174,x] = F[161,x]
F[175,x] = F[172,x]
F[176,x] = F[177,x]
F[177,x] = F[178,x]*F[4,x]
F[178,x] = F[179,x]+F[180,x]
F[179,x] = F[151,x]
F[180,x] = F[181,x]
F[181,x] = F[182,x]*F[4,x]
F[182,x] = F[183,x]+F[184,x]
F[183,x] = F[151,x]
F[184,x] = F[181,x]
F[185,x] = F[106,x]*F[4,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_{20}\! \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_{14}\! \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_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{11}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{101}\! \left(x \right)+F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{43}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{7}\! \left(x \right)
F_{26}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{37}\! \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_{33}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{17}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{15}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{63}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{53}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{7}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{11}\! \left(x \right)
F_{52}\! \left(x \right) = F_{17}\! \left(x \right)
F_{53}\! \left(x \right) = F_{44}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{58}\! \left(x \right)
F_{57}\! \left(x \right) = F_{48}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{48}\! \left(x \right)
F_{62}\! \left(x \right) = F_{59}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{72}\! \left(x \right)
F_{66}\! \left(x \right) = F_{26}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{30}\! \left(x \right)
F_{71}\! \left(x \right) = F_{34}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{92}\! \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_{82}\! \left(x \right)
F_{76}\! \left(x \right) = F_{26}\! \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_{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_{34}\! \left(x \right)
F_{82}\! \left(x \right) = F_{73}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{77}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)+F_{91}\! \left(x \right)
F_{90}\! \left(x \right) = F_{77}\! \left(x \right)
F_{91}\! \left(x \right) = F_{88}\! \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_{96}\! \left(x \right)
F_{95}\! \left(x \right) = F_{67}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{100}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{67}\! \left(x \right)
F_{100}\! \left(x \right) = F_{97}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{109}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{2}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{2}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{185}\! \left(x \right)+F_{22}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{4}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{127}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{15}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{125}\! \left(x \right)+F_{22}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{4}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{120}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{4}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = x^{2}
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{122}\! \left(x \right)
F_{121}\! \left(x \right) = F_{41}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right) F_{4}\! \left(x \right)
F_{124}\! \left(x \right) = F_{118}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{4}\! \left(x \right)
F_{126}\! \left(x \right) = F_{15}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{147}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{4}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{137}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{15}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{4}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{136}\! \left(x \right)
F_{135}\! \left(x \right) = F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{121}\! \left(x \right)
F_{137}\! \left(x \right) = F_{128}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{4}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{142}\! \left(x \right)
F_{141}\! \left(x \right) = F_{132}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right) F_{4}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)+F_{146}\! \left(x \right)
F_{145}\! \left(x \right) = F_{132}\! \left(x \right)
F_{146}\! \left(x \right) = F_{143}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{4}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)+F_{156}\! \left(x \right)
F_{150}\! \left(x \right) = F_{114}\! \left(x \right)+F_{151}\! \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_{155}\! \left(x \right)
F_{154}\! \left(x \right) = F_{118}\! \left(x \right)
F_{155}\! \left(x \right) = F_{122}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right)+F_{176}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \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_{166}\! \left(x \right)
F_{160}\! \left(x \right) = F_{114}\! \left(x \right)+F_{161}\! \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_{118}\! \left(x \right)
F_{165}\! \left(x \right) = F_{122}\! \left(x \right)
F_{166}\! \left(x \right) = F_{157}\! \left(x \right)+F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right) F_{4}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)+F_{171}\! \left(x \right)
F_{170}\! \left(x \right) = F_{161}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right) F_{4}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)+F_{175}\! \left(x \right)
F_{174}\! \left(x \right) = F_{161}\! \left(x \right)
F_{175}\! \left(x \right) = F_{172}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right) F_{4}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right)+F_{180}\! \left(x \right)
F_{179}\! \left(x \right) = F_{151}\! \left(x \right)
F_{180}\! \left(x \right) = F_{181}\! \left(x \right)
F_{181}\! \left(x \right) = F_{182}\! \left(x \right) F_{4}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)+F_{184}\! \left(x \right)
F_{183}\! \left(x \right) = F_{151}\! \left(x \right)
F_{184}\! \left(x \right) = F_{181}\! \left(x \right)
F_{185}\! \left(x \right) = F_{106}\! \left(x \right) F_{4}\! \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_20(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_14(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_4(x))
Eq(F_14(x), F_15(x) + F_17(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_13(x)*F_4(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_11(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_101(x) + F_22(x) + F_23(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_43(x))
Eq(F_25(x), F_26(x) + F_7(x))
Eq(F_26(x), F_22(x) + F_27(x) + F_37(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_33(x))
Eq(F_29(x), F_11(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_4(x))
Eq(F_33(x), F_17(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_30(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x) + F_40(x))
Eq(F_39(x), F_15(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_4(x))
Eq(F_43(x), F_44(x) + F_63(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_53(x))
Eq(F_47(x), F_48(x) + F_7(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_11(x))
Eq(F_52(x), F_17(x))
Eq(F_53(x), F_44(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_58(x))
Eq(F_57(x), F_48(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_48(x))
Eq(F_62(x), F_59(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_72(x))
Eq(F_66(x), F_26(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_30(x))
Eq(F_71(x), F_34(x))
Eq(F_72(x), F_73(x) + F_92(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_82(x))
Eq(F_76(x), F_26(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_80(x) + F_81(x))
Eq(F_80(x), F_30(x))
Eq(F_81(x), F_34(x))
Eq(F_82(x), F_73(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_77(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_90(x) + F_91(x))
Eq(F_90(x), F_77(x))
Eq(F_91(x), F_88(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_96(x))
Eq(F_95(x), F_67(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_100(x) + F_99(x))
Eq(F_99(x), F_67(x))
Eq(F_100(x), F_97(x))
Eq(F_101(x), F_102(x)*F_4(x))
Eq(F_102(x), F_103(x) + F_109(x))
Eq(F_103(x), F_104(x) + F_2(x))
Eq(F_104(x), F_105(x))
Eq(F_105(x), F_106(x)*F_4(x))
Eq(F_106(x), F_107(x) + F_2(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_2(x)*F_4(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_111(x) + F_185(x) + F_22(x))
Eq(F_111(x), F_112(x)*F_4(x))
Eq(F_112(x), F_113(x) + F_127(x))
Eq(F_113(x), F_114(x) + F_15(x))
Eq(F_114(x), F_115(x) + F_125(x) + F_22(x))
Eq(F_115(x), F_116(x)*F_4(x))
Eq(F_116(x), F_117(x) + F_120(x))
Eq(F_117(x), F_118(x) + F_4(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), x**2)
Eq(F_120(x), F_121(x) + F_122(x))
Eq(F_121(x), F_41(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_124(x)*F_4(x))
Eq(F_124(x), F_118(x))
Eq(F_125(x), F_126(x)*F_4(x))
Eq(F_126(x), F_15(x))
Eq(F_127(x), F_128(x) + F_147(x))
Eq(F_128(x), F_129(x))
Eq(F_129(x), F_130(x)*F_4(x))
Eq(F_130(x), F_131(x) + F_137(x))
Eq(F_131(x), F_132(x) + F_15(x))
Eq(F_132(x), F_133(x))
Eq(F_133(x), F_134(x)*F_4(x))
Eq(F_134(x), F_135(x) + F_136(x))
Eq(F_135(x), F_4(x))
Eq(F_136(x), F_121(x))
Eq(F_137(x), F_128(x) + F_138(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_140(x)*F_4(x))
Eq(F_140(x), F_141(x) + F_142(x))
Eq(F_141(x), F_132(x))
Eq(F_142(x), F_143(x))
Eq(F_143(x), F_144(x)*F_4(x))
Eq(F_144(x), F_145(x) + F_146(x))
Eq(F_145(x), F_132(x))
Eq(F_146(x), F_143(x))
Eq(F_147(x), F_148(x))
Eq(F_148(x), F_149(x)*F_4(x))
Eq(F_149(x), F_150(x) + F_156(x))
Eq(F_150(x), F_114(x) + F_151(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_155(x))
Eq(F_154(x), F_118(x))
Eq(F_155(x), F_122(x))
Eq(F_156(x), F_157(x) + F_176(x))
Eq(F_157(x), F_158(x))
Eq(F_158(x), F_159(x)*F_4(x))
Eq(F_159(x), F_160(x) + F_166(x))
Eq(F_160(x), F_114(x) + F_161(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_118(x))
Eq(F_165(x), F_122(x))
Eq(F_166(x), F_157(x) + F_167(x))
Eq(F_167(x), F_168(x))
Eq(F_168(x), F_169(x)*F_4(x))
Eq(F_169(x), F_170(x) + F_171(x))
Eq(F_170(x), F_161(x))
Eq(F_171(x), F_172(x))
Eq(F_172(x), F_173(x)*F_4(x))
Eq(F_173(x), F_174(x) + F_175(x))
Eq(F_174(x), F_161(x))
Eq(F_175(x), F_172(x))
Eq(F_176(x), F_177(x))
Eq(F_177(x), F_178(x)*F_4(x))
Eq(F_178(x), F_179(x) + F_180(x))
Eq(F_179(x), F_151(x))
Eq(F_180(x), F_181(x))
Eq(F_181(x), F_182(x)*F_4(x))
Eq(F_182(x), F_183(x) + F_184(x))
Eq(F_183(x), F_151(x))
Eq(F_184(x), F_181(x))
Eq(F_185(x), F_106(x)*F_4(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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "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, 0], [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, 1, 0], "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, 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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [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, 0], [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, 1, 0], "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, 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, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [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, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "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, 0], [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, 1, 0], "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, 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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [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], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 0], [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, 1, 0], "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, 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