0132_0231_0312_2103
Counting sequence:
1, 1, 2, 6, 20, 62, 178, 506, 1454, 4215, 12241, 35505, 102881, 298069, 863737, 2503273, 7255173, 21027133, 60940578, 176617042, 511870601, 1483504417, 4299498156, 12460820018, 36113985561, 104665662709, 303342365196, 879147876943, 2547949415984, 7384475819122, 21401713397241, 62026520018322, 179765475882379, 520996927619283, 1509955109033122, 4376157153505753, 12682993898119995, 36757897075372569, 106531865295165941, 308751022955637270, 894823289857461459, 2593379974628979225, 7516142873211110218, 21783311448148716101, 63132469093880872189, 182970741770954076772, 530286440950940488960, 1536878009756074020961, 4454185199675705363120, 12909135056309386108556, 37413300173101082915331, 108431356844353874976990, 314256135992010693147460, 910778227652264510013885, 2639620630944489991971232, 7650157704437420352894577, 22171713698806207462872701, 64258137849457862955169307, 186233158878569589964012957, 539741589573361436833916150, 1564280954419778414575286699, 4533604509325775666627513866, 13139308376098410297780560622, 38080389290040781140110871750, 110364716846051416075470290445, 319859406681397960699411236563, 927017646276291235396436756512, 2686685770550492489399352764724, 7786562055936457079221583217194, 22567041265315667645910486181863, 65403877579347468082690342045192, 189553745753494745572762361297211, 549365326017402861811066095485666, 1592172500894211931043096489494768, 4614439886443479021562851882640557, 13373585747550398988897757164044748, 38759372783796667158669933608529665, 112332549172048919637214026677286558, 325562585181099404926333302801063416, 943546618064052206175192077474283554, 2734590094143888709660422648299371705, 7925398533389945185867631561107105232, 22969417627735491326361850165066987235, 66570046154090009972020463887138483761, 192933539577710825988999250012658709309, 559160656248052443735588449130259169994, 1620561361078525739945612301766384252233, 4696716579886929411986205408364063838678, 13612040346996697182593501540507652599229, 39450462734271832783276384806411445698853, 114335468473068010522305400762054572480391, 331367452873990221840147886800565371696616, 960370305825622374593371359976482024443370, 2783348564598855109208402652434988790630595, 8066710502251993758647742252285377925965902, 23378968467975899078818563213167385811560320, 67757007825435535209026444874573628739691094, 196373596026908553009015919994907188021575203, 569130639828273706736950115202003898769831611, 1649456402208755827923732169862317374091612126, 4780460288710485879239011520460010684677751739
Generating function in Maple syntax:
-(2*x-1)*(x-1)^3/(x^9-4*x^8+8*x^7-4*x^6-2*x^5-6*x^4+14*x^3-13*x^2+6*x-1)
Generating function in latex syntax:
-\frac{\left(2 x -1\right) \left(x -1\right)^{3}}{x^{9}-4 x^{8}+8 x^{7}-4 x^{6}-2 x^{5}-6 x^{4}+14 x^{3}-13 x^{2}+6 x -1}
Generating function in sympy syntax:
(1 - 2*x)*(x - 1)**3/(x**9 - 4*x**8 + 8*x**7 - 4*x**6 - 2*x**5 - 6*x**4 + 14*x**3 - 13*x**2 + 6*x - 1)
Implicit equation for the generating function in Maple syntax:
(x^9-4*x^8+8*x^7-4*x^6-2*x^5-6*x^4+14*x^3-13*x^2+6*x-1)*F(x)+(2*x-1)*(x-1)^3 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{9}-4 x^{8}+8 x^{7}-4 x^{6}-2 x^{5}-6 x^{4}+14 x^{3}-13 x^{2}+6 x -1\right) F \! \left(x \right)+\left(2 x -1\right) \left(x -1\right)^{3} = 0
Explicit closed form in Maple syntax:
633380712042/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+7)+633380712042/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+7)+633380712042/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+7)+633380712042/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+7)+633380712042/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+7)+633380712042/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+7)+633380712042/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+7)+633380712042/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 8)^(-n+7)+633380712042/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 9)^(-n+7)-2230503906702/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+6)-2230503906702/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+6)-2230503906702/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+6)-2230503906702/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+6)-2230503906702/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+6)-2230503906702/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+6)-2230503906702/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+6)-2230503906702/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 8)^(-n+6)-2230503906702/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 9)^(-n+6)+787631404094/916775071003*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+5)+787631404094/916775071003*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+5)+787631404094/916775071003*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+5)+787631404094/916775071003*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+5)+787631404094/916775071003*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+5)+787631404094/916775071003*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+5)+787631404094/916775071003*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+5)+787631404094/916775071003*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 8)^(-n+5)+787631404094/916775071003*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 9)^(-n+5)-490944295958/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+4)-490944295958/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+4)-490944295958/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+4)-490944295958/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+4)-490944295958/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+4)-490944295958/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+4)-490944295958/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+4)-490944295958/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 8)^(-n+4)-490944295958/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 9)^(-n+4)-1682986973928/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+3)-1682986973928/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+3)-1682986973928/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+3)-1682986973928/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+3)-1682986973928/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+3)-1682986973928/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+3)-1682986973928/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+3)-1682986973928/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 8)^(-n+3)-1682986973928/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 9)^(-n+3)-4858896244366/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+2)-4858896244366/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+2)-4858896244366/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+2)-4858896244366/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+2)-4858896244366/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 8)^(-n+2)-4858896244366/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 9)^(-n+2)-4858896244366/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+2)-4858896244366/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+2)-4858896244366/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+2)+1308934845621/916775071003*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+1)+1308934845621/916775071003*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+1)+1308934845621/916775071003*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+1)+1308934845621/916775071003*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+1)+1308934845621/916775071003*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+1)+1308934845621/916775071003*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+1)+1308934845621/916775071003*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+1)+1308934845621/916775071003*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 8)^(-n+1)+1308934845621/916775071003*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 9)^(-n+1)+1313225244154/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n-1)+1313225244154/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n-1)+1313225244154/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n-1)+1313225244154/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n-1)+1313225244154/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n-1)+1313225244154/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n-1)+1313225244154/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n-1)+1313225244154/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 8)^(-n-1)+1313225244154/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 9)^(-n-1)-4083286627611/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n)-4083286627611/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n)-4083286627611/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n)-4083286627611/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n)-4083286627611/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n)-4083286627611/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n)-4083286627611/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n)-4083286627611/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 8)^(-n)-4083286627611/4583875355015*RootOf(_Z^9-4*_Z^8+8*_Z^7-4*_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 9)^(-n)
Explicit closed form in latex syntax:
\frac{633380712042 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +7}}{4583875355015}+\frac{633380712042 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +7}}{4583875355015}+\frac{633380712042 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +7}}{4583875355015}+\frac{633380712042 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +7}}{4583875355015}+\frac{633380712042 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +7}}{4583875355015}+\frac{633380712042 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +7}}{4583875355015}+\frac{633380712042 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +7}}{4583875355015}+\frac{633380712042 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +7}}{4583875355015}+\frac{633380712042 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =9\right)^{-n +7}}{4583875355015}-\frac{2230503906702 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +6}}{4583875355015}-\frac{2230503906702 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +6}}{4583875355015}-\frac{2230503906702 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +6}}{4583875355015}-\frac{2230503906702 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +6}}{4583875355015}-\frac{2230503906702 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +6}}{4583875355015}-\frac{2230503906702 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +6}}{4583875355015}-\frac{2230503906702 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +6}}{4583875355015}-\frac{2230503906702 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +6}}{4583875355015}-\frac{2230503906702 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =9\right)^{-n +6}}{4583875355015}+\frac{787631404094 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +5}}{916775071003}+\frac{787631404094 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +5}}{916775071003}+\frac{787631404094 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +5}}{916775071003}+\frac{787631404094 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +5}}{916775071003}+\frac{787631404094 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +5}}{916775071003}+\frac{787631404094 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +5}}{916775071003}+\frac{787631404094 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +5}}{916775071003}+\frac{787631404094 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +5}}{916775071003}+\frac{787631404094 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =9\right)^{-n +5}}{916775071003}-\frac{490944295958 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}}{4583875355015}-\frac{490944295958 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +4}}{4583875355015}-\frac{490944295958 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +4}}{4583875355015}-\frac{490944295958 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +4}}{4583875355015}-\frac{490944295958 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +4}}{4583875355015}-\frac{490944295958 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +4}}{4583875355015}-\frac{490944295958 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +4}}{4583875355015}-\frac{490944295958 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +4}}{4583875355015}-\frac{490944295958 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =9\right)^{-n +4}}{4583875355015}-\frac{1682986973928 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{4583875355015}-\frac{1682986973928 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{4583875355015}-\frac{1682986973928 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{4583875355015}-\frac{1682986973928 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{4583875355015}-\frac{1682986973928 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{4583875355015}-\frac{1682986973928 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +3}}{4583875355015}-\frac{1682986973928 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +3}}{4583875355015}-\frac{1682986973928 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +3}}{4583875355015}-\frac{1682986973928 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =9\right)^{-n +3}}{4583875355015}-\frac{4858896244366 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{4583875355015}-\frac{4858896244366 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{4583875355015}-\frac{4858896244366 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +2}}{4583875355015}-\frac{4858896244366 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +2}}{4583875355015}-\frac{4858896244366 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +2}}{4583875355015}-\frac{4858896244366 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =9\right)^{-n +2}}{4583875355015}-\frac{4858896244366 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{4583875355015}-\frac{4858896244366 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{4583875355015}-\frac{4858896244366 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{4583875355015}+\frac{1308934845621 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{916775071003}+\frac{1308934845621 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{916775071003}+\frac{1308934845621 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{916775071003}+\frac{1308934845621 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{916775071003}+\frac{1308934845621 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{916775071003}+\frac{1308934845621 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +1}}{916775071003}+\frac{1308934845621 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +1}}{916775071003}+\frac{1308934845621 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +1}}{916775071003}+\frac{1308934845621 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =9\right)^{-n +1}}{916775071003}+\frac{1313225244154 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{4583875355015}+\frac{1313225244154 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{4583875355015}+\frac{1313225244154 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{4583875355015}+\frac{1313225244154 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{4583875355015}+\frac{1313225244154 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{4583875355015}+\frac{1313225244154 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =6\right)^{-n -1}}{4583875355015}+\frac{1313225244154 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =7\right)^{-n -1}}{4583875355015}+\frac{1313225244154 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =8\right)^{-n -1}}{4583875355015}+\frac{1313225244154 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =9\right)^{-n -1}}{4583875355015}-\frac{4083286627611 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{4583875355015}-\frac{4083286627611 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{4583875355015}-\frac{4083286627611 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{4583875355015}-\frac{4083286627611 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{4583875355015}-\frac{4083286627611 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{4583875355015}-\frac{4083286627611 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =6\right)^{-n}}{4583875355015}-\frac{4083286627611 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =7\right)^{-n}}{4583875355015}-\frac{4083286627611 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =8\right)^{-n}}{4583875355015}-\frac{4083286627611 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-4 \textit{\_Z}^{8}+8 \textit{\_Z}^{7}-4 \textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =9\right)^{-n}}{4583875355015}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 62
a(6) = 178
a(7) = 506
a(8) = 1454
a(n+9) = a(n)-4*a(n+1)+8*a(n+2)-4*a(n+3)-2*a(n+4)-6*a(n+5)+14*a(n+6)-13*a(n+7)+6*a(n+8), 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) = 20
a \! \left(5\right) = 62
a \! \left(6\right) = 178
a \! \left(7\right) = 506
a \! \left(8\right) = 1454
a \! \left(n +9\right) = a \! \left(n \right)-4 a \! \left(n +1\right)+8 a \! \left(n +2\right)-4 a \! \left(n +3\right)-2 a \! \left(n +4\right)-6 a \! \left(n +5\right)+14 a \! \left(n +6\right)-13 a \! \left(n +7\right)+6 a \! \left(n +8\right), \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15307/
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[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[14,x]+F[17,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[1,x]+F[14,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[22,x]+F[23,x]+F[89,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[38,x]
F[25,x] = F[26,x]+F[7,x]
F[26,x] = F[22,x]+F[27,x]+F[32,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]
F[29,x] = F[11,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[29,x]*F[4,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[13,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[14,x]+F[35,x]
F[38,x] = F[39,x]+F[52,x]
F[39,x] = F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[45,x]
F[42,x] = F[2,x]+F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[42,x]
F[45,x] = F[46,x]+F[49,x]
F[46,x] = F[47,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[2,x]+F[46,x]
F[49,x] = F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[43,x]
F[52,x] = 2*F[22,x]+F[53,x]+F[58,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[43,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[55,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[60,x]+F[88,x]
F[60,x] = F[61,x]+F[85,x]
F[61,x] = F[22,x]+F[62,x]+F[83,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[71,x]
F[64,x] = F[14,x]+F[65,x]
F[65,x] = F[22,x]+F[36,x]+F[66,x]
F[66,x] = F[4,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[70,x] = F[4,x]*F[68,x]
F[71,x] = F[46,x]+F[72,x]
F[72,x] = 2*F[22,x]+F[73,x]+F[80,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[76,x]+F[78,x]
F[76,x] = F[77,x]
F[77,x] = F[2,x]*F[4,x]
F[78,x] = F[79,x]
F[79,x] = F[4,x]*F[75,x]
F[80,x] = F[4,x]*F[81,x]
F[81,x] = F[61,x]+F[82,x]
F[82,x] = F[80,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[2,x]+F[61,x]
F[85,x] = F[86,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[43,x]
F[88,x] = F[82,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[102,x]+F[91,x]
F[91,x] = F[2,x]+F[92,x]
F[92,x] = F[101,x]+F[22,x]+F[93,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[95,x]+F[98,x]
F[95,x] = F[11,x]+F[96,x]
F[96,x] = F[22,x]+F[27,x]+F[97,x]
F[97,x] = F[13,x]*F[4,x]
F[98,x] = F[43,x]+F[99,x]
F[99,x] = 2*F[22,x]+F[100,x]+F[53,x]
F[100,x] = F[4,x]*F[60,x]
F[101,x] = F[4,x]*F[91,x]
F[102,x] = F[103,x]+F[61,x]
F[103,x] = 2*F[22,x]+F[104,x]+F[86,x]
F[104,x] = F[105,x]*F[4,x]
F[105,x] = F[106,x]+F[115,x]
F[106,x] = F[107,x]+F[17,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]*F[4,x]
F[109,x] = F[110,x]
F[110,x] = F[111,x]+F[113,x]
F[111,x] = F[112,x]
F[112,x] = F[11,x]*F[4,x]
F[113,x] = F[114,x]
F[114,x] = F[110,x]*F[4,x]
F[115,x] = F[116,x]+F[49,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[4,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]+F[122,x]
F[120,x] = F[121,x]
F[121,x] = F[4,x]*F[43,x]
F[122,x] = F[123,x]
F[123,x] = F[119,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_{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_{14}\! \left(x \right)+F_{17}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \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_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{89}\! \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_{38}\! \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_{32}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{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_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{13}\! \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_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{14}\! \left(x \right)+F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{52}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \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_{45}\! \left(x \right)
F_{42}\! \left(x \right) = F_{2}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{49}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{2}\! \left(x \right)+F_{46}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{43}\! \left(x \right)
F_{52}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{53}\! \left(x \right)+F_{58}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{43}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{88}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{85}\! \left(x \right)
F_{61}\! \left(x \right) = F_{22}\! \left(x \right)+F_{62}\! \left(x \right)+F_{83}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{71}\! \left(x \right)
F_{64}\! \left(x \right) = F_{14}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{22}\! \left(x \right)+F_{36}\! \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_{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_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{46}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{73}\! \left(x \right)+F_{80}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{78}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{61}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{80}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{2}\! \left(x \right)+F_{61}\! \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_{43}\! \left(x \right)
F_{88}\! \left(x \right) = F_{82}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{102}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{2}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{101}\! \left(x \right)+F_{22}\! \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_{98}\! \left(x \right)
F_{95}\! \left(x \right) = F_{11}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{98}\! \left(x \right) = F_{43}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{100}\! \left(x \right)+F_{53}\! \left(x \right)
F_{100}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{101}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{61}\! \left(x \right)
F_{103}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{104}\! \left(x \right)+F_{86}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{4}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{115}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{17}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \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_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{113}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{110}\! \left(x \right) F_{4}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{49}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \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) = F_{120}\! \left(x \right)+F_{122}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{119}\! \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_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_14(x) + F_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_1(x) + F_14(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_22(x) + F_23(x) + F_89(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_38(x))
Eq(F_25(x), F_26(x) + F_7(x))
Eq(F_26(x), F_22(x) + F_27(x) + F_32(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_11(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_29(x)*F_4(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_13(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_14(x) + F_35(x))
Eq(F_38(x), F_39(x) + F_52(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_45(x))
Eq(F_42(x), F_2(x) + F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_42(x))
Eq(F_45(x), F_46(x) + F_49(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_2(x) + F_46(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_43(x))
Eq(F_52(x), 2*F_22(x) + F_53(x) + F_58(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_43(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_55(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_88(x))
Eq(F_60(x), F_61(x) + F_85(x))
Eq(F_61(x), F_22(x) + F_62(x) + F_83(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_71(x))
Eq(F_64(x), F_14(x) + F_65(x))
Eq(F_65(x), F_22(x) + F_36(x) + F_66(x))
Eq(F_66(x), F_4(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))
Eq(F_70(x), F_4(x)*F_68(x))
Eq(F_71(x), F_46(x) + F_72(x))
Eq(F_72(x), 2*F_22(x) + F_73(x) + F_80(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_76(x) + F_78(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_2(x)*F_4(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_4(x)*F_75(x))
Eq(F_80(x), F_4(x)*F_81(x))
Eq(F_81(x), F_61(x) + F_82(x))
Eq(F_82(x), F_80(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_2(x) + F_61(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_43(x))
Eq(F_88(x), F_82(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_102(x) + F_91(x))
Eq(F_91(x), F_2(x) + F_92(x))
Eq(F_92(x), F_101(x) + F_22(x) + F_93(x))
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_95(x) + F_98(x))
Eq(F_95(x), F_11(x) + F_96(x))
Eq(F_96(x), F_22(x) + F_27(x) + F_97(x))
Eq(F_97(x), F_13(x)*F_4(x))
Eq(F_98(x), F_43(x) + F_99(x))
Eq(F_99(x), F_100(x) + 2*F_22(x) + F_53(x))
Eq(F_100(x), F_4(x)*F_60(x))
Eq(F_101(x), F_4(x)*F_91(x))
Eq(F_102(x), F_103(x) + F_61(x))
Eq(F_103(x), F_104(x) + 2*F_22(x) + F_86(x))
Eq(F_104(x), F_105(x)*F_4(x))
Eq(F_105(x), F_106(x) + F_115(x))
Eq(F_106(x), F_107(x) + F_17(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x)*F_4(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_111(x) + F_113(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_11(x)*F_4(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_110(x)*F_4(x))
Eq(F_115(x), F_116(x) + F_49(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_4(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x) + F_122(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_4(x)*F_43(x))
Eq(F_122(x), F_123(x))
Eq(F_123(x), F_119(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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": 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