0132_1230_1302_30241_420531
Counting sequence:
1, 1, 2, 6, 21, 73, 245, 798, 2545, 8001, 24901, 76914, 236150, 721480, 2195132, 6655424, 20118719, 60663401, 182522071, 548150884, 1643588697, 4921403667, 14718641791, 43974166942, 131261404892, 391504004638, 1166912728120, 3476009618878, 10348953081305, 30797317693513, 91612537252113, 272423046193090, 809838374988753, 2406770862015869, 7151008558104801, 21242641353275370, 63091284290012170, 187352492137074988, 556272110306154164, 1651430225770281796, 4902130072782130683, 14550128624208685177, 43182848566323219619, 128151189670745043416, 380281163133977258329, 1128395253432622892447, 3348073568669345926923, 9933646858483456813590, 29471672610853984420448, 87434992132254151538898, 259389280671591199677424, 769496502699008362426930, 2282709144608256429729733, 6771502887108814832295929, 20086821872787235465601069, 59584052664502933827424390, 176743057360440178126869361, 524262704850329655120164121, 1555072040160262524905746973, 4612619215348532004758302946, 13681721952845137974291086526, 40581719434631590890211831792, 120369668075372495362626898348, 357026931073992014226227033320, 1058967186676386515210956090455, 3140956503755612486897916936393, 9316214544973657155476755058639, 27632195881946876256770810432812, 81957719849637155388015627875737, 243087740484247306129522093145355, 720999755490648359605050699722167, 2138484868356362405727270043859726, 6342732068954489675221760575032964, 18812468014172943002720336486274278, 55797468745253762119044135085222312, 165494138250528153303818699348447814, 490851587756433744171009045159767377, 1455852287655916994099786867272175081, 4318013644637504177104583349216096553, 12807086426373089102720556840039503018, 37985368697367467421122367547350417489, 112663195718535938383642900727316518421, 334154668618487832470975664842258395641, 991089277570363118557667694254199247194, 2939529515469323388959632921587669973394, 8718518616462865787393403985784159152020, 25858743596825420843459922784504963034532, 76695874779882466529874309470166896284588, 227476465302239928560143156996083747114707, 674684653557109799546253596489711710131033, 2001082985015365471273966445515147233623387, 5935116997889680478931644154638808791788896, 17603271908975878354333114856569545188155673, 52210451174916941230005568695027525029425751, 154853647173806561214360798994883447829671299, 459288298607264139681116579706753613442282118, 1362226358290995019065180858546742800180872264, 4040295585225811841004600866484785393736783706, 11983314687424063172712867826772880321724472160, 35541909709083793392534968825370360307884757754, 105415513236024448198107821063911811020673431933
Generating function in Maple syntax:
(x^7-6*x^6+17*x^5-34*x^4+39*x^3-25*x^2+8*x-1)/(x^2-3*x+1)/(2*x^5-7*x^4+14*x^3-13*x^2+6*x-1)
Generating function in latex syntax:
\frac{x^{7}-6 x^{6}+17 x^{5}-34 x^{4}+39 x^{3}-25 x^{2}+8 x -1}{\left(x^{2}-3 x +1\right) \left(2 x^{5}-7 x^{4}+14 x^{3}-13 x^{2}+6 x -1\right)}
Generating function in sympy syntax:
(x**7 - 6*x**6 + 17*x**5 - 34*x**4 + 39*x**3 - 25*x**2 + 8*x - 1)/((x**2 - 3*x + 1)*(2*x**5 - 7*x**4 + 14*x**3 - 13*x**2 + 6*x - 1))
Implicit equation for the generating function in Maple syntax:
(x^2-3*x+1)*(2*x^5-7*x^4+14*x^3-13*x^2+6*x-1)*F(x)-x^7+6*x^6-17*x^5+34*x^4-39*x^3+25*x^2-8*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}-3 x +1\right) \left(2 x^{5}-7 x^{4}+14 x^{3}-13 x^{2}+6 x -1\right) F \! \left(x \right)-x^{7}+6 x^{6}-17 x^{5}+34 x^{4}-39 x^{3}+25 x^{2}-8 x +1 = 0
Explicit closed form in Maple syntax:
1/2396*piecewise(n = 0,2122*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^4+2122*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^4+2122*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^4+2122*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^4+2122*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^4-6781*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^3-6781*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^3-6781*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^3-6781*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^3-6781*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^3+12985*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^2+12985*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^2+12985*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^2+12985*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^2+12985*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^2-9897*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)-9897*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)-9897*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)-9897*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)-9897*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)+18140,33952*(RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^2-2*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)+3)*(RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^2-2*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)+3)*(RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^2-2*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)+3)*(RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^2-3/2*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)+1)*(RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^2-3/2*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)+1)*(RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^2-3/2*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)+1)*(RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^2-3/2*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)+1)*(RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^2-2*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)+3)*(RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^2-2*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)+3)*(RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^2-3/2*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)+1)*(-2738/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+1)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)+3896/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+2)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)-1869/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)+646/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)-2738/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+1)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)+3896/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+2)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)-1869/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)+646/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)-2738/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+1)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)+3896/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+2)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)-1869/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)+646/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)-2738/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+1)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)+3896/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+2)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)-1869/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)+646/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)-2738/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+1)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)+3896/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+2)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)-1869/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)+646/1061*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)+RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)+(RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)+(RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)+RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)*(RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n)*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)+(RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n)-1797/5305*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)*((5^(1/2)+5/3)*(3/2-1/2*5^(1/2))^(-n)-(3/2+1/2*5^(1/2))^(-n)*(5^(1/2)-5/3)))*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)))*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2))*RootOf(2*_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)))
Explicit closed form in latex syntax:
\frac{\left(\left\{\begin{array}{cc}2122 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =1\right)^{4}\\+\\2122 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =2\right)^{4}\\+\\2122 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =3\right)^{4}\\+\\2122 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =4\right)^{4}\\+\\2122 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =5\right)^{4}\\-\\6781 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =1\right)^{3}\\-\\6781 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =2\right)^{3}\\-\\6781 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =3\right)^{3}\\-\\6781 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =4\right)^{3}\\-\\6781 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =5\right)^{3}\\+\\12985 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =1\right)^{2}\\+\\12985 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =2\right)^{2}\\+\\12985 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =3\right)^{2}\\+\\12985 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =4\right)^{2}\\+\\12985 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =5\right)^{2}\\-\\9897 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =1\right)\\-\\9897 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =2\right)\\-\\9897 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =3\right)\\-\\9897 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =4\right)\\-\\9897 \\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} \\-1, \mathit{index} =5\right)\\+18140 & n =0 \\ 33952 \\\left(\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{2}\right. \\-\\2 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)\\ \left. +3\right)\\ \\\left(\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{2}\right. \\-\\2 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)\\ \left. +3\right)\\ \\\left(\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{2}\right. \\-\\2 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)\\ \left. +3\right)\\ \\\left(\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{2}\right. \\-\\\frac{3 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)}{2}\\ \left. +1\right)\\ \\\left(\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{2}\right. \\-\\\frac{3 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)}{2}\\ \left. +1\right)\\ \\\left(\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{2}\right. \\-\\\frac{3 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)}{2}\\ \left. +1\right)\\ \\\left(\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{2}\right. \\-\\\frac{3 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)}{2}\\ \left. +1\right)\\ \\\left(\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{2}\right. \\-\\2 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)\\ \left. +3\right)\\ \\\left(\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{2}\right. \\-\\2 \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)\\ \left. +3\right)\\ \\\left(\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{2}\right. \\-\\\frac{3 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)}{2}\\ \left. +1\right)\\ \\\left(-\frac{2738 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)}{1061}\right. \\+\\\frac{3896 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)}{1061}\\-\\\frac{1869 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)}{1061}\\+\\\frac{646 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)}{1061}\\-\\\frac{2738 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)}{1061}\\+\\\frac{3896 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)}{1061}\\-\\\frac{1869 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)}{1061}\\+\\\frac{646 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +4} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)}{1061}\\-\\\frac{2738 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)}{1061}\\+\\\frac{3896 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)}{1061}\\-\\\frac{1869 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)}{1061}\\+\\\frac{646 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +4} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)}{1061}\\-\\\frac{2738 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)}{1061}\\+\\\frac{3896 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)}{1061}\\-\\\frac{1869 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)}{1061}\\+\\\frac{646 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +4} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)}{1061}\\-\\\frac{2738 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)}{1061}\\+\\\frac{3896 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)}{1061}\\-\\\frac{1869 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)}{1061}\\+\\\frac{646 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +4} \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)}{1061}\\+\\\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n} \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)\\+\\ \left. \left(\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n} \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)+\left(\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n} \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)+\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right) \left(\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n} \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)+\left(\mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}-\frac{1797 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right) \left(\left(\sqrt{5}+\frac{5}{3}\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}-\left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n} \left(\sqrt{5}-\frac{5}{3}\right)\right)}{5305}\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)\right)\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)\right) \mathit{RootOf}\! \left(2 \textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)\right) & \mathit{\text{otherwise}} \end{array}\right.\right)}{2396}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 73
a(6) = 245
a(7) = 798
a(n+7) = 2*a(n)-13*a(n+1)+37*a(n+2)-62*a(n+3)+59*a(n+4)-32*a(n+5)+9*a(n+6), n >= 8
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) = 21
a \! \left(5\right) = 73
a \! \left(6\right) = 245
a \! \left(7\right) = 798
a \! \left(n +7\right) = 2 a \! \left(n \right)-13 a \! \left(n +1\right)+37 a \! \left(n +2\right)-62 a \! \left(n +3\right)+59 a \! \left(n +4\right)-32 a \! \left(n +5\right)+9 a \! \left(n +6\right), \quad n \geq 8
Specification 1
Strategy pack name: all_the_strategies_1_expand_verified
Tree: http://www.permpal.com/tree/24075/
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[12,x]*F[4,x]
F[4,x] = F[40,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[14,x]+F[26,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[12,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]+F[21,x]+F[25,x]
F[20,x] = 0
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[23,x]+F[24,x]
F[23,x] = F[12,x]
F[24,x] = F[19,x]
F[25,x] = F[12,x]*F[14,x]
F[26,x] = F[20,x]+F[27,x]+F[39,x]
F[27,x] = F[12,x]*F[28,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[10,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[10,x]*F[12,x]
F[32,x] = F[26,x]+F[33,x]
F[33,x] = 2*F[20,x]+F[34,x]+F[38,x]
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[30,x]
F[37,x] = F[33,x]
F[38,x] = F[12,x]*F[26,x]
F[39,x] = F[12,x]*F[13,x]
F[40,x] = F[41,x]+F[63,x]
F[41,x] = F[42,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[44,x]+F[47,x]
F[44,x] = F[1,x]+F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[12,x]*F[44,x]
F[47,x] = F[41,x]+F[48,x]
F[48,x] = F[20,x]+F[49,x]+F[53,x]
F[49,x] = F[12,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[45,x]
F[52,x] = F[48,x]
F[53,x] = F[12,x]*F[54,x]
F[54,x] = F[41,x]+F[55,x]
F[55,x] = F[20,x]+F[53,x]+F[56,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[51,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[20,x]+F[56,x]+F[60,x]
F[60,x] = F[12,x]*F[61,x]
F[61,x] = F[41,x]+F[62,x]
F[62,x] = F[60,x]
F[63,x] = F[20,x]+F[64,x]+F[98,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[66,x]+F[71,x]
F[66,x] = F[6,x]+F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[12,x]*F[69,x]
F[69,x] = F[10,x]+F[70,x]
F[70,x] = F[68,x]
F[71,x] = F[63,x]+F[72,x]
F[72,x] = 2*F[20,x]+F[73,x]+F[77,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = F[67,x]
F[76,x] = F[72,x]
F[77,x] = F[12,x]*F[78,x]
F[78,x] = F[79,x]+F[90,x]
F[79,x] = F[20,x]+F[80,x]+F[88,x]
F[80,x] = F[12,x]*F[81,x]
F[81,x] = F[69,x]+F[82,x]
F[82,x] = F[79,x]+F[83,x]
F[83,x] = 2*F[20,x]+F[77,x]+F[84,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[70,x]
F[87,x] = F[83,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[41,x]+F[79,x]
F[90,x] = 2*F[20,x]+F[77,x]+F[91,x]
F[91,x] = F[12,x]*F[92,x]
F[92,x] = F[86,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = 2*F[20,x]+F[91,x]+F[95,x]
F[95,x] = F[12,x]*F[96,x]
F[96,x] = F[79,x]+F[97,x]
F[97,x] = F[95,x]
F[98,x] = F[12,x]*F[99,x]
F[99,x] = F[100,x]+F[89,x]
F[100,x] = F[101,x]+F[114,x]
F[101,x] = F[102,x]+F[20,x]+F[56,x]
F[102,x] = F[103,x]*F[12,x]
F[103,x] = F[104,x]+F[107,x]
F[104,x] = F[105,x]+F[41,x]
F[105,x] = F[106,x]
F[106,x] = F[12,x]*F[41,x]
F[107,x] = F[101,x]+F[108,x]
F[108,x] = 2*F[20,x]+F[109,x]+F[113,x]
F[109,x] = F[110,x]*F[12,x]
F[110,x] = F[111,x]+F[112,x]
F[111,x] = F[105,x]
F[112,x] = F[108,x]
F[113,x] = F[101,x]*F[12,x]
F[114,x] = F[115,x]+F[127,x]+F[20,x]+F[91,x]
F[115,x] = F[116,x]*F[12,x]
F[116,x] = F[117,x]+F[120,x]
F[117,x] = F[118,x]+F[79,x]
F[118,x] = F[119,x]
F[119,x] = F[12,x]*F[79,x]
F[120,x] = F[114,x]+F[121,x]
F[121,x] = 3*F[20,x]+F[122,x]+F[126,x]
F[122,x] = F[12,x]*F[123,x]
F[123,x] = F[124,x]+F[125,x]
F[124,x] = F[118,x]
F[125,x] = F[121,x]
F[126,x] = F[114,x]*F[12,x]
F[127,x] = F[100,x]*F[12,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{40}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{26}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{25}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right)
F_{24}\! \left(x \right) = F_{19}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{26}\! \left(x \right) = F_{20}\! \left(x \right)+F_{27}\! \left(x \right)+F_{39}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = F_{10}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{32}\! \left(x \right) = F_{26}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)
F_{37}\! \left(x \right) = F_{33}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{63}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{47}\! \left(x \right)
F_{44}\! \left(x \right) = F_{1}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{41}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{20}\! \left(x \right)+F_{49}\! \left(x \right)+F_{53}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \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_{45}\! \left(x \right)
F_{52}\! \left(x \right) = F_{48}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{41}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{20}\! \left(x \right)+F_{53}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{51}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{20}\! \left(x \right)+F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{41}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{20}\! \left(x \right)+F_{64}\! \left(x \right)+F_{98}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{71}\! \left(x \right)
F_{66}\! \left(x \right) = F_{6}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{10}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{63}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{73}\! \left(x \right)+F_{77}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{67}\! \left(x \right)
F_{76}\! \left(x \right) = F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{90}\! \left(x \right)
F_{79}\! \left(x \right) = F_{20}\! \left(x \right)+F_{80}\! \left(x \right)+F_{88}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{69}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{79}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{77}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \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_{70}\! \left(x \right)
F_{87}\! \left(x \right) = F_{83}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{41}\! \left(x \right)+F_{79}\! \left(x \right)
F_{90}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{77}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{86}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{91}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{12}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{79}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{95}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{89}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{114}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{20}\! \left(x \right)+F_{56}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{12}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{107}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{41}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{107}\! \left(x \right) = F_{101}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{109}\! \left(x \right)+F_{113}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{12}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{112}\! \left(x \right)
F_{111}\! \left(x \right) = F_{105}\! \left(x \right)
F_{112}\! \left(x \right) = F_{108}\! \left(x \right)
F_{113}\! \left(x \right) = F_{101}\! \left(x \right) F_{12}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{127}\! \left(x \right)+F_{20}\! \left(x \right)+F_{91}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{12}\! \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_{79}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{12}\! \left(x \right) F_{79}\! \left(x \right)
F_{120}\! \left(x \right) = F_{114}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = 3 F_{20}\! \left(x \right)+F_{122}\! \left(x \right)+F_{126}\! \left(x \right)
F_{122}\! \left(x \right) = F_{12}\! \left(x \right) F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{125}\! \left(x \right)
F_{124}\! \left(x \right) = F_{118}\! \left(x \right)
F_{125}\! \left(x \right) = F_{121}\! \left(x \right)
F_{126}\! \left(x \right) = F_{114}\! \left(x \right) F_{12}\! \left(x \right)
F_{127}\! \left(x \right) = F_{100}\! \left(x \right) F_{12}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_40(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_26(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_12(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_25(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_12(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_24(x))
Eq(F_23(x), F_12(x))
Eq(F_24(x), F_19(x))
Eq(F_25(x), F_12(x)*F_14(x))
Eq(F_26(x), F_20(x) + F_27(x) + F_39(x))
Eq(F_27(x), F_12(x)*F_28(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_10(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_10(x)*F_12(x))
Eq(F_32(x), F_26(x) + F_33(x))
Eq(F_33(x), 2*F_20(x) + F_34(x) + F_38(x))
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_30(x))
Eq(F_37(x), F_33(x))
Eq(F_38(x), F_12(x)*F_26(x))
Eq(F_39(x), F_12(x)*F_13(x))
Eq(F_40(x), F_41(x) + F_63(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_47(x))
Eq(F_44(x), F_1(x) + F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_12(x)*F_44(x))
Eq(F_47(x), F_41(x) + F_48(x))
Eq(F_48(x), F_20(x) + F_49(x) + F_53(x))
Eq(F_49(x), F_12(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_45(x))
Eq(F_52(x), F_48(x))
Eq(F_53(x), F_12(x)*F_54(x))
Eq(F_54(x), F_41(x) + F_55(x))
Eq(F_55(x), F_20(x) + F_53(x) + F_56(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_51(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_20(x) + F_56(x) + F_60(x))
Eq(F_60(x), F_12(x)*F_61(x))
Eq(F_61(x), F_41(x) + F_62(x))
Eq(F_62(x), F_60(x))
Eq(F_63(x), F_20(x) + F_64(x) + F_98(x))
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_71(x))
Eq(F_66(x), F_6(x) + F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_12(x)*F_69(x))
Eq(F_69(x), F_10(x) + F_70(x))
Eq(F_70(x), F_68(x))
Eq(F_71(x), F_63(x) + F_72(x))
Eq(F_72(x), 2*F_20(x) + F_73(x) + F_77(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), F_67(x))
Eq(F_76(x), F_72(x))
Eq(F_77(x), F_12(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_90(x))
Eq(F_79(x), F_20(x) + F_80(x) + F_88(x))
Eq(F_80(x), F_12(x)*F_81(x))
Eq(F_81(x), F_69(x) + F_82(x))
Eq(F_82(x), F_79(x) + F_83(x))
Eq(F_83(x), 2*F_20(x) + F_77(x) + F_84(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_70(x))
Eq(F_87(x), F_83(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_41(x) + F_79(x))
Eq(F_90(x), 2*F_20(x) + F_77(x) + F_91(x))
Eq(F_91(x), F_12(x)*F_92(x))
Eq(F_92(x), F_86(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), 2*F_20(x) + F_91(x) + F_95(x))
Eq(F_95(x), F_12(x)*F_96(x))
Eq(F_96(x), F_79(x) + F_97(x))
Eq(F_97(x), F_95(x))
Eq(F_98(x), F_12(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_89(x))
Eq(F_100(x), F_101(x) + F_114(x))
Eq(F_101(x), F_102(x) + F_20(x) + F_56(x))
Eq(F_102(x), F_103(x)*F_12(x))
Eq(F_103(x), F_104(x) + F_107(x))
Eq(F_104(x), F_105(x) + F_41(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_12(x)*F_41(x))
Eq(F_107(x), F_101(x) + F_108(x))
Eq(F_108(x), F_109(x) + F_113(x) + 2*F_20(x))
Eq(F_109(x), F_110(x)*F_12(x))
Eq(F_110(x), F_111(x) + F_112(x))
Eq(F_111(x), F_105(x))
Eq(F_112(x), F_108(x))
Eq(F_113(x), F_101(x)*F_12(x))
Eq(F_114(x), F_115(x) + F_127(x) + F_20(x) + F_91(x))
Eq(F_115(x), F_116(x)*F_12(x))
Eq(F_116(x), F_117(x) + F_120(x))
Eq(F_117(x), F_118(x) + F_79(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_12(x)*F_79(x))
Eq(F_120(x), F_114(x) + F_121(x))
Eq(F_121(x), F_122(x) + F_126(x) + 3*F_20(x))
Eq(F_122(x), F_12(x)*F_123(x))
Eq(F_123(x), F_124(x) + F_125(x))
Eq(F_124(x), F_118(x))
Eq(F_125(x), F_121(x))
Eq(F_126(x), F_114(x)*F_12(x))
Eq(F_127(x), F_100(x)*F_12(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "limited_insertion": true, "maxreqlen": 1, "strategy_class": "RequirementInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "ignore_parent": false, "strategy_class": "AllPlacementsFactory"}]], "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": "all_the_strategies_1_expand_verified", "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:
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