01234_01243_01324_02134_02143_02314_02341_02413_02431_03124_03214_03241_20134_20143_20314_20341_20413_20431_24013_24031
Counting sequence:
1, 1, 2, 6, 24, 100, 405, 1588, 6078, 22910, 85627, 318756, 1184874, 4403425, 16368973, 60870425, 226422622, 842403635, 3134521519, 11664005791, 43404496451, 161519361340, 601054795049, 2236671441312, 8323174728202, 30972401884536, 115255108613889, 428889270554857, 1595989567703288, 5939021189088542, 22100378002950871, 82240272930242561, 306033802644597434, 1138817849349798039, 4237787145127330390, 15769721254656375904, 58682539006909496803, 218370403224810121767, 812603439110776474296, 3023872921052549529246, 11252484298428594862452, 41872924608956112371859, 155818196984626892500071, 579833167511336715071755, 2157684459423509312496614, 8029209930037999373063370, 29878424446545163525053757, 111184071059117938974839562, 413739944000093143007377591, 1539615698823691768837060390, 5729242569987440105204426329, 21319749110688422734286849880, 79335391474616695230721312109, 295224128002372569485008270809, 1098592748264855191791288149929, 4088100910676285589626640753080, 15212706512279374333206138293657, 56609766853933847258265926815536, 210657170088039771852451310203431, 783900831529690220958591843354916, 2917064315523260679965841300536976, 10855026399569358579245863390907593, 40393897902182882003301250736914568, 150314419115250262926668789345017734, 559352421216426388417389226573638595, 2081471178628502086834333664483701436, 7745603850322431738213546445658090931, 28823064965838471945717398606095692435, 107256850476591593747999544340373873103, 399125907941874946879382057484473150299, 1485233714047877916044105793536434661071, 5526875458221828887108239167461057332761, 20566697376834566199784662214730831436931, 76533123314919568256424262710710645761260, 284796282894409416604259699150149557157182, 1059788484219105309507628610210033817813335, 3943701862498839574711715265632410743688745, 14675366464032426156479399320205109196610937, 54610208469761313194023928455273578802928757, 203216381438922869416319126379683719224046605, 756212049767153968059831237080228001939603956, 2814028377849614099553094588971479085492479777, 10471607419878065599518634424954668162134133469, 38967113060828366117687745305003639730188188312, 145005044537189280833570298731356832961690458387, 539595091594534065408119568032716694218086644681, 2007949887551942341836478555532995961937448338263, 7472015245738197967241722539573746151125385846702, 27804982673453202422548584739660310452710663903828, 103468346362381206970216584196320773685909175663374, 385028065821704196554175489962008692724106964379060, 1432772598406016036577963757827952568491155720371144, 5331656315396340104022519664425313511095261940623506, 19840244779339519523745988694795862945518849304012195, 73829836286971422081225339894298585212671995405643920, 274736767957479827604468921980194661904684128312850943, 1022354856298685094473533284258011166476494677435263166, 3804403247399594260097130676071686320432991966985746566, 14157006228956662448125146057071274226740787368570724424, 52681278070012803804643776479697869662701476381230824622, 196038414775391831287678674366533184107507870183860042067
Generating function in Maple syntax:
(x-1)*(2*x^3-2*x^2+3*x-1)*(x^2-3*x+1)^2/(3*x^8-28*x^7+91*x^6-153*x^5+167*x^4-117*x^3+49*x^2-11*x+1)
Generating function in latex syntax:
\frac{\left(x -1\right) \left(2 x^{3}-2 x^{2}+3 x -1\right) \left(x^{2}-3 x +1\right)^{2}}{3 x^{8}-28 x^{7}+91 x^{6}-153 x^{5}+167 x^{4}-117 x^{3}+49 x^{2}-11 x +1}
Generating function in sympy syntax:
(x - 1)*(x**2 - 3*x + 1)**2*(2*x**3 - 2*x**2 + 3*x - 1)/(3*x**8 - 28*x**7 + 91*x**6 - 153*x**5 + 167*x**4 - 117*x**3 + 49*x**2 - 11*x + 1)
Implicit equation for the generating function in Maple syntax:
(3*x^8-28*x^7+91*x^6-153*x^5+167*x^4-117*x^3+49*x^2-11*x+1)*F(x)-(x-1)*(2*x^3-2*x^2+3*x-1)*(x^2-3*x+1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(3 x^{8}-28 x^{7}+91 x^{6}-153 x^{5}+167 x^{4}-117 x^{3}+49 x^{2}-11 x +1\right) F \! \left(x \right)-\left(x -1\right) \left(2 x^{3}-2 x^{2}+3 x -1\right) \left(x^{2}-3 x +1\right)^{2} = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,2/3,0)+1682813210364/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 1)^(-n)+1682813210364/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 2)^(-n)+1682813210364/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 3)^(-n)+1682813210364/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 4)^(-n)+1682813210364/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 5)^(-n)+1682813210364/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 6)^(-n)+1682813210364/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 7)^(-n)+1682813210364/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 8)^(-n)-186388728527/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 1)^(-n-1)-186388728527/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 2)^(-n-1)-186388728527/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 3)^(-n-1)-186388728527/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 4)^(-n-1)-186388728527/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 5)^(-n-1)-186388728527/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 6)^(-n-1)-186388728527/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 7)^(-n-1)-186388728527/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 8)^(-n-1)-5520003542429/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 1)^(-n+1)-5520003542429/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 2)^(-n+1)-5520003542429/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 3)^(-n+1)-5520003542429/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 4)^(-n+1)-5520003542429/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 5)^(-n+1)-5520003542429/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 6)^(-n+1)-5520003542429/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 7)^(-n+1)-5520003542429/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 8)^(-n+1)+9273391394974/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 1)^(-n+2)+9273391394974/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 2)^(-n+2)+9273391394974/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 3)^(-n+2)+9273391394974/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 4)^(-n+2)+9273391394974/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 5)^(-n+2)+9273391394974/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 6)^(-n+2)+9273391394974/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 7)^(-n+2)+9273391394974/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 8)^(-n+2)-9374180977152/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 1)^(-n+3)-9374180977152/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 2)^(-n+3)-9374180977152/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 3)^(-n+3)-9374180977152/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 4)^(-n+3)-9374180977152/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 5)^(-n+3)-9374180977152/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 6)^(-n+3)-9374180977152/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 7)^(-n+3)-9374180977152/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 8)^(-n+3)+6114854108486/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 1)^(-n+4)+6114854108486/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 2)^(-n+4)+6114854108486/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 3)^(-n+4)+6114854108486/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 4)^(-n+4)+6114854108486/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 5)^(-n+4)+6114854108486/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 6)^(-n+4)+6114854108486/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 7)^(-n+4)+6114854108486/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 8)^(-n+4)-2006936200224/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 1)^(-n+5)-2006936200224/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 2)^(-n+5)-2006936200224/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 3)^(-n+5)-2006936200224/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 4)^(-n+5)-2006936200224/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 5)^(-n+5)-2006936200224/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 6)^(-n+5)-2006936200224/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 7)^(-n+5)-2006936200224/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 8)^(-n+5)+222457861764/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 1)^(-n+6)+222457861764/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 2)^(-n+6)+222457861764/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 3)^(-n+6)+222457861764/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 4)^(-n+6)+222457861764/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 5)^(-n+6)+222457861764/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 6)^(-n+6)+222457861764/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 7)^(-n+6)+222457861764/135913855817*RootOf(3*_Z^8-28*_Z^7+91*_Z^6-153*_Z^5+167*_Z^4-117*_Z^3+49*_Z^2-11*_Z+1,index = 8)^(-n+6)
Explicit closed form in latex syntax:
\left(\left\{\begin{array}{cc}\frac{2}{3} & n =0 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)+\frac{1682813210364 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{135913855817}+\frac{1682813210364 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{135913855817}+\frac{1682813210364 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{135913855817}+\frac{1682813210364 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{135913855817}+\frac{1682813210364 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{135913855817}+\frac{1682813210364 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{135913855817}+\frac{1682813210364 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =7\right)^{-n}}{135913855817}+\frac{1682813210364 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =8\right)^{-n}}{135913855817}-\frac{186388728527 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{135913855817}-\frac{186388728527 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{135913855817}-\frac{186388728527 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{135913855817}-\frac{186388728527 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{135913855817}-\frac{186388728527 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{135913855817}-\frac{186388728527 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{135913855817}-\frac{186388728527 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =7\right)^{-n -1}}{135913855817}-\frac{186388728527 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =8\right)^{-n -1}}{135913855817}-\frac{5520003542429 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{135913855817}-\frac{5520003542429 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{135913855817}-\frac{5520003542429 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{135913855817}-\frac{5520003542429 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{135913855817}-\frac{5520003542429 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{135913855817}-\frac{5520003542429 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{135913855817}-\frac{5520003542429 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +1}}{135913855817}-\frac{5520003542429 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +1}}{135913855817}+\frac{9273391394974 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{135913855817}+\frac{9273391394974 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{135913855817}+\frac{9273391394974 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{135913855817}+\frac{9273391394974 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{135913855817}+\frac{9273391394974 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{135913855817}+\frac{9273391394974 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{135913855817}+\frac{9273391394974 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +2}}{135913855817}+\frac{9273391394974 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +2}}{135913855817}-\frac{9374180977152 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{135913855817}-\frac{9374180977152 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{135913855817}-\frac{9374180977152 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{135913855817}-\frac{9374180977152 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{135913855817}-\frac{9374180977152 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{135913855817}-\frac{9374180977152 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +3}}{135913855817}-\frac{9374180977152 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +3}}{135913855817}-\frac{9374180977152 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +3}}{135913855817}+\frac{6114854108486 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{135913855817}+\frac{6114854108486 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +4}}{135913855817}+\frac{6114854108486 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +4}}{135913855817}+\frac{6114854108486 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +4}}{135913855817}+\frac{6114854108486 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +4}}{135913855817}+\frac{6114854108486 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +4}}{135913855817}+\frac{6114854108486 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +4}}{135913855817}+\frac{6114854108486 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +4}}{135913855817}-\frac{2006936200224 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +5}}{135913855817}-\frac{2006936200224 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +5}}{135913855817}-\frac{2006936200224 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +5}}{135913855817}-\frac{2006936200224 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +5}}{135913855817}-\frac{2006936200224 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +5}}{135913855817}-\frac{2006936200224 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +5}}{135913855817}-\frac{2006936200224 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +5}}{135913855817}-\frac{2006936200224 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +5}}{135913855817}+\frac{222457861764 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +6}}{135913855817}+\frac{222457861764 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +6}}{135913855817}+\frac{222457861764 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +6}}{135913855817}+\frac{222457861764 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +6}}{135913855817}+\frac{222457861764 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +6}}{135913855817}+\frac{222457861764 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +6}}{135913855817}+\frac{222457861764 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +6}}{135913855817}+\frac{222457861764 \mathit{RootOf}\! \left(3 \textit{\_Z}^{8}-28 \textit{\_Z}^{7}+91 \textit{\_Z}^{6}-153 \textit{\_Z}^{5}+167 \textit{\_Z}^{4}-117 \textit{\_Z}^{3}+49 \textit{\_Z}^{2}-11 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +6}}{135913855817}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 100
a(6) = 405
a(7) = 1588
a(8) = 6078
a(n+8) = -3*a(n)+28*a(n+1)-91*a(n+2)+153*a(n+3)-167*a(n+4)+117*a(n+5)-49*a(n+6)+11*a(n+7), n >= 9
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 100
a(6) = 405
a(7) = 1588
a(8) = 6078
a{\left(n + 8 \right)} = - 3 a{\left(n \right)} + 28 a{\left(n + 1 \right)} - 91 a{\left(n + 2 \right)} + 153 a{\left(n + 3 \right)} - 167 a{\left(n + 4 \right)} + 117 a{\left(n + 5 \right)} - 49 a{\left(n + 6 \right)} + 11 a{\left(n + 7 \right)}, \quad n \geq 9
Specification 1
Strategy pack name: regular_insertion_encoding_left
Tree: http://permpal.com/tree/24874/
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[19,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[32,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[19,x]*F[8,x]
F[8,x] = F[10,x]+F[9,x]
F[9,x] = F[1,x]+F[6,x]
F[10,x] = F[11,x]+F[20,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[19,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[1,x]+F[11,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[19,x]
F[18,x] = F[1,x]+F[16,x]
F[19,x] = x
F[20,x] = F[21,x]+F[22,x]+F[29,x]
F[21,x] = 0
F[22,x] = F[19,x]*F[23,x]
F[23,x] = F[24,x]+F[25,x]
F[24,x] = F[20,x]+F[6,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[19,x]*F[28,x]
F[28,x] = F[26,x]+F[6,x]
F[29,x] = F[19,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[16,x]+F[26,x]
F[32,x] = F[21,x]+F[33,x]+F[91,x]
F[33,x] = F[19,x]*F[34,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[2,x]+F[32,x]
F[36,x] = F[127,x]+F[37,x]
F[37,x] = F[21,x]+F[38,x]+F[91,x]
F[38,x] = F[19,x]*F[39,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[2,x]+F[37,x]
F[41,x] = F[42,x]
F[42,x] = F[21,x]+F[43,x]+F[45,x]
F[43,x] = F[19,x]*F[44,x]
F[44,x] = F[2,x]+F[42,x]
F[45,x] = F[19,x]*F[46,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[16,x]+F[42,x]
F[48,x] = F[49,x]+F[52,x]
F[49,x] = F[21,x]+F[29,x]+F[50,x]
F[50,x] = F[19,x]*F[51,x]
F[51,x] = F[49,x]+F[6,x]
F[52,x] = F[21,x]+F[53,x]+F[86,x]+F[90,x]
F[53,x] = F[19,x]*F[54,x]
F[54,x] = F[55,x]+F[79,x]
F[55,x] = F[56,x]
F[56,x] = F[19,x]*F[57,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[2,x]+F[55,x]
F[59,x] = F[60,x]+F[68,x]
F[60,x] = F[61,x]
F[61,x] = F[19,x]*F[62,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = F[2,x]+F[60,x]
F[64,x] = F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[19,x]*F[67,x]
F[67,x] = F[2,x]+F[65,x]
F[68,x] = 2*F[21,x]+F[69,x]+F[76,x]
F[69,x] = F[19,x]*F[70,x]
F[70,x] = F[71,x]+F[72,x]
F[71,x] = F[55,x]+F[68,x]
F[72,x] = F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[19,x]*F[75,x]
F[75,x] = F[55,x]+F[73,x]
F[76,x] = F[19,x]*F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[65,x]+F[73,x]
F[79,x] = 2*F[21,x]+F[53,x]+F[80,x]
F[80,x] = F[19,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[42,x]+F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[19,x]*F[85,x]
F[85,x] = F[55,x]+F[83,x]
F[86,x] = F[19,x]*F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[42,x]+F[89,x]
F[89,x] = F[84,x]
F[90,x] = 0
F[91,x] = F[19,x]*F[92,x]
F[92,x] = F[93,x]+F[94,x]
F[93,x] = F[11,x]+F[37,x]
F[94,x] = F[108,x]+F[95,x]
F[95,x] = F[100,x]+F[21,x]+F[96,x]
F[96,x] = F[19,x]*F[97,x]
F[97,x] = F[98,x]+F[99,x]
F[98,x] = F[6,x]+F[95,x]
F[99,x] = F[49,x]
F[100,x] = F[101,x]*F[19,x]
F[101,x] = F[102,x]
F[102,x] = F[103,x]+F[11,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[19,x]
F[105,x] = F[106,x]+F[107,x]
F[106,x] = F[103,x]+F[6,x]
F[107,x] = F[26,x]
F[108,x] = F[109,x]+F[122,x]+F[126,x]+F[21,x]
F[109,x] = F[110,x]*F[19,x]
F[110,x] = F[111,x]+F[121,x]
F[111,x] = F[112,x]+F[55,x]
F[112,x] = 2*F[21,x]+F[109,x]+F[113,x]
F[113,x] = F[114,x]*F[19,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]+F[37,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[19,x]
F[118,x] = F[119,x]+F[120,x]
F[119,x] = F[116,x]+F[55,x]
F[120,x] = F[83,x]
F[121,x] = F[79,x]
F[122,x] = F[123,x]*F[19,x]
F[123,x] = F[124,x]
F[124,x] = F[125,x]+F[37,x]
F[125,x] = F[117,x]
F[126,x] = 0
F[127,x] = F[126,x]+F[128,x]+F[21,x]+F[86,x]
F[128,x] = F[129,x]*F[19,x]
F[129,x] = F[130,x]+F[132,x]
F[130,x] = F[131,x]+F[55,x]
F[131,x] = 2*F[21,x]+F[128,x]+F[80,x]
F[132,x] = F[83,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_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{32}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{19}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{10}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{20}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{19}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{19}\! \left(x \right) = x
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)+F_{29}\! \left(x \right)
F_{21}\! \left(x \right) = 0
F_{22}\! \left(x \right) = F_{19}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)
F_{24}\! \left(x \right) = F_{20}\! \left(x \right)+F_{6}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{19}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{26}\! \left(x \right)+F_{6}\! \left(x \right)
F_{29}\! \left(x \right) = F_{19}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{16}\! \left(x \right)+F_{26}\! \left(x \right)
F_{32}\! \left(x \right) = F_{21}\! \left(x \right)+F_{33}\! \left(x \right)+F_{91}\! \left(x \right)
F_{33}\! \left(x \right) = F_{19}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{2}\! \left(x \right)+F_{32}\! \left(x \right)
F_{36}\! \left(x \right) = F_{127}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{21}\! \left(x \right)+F_{38}\! \left(x \right)+F_{91}\! \left(x \right)
F_{38}\! \left(x \right) = F_{19}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{2}\! \left(x \right)+F_{37}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{21}\! \left(x \right)+F_{43}\! \left(x \right)+F_{45}\! \left(x \right)
F_{43}\! \left(x \right) = F_{19}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{2}\! \left(x \right)+F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{19}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{16}\! \left(x \right)+F_{42}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{52}\! \left(x \right)
F_{49}\! \left(x \right) = F_{21}\! \left(x \right)+F_{29}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{19}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{49}\! \left(x \right)+F_{6}\! \left(x \right)
F_{52}\! \left(x \right) = F_{21}\! \left(x \right)+F_{53}\! \left(x \right)+F_{86}\! \left(x \right)+F_{90}\! \left(x \right)
F_{53}\! \left(x \right) = F_{19}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{79}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{19}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{2}\! \left(x \right)+F_{55}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{68}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{19}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = F_{2}\! \left(x \right)+F_{60}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{19}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{2}\! \left(x \right)+F_{65}\! \left(x \right)
F_{68}\! \left(x \right) = 2 F_{21}\! \left(x \right)+F_{69}\! \left(x \right)+F_{76}\! \left(x \right)
F_{69}\! \left(x \right) = F_{19}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{72}\! \left(x \right)
F_{71}\! \left(x \right) = F_{55}\! \left(x \right)+F_{68}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{19}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{55}\! \left(x \right)+F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{19}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{65}\! \left(x \right)+F_{73}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{21}\! \left(x \right)+F_{53}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{19}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{42}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{19}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{55}\! \left(x \right)+F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{19}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{42}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{84}\! \left(x \right)
F_{90}\! \left(x \right) = 0
F_{91}\! \left(x \right) = F_{19}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{11}\! \left(x \right)+F_{37}\! \left(x \right)
F_{94}\! \left(x \right) = F_{108}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{100}\! \left(x \right)+F_{21}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{19}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)+F_{99}\! \left(x \right)
F_{98}\! \left(x \right) = F_{6}\! \left(x \right)+F_{95}\! \left(x \right)
F_{99}\! \left(x \right) = F_{49}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{19}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{11}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{19}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{107}\! \left(x \right)
F_{106}\! \left(x \right) = F_{103}\! \left(x \right)+F_{6}\! \left(x \right)
F_{107}\! \left(x \right) = F_{26}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{122}\! \left(x \right)+F_{126}\! \left(x \right)+F_{21}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{19}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{121}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{55}\! \left(x \right)
F_{112}\! \left(x \right) = 2 F_{21}\! \left(x \right)+F_{109}\! \left(x \right)+F_{113}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{19}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{37}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{19}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{120}\! \left(x \right)
F_{119}\! \left(x \right) = F_{116}\! \left(x \right)+F_{55}\! \left(x \right)
F_{120}\! \left(x \right) = F_{83}\! \left(x \right)
F_{121}\! \left(x \right) = F_{79}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{19}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{37}\! \left(x \right)
F_{125}\! \left(x \right) = F_{117}\! \left(x \right)
F_{126}\! \left(x \right) = 0
F_{127}\! \left(x \right) = F_{126}\! \left(x \right)+F_{128}\! \left(x \right)+F_{21}\! \left(x \right)+F_{86}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{19}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{132}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{55}\! \left(x \right)
F_{131}\! \left(x \right) = 2 F_{21}\! \left(x \right)+F_{128}\! \left(x \right)+F_{80}\! \left(x \right)
F_{132}\! \left(x \right) = F_{83}\! \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_19(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_32(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_19(x)*F_8(x))
Eq(F_8(x), F_10(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_6(x))
Eq(F_10(x), F_11(x) + F_20(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_19(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_1(x) + F_11(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_19(x))
Eq(F_18(x), F_1(x) + F_16(x))
Eq(F_19(x), x)
Eq(F_20(x), F_21(x) + F_22(x) + F_29(x))
Eq(F_21(x), 0)
Eq(F_22(x), F_19(x)*F_23(x))
Eq(F_23(x), F_24(x) + F_25(x))
Eq(F_24(x), F_20(x) + F_6(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_19(x)*F_28(x))
Eq(F_28(x), F_26(x) + F_6(x))
Eq(F_29(x), F_19(x)*F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_16(x) + F_26(x))
Eq(F_32(x), F_21(x) + F_33(x) + F_91(x))
Eq(F_33(x), F_19(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_2(x) + F_32(x))
Eq(F_36(x), F_127(x) + F_37(x))
Eq(F_37(x), F_21(x) + F_38(x) + F_91(x))
Eq(F_38(x), F_19(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_2(x) + F_37(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_21(x) + F_43(x) + F_45(x))
Eq(F_43(x), F_19(x)*F_44(x))
Eq(F_44(x), F_2(x) + F_42(x))
Eq(F_45(x), F_19(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_16(x) + F_42(x))
Eq(F_48(x), F_49(x) + F_52(x))
Eq(F_49(x), F_21(x) + F_29(x) + F_50(x))
Eq(F_50(x), F_19(x)*F_51(x))
Eq(F_51(x), F_49(x) + F_6(x))
Eq(F_52(x), F_21(x) + F_53(x) + F_86(x) + F_90(x))
Eq(F_53(x), F_19(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_79(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_19(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_2(x) + F_55(x))
Eq(F_59(x), F_60(x) + F_68(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_19(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), F_2(x) + F_60(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_19(x)*F_67(x))
Eq(F_67(x), F_2(x) + F_65(x))
Eq(F_68(x), 2*F_21(x) + F_69(x) + F_76(x))
Eq(F_69(x), F_19(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_72(x))
Eq(F_71(x), F_55(x) + F_68(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_19(x)*F_75(x))
Eq(F_75(x), F_55(x) + F_73(x))
Eq(F_76(x), F_19(x)*F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_65(x) + F_73(x))
Eq(F_79(x), 2*F_21(x) + F_53(x) + F_80(x))
Eq(F_80(x), F_19(x)*F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_42(x) + F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_19(x)*F_85(x))
Eq(F_85(x), F_55(x) + F_83(x))
Eq(F_86(x), F_19(x)*F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_42(x) + F_89(x))
Eq(F_89(x), F_84(x))
Eq(F_90(x), 0)
Eq(F_91(x), F_19(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_94(x))
Eq(F_93(x), F_11(x) + F_37(x))
Eq(F_94(x), F_108(x) + F_95(x))
Eq(F_95(x), F_100(x) + F_21(x) + F_96(x))
Eq(F_96(x), F_19(x)*F_97(x))
Eq(F_97(x), F_98(x) + F_99(x))
Eq(F_98(x), F_6(x) + F_95(x))
Eq(F_99(x), F_49(x))
Eq(F_100(x), F_101(x)*F_19(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_103(x) + F_11(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_19(x))
Eq(F_105(x), F_106(x) + F_107(x))
Eq(F_106(x), F_103(x) + F_6(x))
Eq(F_107(x), F_26(x))
Eq(F_108(x), F_109(x) + F_122(x) + F_126(x) + F_21(x))
Eq(F_109(x), F_110(x)*F_19(x))
Eq(F_110(x), F_111(x) + F_121(x))
Eq(F_111(x), F_112(x) + F_55(x))
Eq(F_112(x), F_109(x) + F_113(x) + 2*F_21(x))
Eq(F_113(x), F_114(x)*F_19(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x) + F_37(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_19(x))
Eq(F_118(x), F_119(x) + F_120(x))
Eq(F_119(x), F_116(x) + F_55(x))
Eq(F_120(x), F_83(x))
Eq(F_121(x), F_79(x))
Eq(F_122(x), F_123(x)*F_19(x))
Eq(F_123(x), F_124(x))
Eq(F_124(x), F_125(x) + F_37(x))
Eq(F_125(x), F_117(x))
Eq(F_126(x), 0)
Eq(F_127(x), F_126(x) + F_128(x) + F_21(x) + F_86(x))
Eq(F_128(x), F_129(x)*F_19(x))
Eq(F_129(x), F_130(x) + F_132(x))
Eq(F_130(x), F_131(x) + F_55(x))
Eq(F_131(x), F_128(x) + 2*F_21(x) + F_80(x))
Eq(F_132(x), F_83(x))
Pack JSON:
{"name": "regular_insertion_encoding_left", "initial_strats": [{"class_module": "tilings.strategies.factor", "strategy_class": "FactorFactory", "interleaving": null, "unions": false, "ignore_parent": true, "workable": true, "tracked": false}, {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "CellInsertionFactory", "ignore_parent": true, "maxreqlen": 1, "extra_basis": [], "one_cell_only": true}], "inferral_strats": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}], "expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "strategy_class": "RowAndColumnPlacementFactory", "partial": false, "ignore_parent": false, "dirs": [0], "place_row": false, "place_col": true}]], "symmetries": [], "iterative": false}
Specification JSON:
{"root": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "rules": [{"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": [], "assumptions": []}, {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 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{"patt": [2, 4, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]], "assumptions": []}], "strategy": {"class_module": "tilings.strategies.requirement_insertion", "strategy_class": "RequirementInsertionStrategy", "ignore_parent": true, "gps": [{"patt": [0], "pos": [[0, 0]]}]}}, {"class_module": "comb_spec_searcher.strategies.rule", "rule_class": "Rule", "comb_class": {"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], 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{"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 2, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 3, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 1, 2, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 3, 2, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 3, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 1, 4], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 3, 4, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 4, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 1, 3], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [2, 4, 0, 3, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]], "assumptions": []}, "children": [{"class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 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