02341_02413_02431_03241_03412_03421_04123_04132_04213_04231_04312_04321_40123_40132_40213_40231_40312_40321_41023_41032
Counting sequence:
1, 1, 2, 6, 24, 100, 409, 1655, 6670, 26857, 108141, 435477, 1753741, 7062752, 28443570, 114549745, 461321696, 1857862208, 7482092614, 30132325640, 121350683319, 488710648211, 1968164426688, 7926308187529, 31921297141243, 128555335856945, 517725652056759, 2085015367184780, 8396897206304156, 33816481069119713, 136187732659128594, 548463291876136432, 2208803808258847112, 8895425337746490664, 35824183045844009965, 144273268806644506943, 581025841273693111742, 2339941633125699238345, 9423551342281527082365, 37951083327660741193413, 152838847418466244328269, 615521646075895306201584, 2478865178501760894329850, 9983032460942732787529353, 40204258779604911128469008, 161912968864051746596782552, 652065484656325111753304910, 2626036686641780132287337312, 10575730263078027901082954959, 42591206423858110238807304915, 171525825594546799515603519312, 690778949839988697610727521233, 2781945843362307824630082283435, 11203616840370609823101048338065, 45119868384687546611026526646295, 181709402602542368549700321466940, 731790853480821425337286440648788, 2947111407380172674967014043132505, 11868781368607210137572140520264946, 47798658314387195600070403319198888, 192497583846187644982786954599936096, 775237655059170286029858489928328896, 3122082936385612099853478550561726133, 12573437059021897153232701626798644543, 50636489388140703586586741479577394942, 203926264991757706878057622898320071921, 821263915725330617163781507576947857757, 3307442615593257992982977029977047581445, 13319928522344756599983715195473246294685, 53642803960953786285663429076583594876224, 216033472849805751945738271466057874955714, 870022779299882503082264243623580319541249, 3503807194855140552494495426701991919081024, 14110739570057952440740668074844987025327472, 56827604985334047171712242603153347636446998, 228859491902301481248551144032109105101528888, 921676481831266003094912185137812208718471655, 3711830040781093351143825540011584122488610451, 14948501478816396155492066939417534386983677984, 60201489294254701312235007991446883837683713497, 242446998341751150189947813774417439874791587291, 976396891406053251060133129546397823808454231089, 3932203310694608562591436702047644887580811988151, 15836001745531346930382958093798271308288034295084, 63775682860145075117949450091640461159275673557580, 256841202068289524851375847418341010381938042802385, 1034366080008035691572301435416866373766891665176146, 4165660255657576053675409956551346301469317431158688, 16776193362247854814309935367656058383613225527708472, 67562078147225614033910530761026067997183733669409368, 272089997117212652921150783566975973232189319102100989, 1095776929328881188533857761083218296277718445514814783, 4412977660226792754259940861897800076841060188602404094, 17772204641676476226146124193412550252998315259870891993, 71573273681470344643330247738575719476921452362932034365, 288244121017471082040836824959448930612805722917828755845, 1160833772546083274985460402307528678270850955934122688173, 4674978427060078247059437890348417542928419838680143434192, 18827349626071890854474282636519419691663363147834343689034, 75822615969858480488186762035250956875869597472598973602681, 305357323611359267950138046065984406932088133727302249454704
Generating function in Maple syntax:
(2*x^7-2*x^6+5*x^5+2*x^4-5*x^3+4*x-1)/(2*x^8+2*x^7-8*x^6+7*x^5+8*x^4-6*x^3-3*x^2+5*x-1)
Generating function in latex syntax:
\frac{2 x^{7}-2 x^{6}+5 x^{5}+2 x^{4}-5 x^{3}+4 x -1}{2 x^{8}+2 x^{7}-8 x^{6}+7 x^{5}+8 x^{4}-6 x^{3}-3 x^{2}+5 x -1}
Generating function in sympy syntax:
(2*x**7 - 2*x**6 + 5*x**5 + 2*x**4 - 5*x**3 + 4*x - 1)/(2*x**8 + 2*x**7 - 8*x**6 + 7*x**5 + 8*x**4 - 6*x**3 - 3*x**2 + 5*x - 1)
Implicit equation for the generating function in Maple syntax:
(2*x^8+2*x^7-8*x^6+7*x^5+8*x^4-6*x^3-3*x^2+5*x-1)*F(x)-2*x^7+2*x^6-5*x^5-2*x^4+5*x^3-4*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{8}+2 x^{7}-8 x^{6}+7 x^{5}+8 x^{4}-6 x^{3}-3 x^{2}+5 x -1\right) F \! \left(x \right)-2 x^{7}+2 x^{6}-5 x^{5}-2 x^{4}+5 x^{3}-4 x +1 = 0
Explicit closed form in Maple syntax:
-2698738997/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 1)^(-n+6)-2698738997/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 2)^(-n+6)-2698738997/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 3)^(-n+6)-2698738997/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 4)^(-n+6)-2698738997/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 5)^(-n+6)-2698738997/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 6)^(-n+6)-2698738997/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 7)^(-n+6)-2698738997/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 8)^(-n+6)-4064979733/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 1)^(-n+5)-4064979733/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 2)^(-n+5)-4064979733/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 3)^(-n+5)-4064979733/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 4)^(-n+5)-4064979733/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 5)^(-n+5)-4064979733/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 6)^(-n+5)-4064979733/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 7)^(-n+5)-4064979733/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 8)^(-n+5)+9994117493/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 1)^(-n+4)+9994117493/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 2)^(-n+4)+9994117493/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 3)^(-n+4)+9994117493/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 4)^(-n+4)+9994117493/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 5)^(-n+4)+9994117493/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 6)^(-n+4)+9994117493/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 7)^(-n+4)+9994117493/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 8)^(-n+4)-4618685113/113338401126*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 1)^(-n+3)-4618685113/113338401126*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 2)^(-n+3)-4618685113/113338401126*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 3)^(-n+3)-4618685113/113338401126*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 4)^(-n+3)-4618685113/113338401126*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 5)^(-n+3)-4618685113/113338401126*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 6)^(-n+3)-4618685113/113338401126*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 7)^(-n+3)-4618685113/113338401126*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 8)^(-n+3)-3697551091/18889733521*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 1)^(-n+2)-3697551091/18889733521*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 2)^(-n+2)-3697551091/18889733521*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 3)^(-n+2)-3697551091/18889733521*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 4)^(-n+2)-3697551091/18889733521*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 5)^(-n+2)-3697551091/18889733521*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 6)^(-n+2)-3697551091/18889733521*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 7)^(-n+2)-3697551091/18889733521*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 8)^(-n+2)+13474226195/113338401126*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 1)^(-n+1)+13474226195/113338401126*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 2)^(-n+1)+13474226195/113338401126*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 3)^(-n+1)+13474226195/113338401126*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 4)^(-n+1)+13474226195/113338401126*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 5)^(-n+1)+13474226195/113338401126*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 6)^(-n+1)+13474226195/113338401126*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 7)^(-n+1)+13474226195/113338401126*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 8)^(-n+1)-1547411618/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 1)^(-n-1)-1547411618/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 2)^(-n-1)-1547411618/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 3)^(-n-1)-1547411618/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 4)^(-n-1)-1547411618/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 5)^(-n-1)-1547411618/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 6)^(-n-1)-1547411618/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 7)^(-n-1)-1547411618/56669200563*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 8)^(-n-1)+7136522501/37779467042*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 1)^(-n)+7136522501/37779467042*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 2)^(-n)+7136522501/37779467042*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 3)^(-n)+7136522501/37779467042*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 4)^(-n)+7136522501/37779467042*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 5)^(-n)+7136522501/37779467042*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 6)^(-n)+7136522501/37779467042*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 7)^(-n)+7136522501/37779467042*RootOf(2*_Z^8+2*_Z^7-8*_Z^6+7*_Z^5+8*_Z^4-6*_Z^3-3*_Z^2+5*_Z-1,index = 8)^(-n)
Explicit closed form in latex syntax:
-\frac{2698738997 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +6}}{56669200563}-\frac{2698738997 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +6}}{56669200563}-\frac{2698738997 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +6}}{56669200563}-\frac{2698738997 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +6}}{56669200563}-\frac{2698738997 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +6}}{56669200563}-\frac{2698738997 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +6}}{56669200563}-\frac{2698738997 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +6}}{56669200563}-\frac{2698738997 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +6}}{56669200563}-\frac{4064979733 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +5}}{56669200563}-\frac{4064979733 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +5}}{56669200563}-\frac{4064979733 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +5}}{56669200563}-\frac{4064979733 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +5}}{56669200563}-\frac{4064979733 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +5}}{56669200563}-\frac{4064979733 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +5}}{56669200563}-\frac{4064979733 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +5}}{56669200563}-\frac{4064979733 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +5}}{56669200563}+\frac{9994117493 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}}{56669200563}+\frac{9994117493 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +4}}{56669200563}+\frac{9994117493 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +4}}{56669200563}+\frac{9994117493 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +4}}{56669200563}+\frac{9994117493 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +4}}{56669200563}+\frac{9994117493 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +4}}{56669200563}+\frac{9994117493 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +4}}{56669200563}+\frac{9994117493 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +4}}{56669200563}-\frac{4618685113 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{113338401126}-\frac{4618685113 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{113338401126}-\frac{4618685113 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{113338401126}-\frac{4618685113 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{113338401126}-\frac{4618685113 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{113338401126}-\frac{4618685113 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +3}}{113338401126}-\frac{4618685113 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +3}}{113338401126}-\frac{4618685113 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +3}}{113338401126}-\frac{3697551091 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{18889733521}-\frac{3697551091 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{18889733521}-\frac{3697551091 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{18889733521}-\frac{3697551091 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{18889733521}-\frac{3697551091 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{18889733521}-\frac{3697551091 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +2}}{18889733521}-\frac{3697551091 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +2}}{18889733521}-\frac{3697551091 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +2}}{18889733521}+\frac{13474226195 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{113338401126}+\frac{13474226195 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{113338401126}+\frac{13474226195 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{113338401126}+\frac{13474226195 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{113338401126}+\frac{13474226195 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{113338401126}+\frac{13474226195 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +1}}{113338401126}+\frac{13474226195 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +1}}{113338401126}+\frac{13474226195 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +1}}{113338401126}-\frac{1547411618 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{56669200563}-\frac{1547411618 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{56669200563}-\frac{1547411618 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{56669200563}-\frac{1547411618 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{56669200563}-\frac{1547411618 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{56669200563}-\frac{1547411618 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =6\right)^{-n -1}}{56669200563}-\frac{1547411618 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =7\right)^{-n -1}}{56669200563}-\frac{1547411618 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =8\right)^{-n -1}}{56669200563}+\frac{7136522501 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{37779467042}+\frac{7136522501 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{37779467042}+\frac{7136522501 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{37779467042}+\frac{7136522501 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{37779467042}+\frac{7136522501 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{37779467042}+\frac{7136522501 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =6\right)^{-n}}{37779467042}+\frac{7136522501 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =7\right)^{-n}}{37779467042}+\frac{7136522501 \mathit{RootOf}\! \left(2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-8 \textit{\_Z}^{6}+7 \textit{\_Z}^{5}+8 \textit{\_Z}^{4}-6 \textit{\_Z}^{3}-3 \textit{\_Z}^{2}+5 \textit{\_Z} -1, \mathit{index} =8\right)^{-n}}{37779467042}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 100
a(6) = 409
a(7) = 1655
a(n+8) = 2*a(n)+2*a(n+1)-8*a(n+2)+7*a(n+3)+8*a(n+4)-6*a(n+5)-3*a(n+6)+5*a(n+7), n >= 8
Recurrence in latex format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 24
a(5) = 100
a(6) = 409
a(7) = 1655
a{\left(n + 8 \right)} = 2 a{\left(n \right)} + 2 a{\left(n + 1 \right)} - 8 a{\left(n + 2 \right)} + 7 a{\left(n + 3 \right)} + 8 a{\left(n + 4 \right)} - 6 a{\left(n + 5 \right)} - 3 a{\left(n + 6 \right)} + 5 a{\left(n + 7 \right)}, \quad n \geq 8
Specification 1
Strategy pack name: regular_insertion_encoding_left
Tree: http://permpal.com/tree/25668/
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[20,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[2,x]+F[6,x]
F[6,x] = F[7,x]+F[75,x]+F[8,x]
F[7,x] = 0
F[8,x] = F[20,x]*F[9,x]
F[9,x] = F[10,x]+F[11,x]
F[10,x] = F[2,x]+F[6,x]
F[11,x] = F[12,x]+F[27,x]
F[12,x] = F[13,x]+F[21,x]+F[7,x]
F[13,x] = F[14,x]*F[20,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]+F[2,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[20,x]
F[18,x] = F[19,x]
F[19,x] = F[2,x]
F[20,x] = x
F[21,x] = F[20,x]*F[22,x]
F[22,x] = F[19,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[20,x]*F[26,x]
F[26,x] = F[2,x]
F[27,x] = F[28,x]+F[43,x]+F[44,x]+F[7,x]
F[28,x] = F[20,x]*F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]+F[6,x]
F[31,x] = F[32,x]
F[32,x] = F[20,x]*F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[20,x]*F[37,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[2,x]+F[35,x]
F[39,x] = F[24,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[20,x]*F[42,x]
F[42,x] = F[35,x]
F[43,x] = 0
F[44,x] = F[20,x]*F[45,x]
F[45,x] = F[34,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[20,x]*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[50,x]+F[68,x]+F[7,x]
F[50,x] = F[20,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[2,x]+F[49,x]
F[53,x] = F[12,x]+F[54,x]
F[54,x] = F[55,x]+F[62,x]+F[63,x]+F[7,x]
F[55,x] = F[20,x]*F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[49,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[20,x]*F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[35,x]
F[62,x] = 0
F[63,x] = F[20,x]*F[64,x]
F[64,x] = F[61,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[20,x]*F[67,x]
F[67,x] = F[35,x]
F[68,x] = F[20,x]*F[69,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[2,x]+F[24,x]
F[71,x] = F[35,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[20,x]*F[74,x]
F[74,x] = F[6,x]
F[75,x] = F[20,x]*F[76,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[12,x]+F[2,x]
F[78,x] = F[49,x]+F[79,x]
F[79,x] = F[44,x]+F[7,x]+F[80,x]+F[84,x]
F[80,x] = F[20,x]*F[81,x]
F[81,x] = F[82,x]
F[82,x] = F[6,x]+F[83,x]
F[83,x] = F[32,x]
F[84,x] = 0
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_{20}\! \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_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)+F_{75}\! \left(x \right)+F_{8}\! \left(x \right)
F_{7}\! \left(x \right) = 0
F_{8}\! \left(x \right) = F_{20}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{2}\! \left(x \right)+F_{6}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{27}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{21}\! \left(x \right)+F_{7}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{20}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{2}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{20}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)
F_{20}\! \left(x \right) = x
F_{21}\! \left(x \right) = F_{20}\! \left(x \right) F_{22}\! \left(x \right)
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_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{20}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{2}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{43}\! \left(x \right)+F_{44}\! \left(x \right)+F_{7}\! \left(x \right)
F_{28}\! \left(x \right) = F_{20}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{6}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{20}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{20}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right)+F_{35}\! \left(x \right)
F_{39}\! \left(x \right) = F_{24}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{20}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{35}\! \left(x \right)
F_{43}\! \left(x \right) = 0
F_{44}\! \left(x \right) = F_{20}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{34}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{20}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{68}\! \left(x \right)+F_{7}\! \left(x \right)
F_{50}\! \left(x \right) = F_{20}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{2}\! \left(x \right)+F_{49}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{62}\! \left(x \right)+F_{63}\! \left(x \right)+F_{7}\! \left(x \right)
F_{55}\! \left(x \right) = F_{20}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{49}\! \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_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{35}\! \left(x \right)
F_{62}\! \left(x \right) = 0
F_{63}\! \left(x \right) = F_{20}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{61}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{20}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{35}\! \left(x \right)
F_{68}\! \left(x \right) = F_{20}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{2}\! \left(x \right)+F_{24}\! \left(x \right)
F_{71}\! \left(x \right) = F_{35}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{20}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{6}\! \left(x \right)
F_{75}\! \left(x \right) = F_{20}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right)+F_{2}\! \left(x \right)
F_{78}\! \left(x \right) = F_{49}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{44}\! \left(x \right)+F_{7}\! \left(x \right)+F_{80}\! \left(x \right)+F_{84}\! \left(x \right)
F_{80}\! \left(x \right) = F_{20}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{6}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{32}\! \left(x \right)
F_{84}\! \left(x \right) = 0
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_20(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_2(x) + F_6(x))
Eq(F_6(x), F_7(x) + F_75(x) + F_8(x))
Eq(F_7(x), 0)
Eq(F_8(x), F_20(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_11(x))
Eq(F_10(x), F_2(x) + F_6(x))
Eq(F_11(x), F_12(x) + F_27(x))
Eq(F_12(x), F_13(x) + F_21(x) + F_7(x))
Eq(F_13(x), F_14(x)*F_20(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x) + F_2(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_20(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_2(x))
Eq(F_20(x), x)
Eq(F_21(x), F_20(x)*F_22(x))
Eq(F_22(x), F_19(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_20(x)*F_26(x))
Eq(F_26(x), F_2(x))
Eq(F_27(x), F_28(x) + F_43(x) + F_44(x) + F_7(x))
Eq(F_28(x), F_20(x)*F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x) + F_6(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_20(x)*F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_20(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_2(x) + F_35(x))
Eq(F_39(x), F_24(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_20(x)*F_42(x))
Eq(F_42(x), F_35(x))
Eq(F_43(x), 0)
Eq(F_44(x), F_20(x)*F_45(x))
Eq(F_45(x), F_34(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_20(x)*F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_50(x) + F_68(x) + F_7(x))
Eq(F_50(x), F_20(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_2(x) + F_49(x))
Eq(F_53(x), F_12(x) + F_54(x))
Eq(F_54(x), F_55(x) + F_62(x) + F_63(x) + F_7(x))
Eq(F_55(x), F_20(x)*F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_49(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_20(x)*F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_35(x))
Eq(F_62(x), 0)
Eq(F_63(x), F_20(x)*F_64(x))
Eq(F_64(x), F_61(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_20(x)*F_67(x))
Eq(F_67(x), F_35(x))
Eq(F_68(x), F_20(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_2(x) + F_24(x))
Eq(F_71(x), F_35(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_20(x)*F_74(x))
Eq(F_74(x), F_6(x))
Eq(F_75(x), F_20(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_12(x) + F_2(x))
Eq(F_78(x), F_49(x) + F_79(x))
Eq(F_79(x), F_44(x) + F_7(x) + F_80(x) + F_84(x))
Eq(F_80(x), F_20(x)*F_81(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_6(x) + F_83(x))
Eq(F_83(x), F_32(x))
Eq(F_84(x), 0)
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, 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, 2, 4, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 4, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 4, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [4, 1, 0, 3, 2], "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, 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, 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