0132_0231_1032_1302_2013
Counting sequence:
1, 1, 2, 6, 19, 58, 173, 511, 1505, 4430, 13039, 38378, 112959, 332479, 978621, 2880519, 8478727, 24956999, 73460645, 216230651, 636472640, 1873450221, 5514479513, 16231806953, 47778135387, 140634385286, 413955674369, 1218473703700, 3586563150527, 10557006854150, 31074426712036, 91467213108449, 269232676511143, 792483247720425, 2332665210110494, 6866172878858276, 20210499902789987, 59489371084308336, 175106270949368664, 515423269180509375, 1517142390002953280, 4465690955713403534, 13144709318880442505, 38691298791468489675, 113887387378013453319, 335226198368141908741, 986734410715373764307, 2904441246028666136643, 8549188981376147918122, 25164438199333430970946, 74071230764410890213976, 218027805091231493120461, 641762305045156268350385, 1889019870674449446040832, 5560307989033152798782692, 16366701808100827646564079, 48175196158849638418732648, 141803128825559603534246297, 417395858200869007432017539, 1228599847451584739216410579, 3616369342198026249932627408, 10644741041045223634859011495, 31332671281314014651490066016, 92227353003458485971429533307, 271470139448251578262919384625, 799069193813787414237030348601, 2352050865704627799558137844205, 6923234330256363809803395782743, 20378459620294416208284173656777, 59983758556471159795903504220715, 176561494715617004530472324793515, 519706703388124822513114683558718, 1529750628706374620270708636299197, 4502803159496479970035512929027239, 13253948658492872660176286824754683, 39012843515373380648938284767584567, 114833850527988998001009809562111114, 338012101627202087248686329379296223, 994934684512653932321551050453350070, 2928578656447224552409030673669843409, 8620237167829031490288811123359865654, 25373567708701281868027498211668427482, 74686801039627441286997060904498505421, 219839729027148483994885553372271350871, 647095682048121535981956703414459778541, 1904718603767990351568452216070290323868, 5606517027060131762481092315744285260990, 16502717573363906688545385183033494346877, 48575556979806346190985407084177086109544, 142981586239280002587024211163845663572036, 420864633873358555828908934094923915553299, 1238810148244779229393917096356389838337930, 3646423243669460229539886665298900705227066, 10733204350006375829464785229016827487034339, 31593062000961332211994453344511278517921351, 92993810054123673111563766450703607540494993, 273726196850412642507018630788159838412358997, 805709872502082389017585812045661595763098735, 2371597626083567299012238146948727949197376723, 6980769991782215890794010192776212920942540834, 20547815169911944034445557469131076824333907680
Generating function in Maple syntax:
(2*x-1)*(x-1)^4/(x^8-x^7+8*x^5-21*x^4+27*x^3-19*x^2+7*x-1)
Generating function in latex syntax:
\frac{\left(2 x -1\right) \left(x -1\right)^{4}}{x^{8}-x^{7}+8 x^{5}-21 x^{4}+27 x^{3}-19 x^{2}+7 x -1}
Generating function in sympy syntax:
(x - 1)**4*(2*x - 1)/(x**8 - x**7 + 8*x**5 - 21*x**4 + 27*x**3 - 19*x**2 + 7*x - 1)
Implicit equation for the generating function in Maple syntax:
(x^8-x^7+8*x^5-21*x^4+27*x^3-19*x^2+7*x-1)*F(x)-(2*x-1)*(x-1)^4 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{8}-x^{7}+8 x^{5}-21 x^{4}+27 x^{3}-19 x^{2}+7 x -1\right) F \! \left(x \right)-\left(2 x -1\right) \left(x -1\right)^{4} = 0
Explicit closed form in Maple syntax:
30105136/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+6)+30105136/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+6)+30105136/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+6)+30105136/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+6)+30105136/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+6)+30105136/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n+6)+30105136/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n+6)+30105136/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 8)^(-n+6)-29856681/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+5)-29856681/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+5)-29856681/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+5)-29856681/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+5)-29856681/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+5)-29856681/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n+5)-29856681/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n+5)-29856681/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 8)^(-n+5)-15686711/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+4)-15686711/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+4)-15686711/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+4)-15686711/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+4)-15686711/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+4)-15686711/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n+4)-15686711/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n+4)-15686711/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 8)^(-n+4)+233756932/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+3)+233756932/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+3)+233756932/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+3)+233756932/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+3)+233756932/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+3)+233756932/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n+3)+233756932/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n+3)+233756932/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 8)^(-n+3)-627883346/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+2)-627883346/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+2)-627883346/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+2)-627883346/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+2)-627883346/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+2)-627883346/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n+2)-627883346/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n+2)-627883346/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 8)^(-n+2)+697618567/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n+1)+697618567/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n+1)+697618567/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n+1)+697618567/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n+1)+697618567/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n+1)+697618567/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n+1)+697618567/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n+1)+697618567/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 8)^(-n+1)+91919840/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n-1)+91919840/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n-1)+91919840/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n-1)+91919840/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n-1)+91919840/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n-1)+91919840/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n-1)+91919840/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n-1)+91919840/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 8)^(-n-1)-379849061/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 1)^(-n)-379849061/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 2)^(-n)-379849061/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 3)^(-n)-379849061/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 4)^(-n)-379849061/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 5)^(-n)-379849061/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 6)^(-n)-379849061/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 7)^(-n)-379849061/240132811*RootOf(_Z^8-_Z^7+8*_Z^5-21*_Z^4+27*_Z^3-19*_Z^2+7*_Z-1,index = 8)^(-n)
Explicit closed form in latex syntax:
\frac{30105136 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +6}}{240132811}+\frac{30105136 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +6}}{240132811}+\frac{30105136 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +6}}{240132811}+\frac{30105136 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +6}}{240132811}+\frac{30105136 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +6}}{240132811}+\frac{30105136 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +6}}{240132811}+\frac{30105136 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +6}}{240132811}+\frac{30105136 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +6}}{240132811}-\frac{29856681 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +5}}{240132811}-\frac{29856681 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +5}}{240132811}-\frac{29856681 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +5}}{240132811}-\frac{29856681 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +5}}{240132811}-\frac{29856681 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +5}}{240132811}-\frac{29856681 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +5}}{240132811}-\frac{29856681 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +5}}{240132811}-\frac{29856681 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +5}}{240132811}-\frac{15686711 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}}{240132811}-\frac{15686711 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +4}}{240132811}-\frac{15686711 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +4}}{240132811}-\frac{15686711 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +4}}{240132811}-\frac{15686711 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +4}}{240132811}-\frac{15686711 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +4}}{240132811}-\frac{15686711 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +4}}{240132811}-\frac{15686711 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +4}}{240132811}+\frac{233756932 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{240132811}+\frac{233756932 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{240132811}+\frac{233756932 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{240132811}+\frac{233756932 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{240132811}+\frac{233756932 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{240132811}+\frac{233756932 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +3}}{240132811}+\frac{233756932 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +3}}{240132811}+\frac{233756932 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +3}}{240132811}-\frac{627883346 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{240132811}-\frac{627883346 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{240132811}-\frac{627883346 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{240132811}-\frac{627883346 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{240132811}-\frac{627883346 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{240132811}-\frac{627883346 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +2}}{240132811}-\frac{627883346 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +2}}{240132811}-\frac{627883346 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +2}}{240132811}+\frac{697618567 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{240132811}+\frac{697618567 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{240132811}+\frac{697618567 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{240132811}+\frac{697618567 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{240132811}+\frac{697618567 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{240132811}+\frac{697618567 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +1}}{240132811}+\frac{697618567 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +1}}{240132811}+\frac{697618567 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =8\right)^{-n +1}}{240132811}+\frac{91919840 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{240132811}+\frac{91919840 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{240132811}+\frac{91919840 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{240132811}+\frac{91919840 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{240132811}+\frac{91919840 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{240132811}+\frac{91919840 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n -1}}{240132811}+\frac{91919840 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n -1}}{240132811}+\frac{91919840 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =8\right)^{-n -1}}{240132811}-\frac{379849061 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{240132811}-\frac{379849061 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{240132811}-\frac{379849061 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{240132811}-\frac{379849061 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{240132811}-\frac{379849061 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{240132811}-\frac{379849061 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =6\right)^{-n}}{240132811}-\frac{379849061 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =7\right)^{-n}}{240132811}-\frac{379849061 \mathit{RootOf}\! \left(\textit{\_Z}^{8}-\textit{\_Z}^{7}+8 \textit{\_Z}^{5}-21 \textit{\_Z}^{4}+27 \textit{\_Z}^{3}-19 \textit{\_Z}^{2}+7 \textit{\_Z} -1, \mathit{index} =8\right)^{-n}}{240132811}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 58
a(6) = 173
a(7) = 511
a(n+1) = a(n)+8*a(n+3)-21*a(n+4)+27*a(n+5)-19*a(n+6)+7*a(n+7)-a(n+8), n >= 8
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 58
a \! \left(6\right) = 173
a \! \left(7\right) = 511
a \! \left(n +1\right) = a \! \left(n \right)+8 a \! \left(n +3\right)-21 a \! \left(n +4\right)+27 a \! \left(n +5\right)-19 a \! \left(n +6\right)+7 a \! \left(n +7\right)-a \! \left(n +8\right), \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18874/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[19,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[7,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[11,x]
F[18,x] = F[14,x]
F[19,x] = F[2,x]+F[20,x]
F[20,x] = F[21,x]+F[22,x]+F[47,x]
F[21,x] = 0
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[24,x]+F[28,x]
F[24,x] = F[11,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[7,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[21,x]+F[22,x]+F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[2,x]+F[29,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]+F[41,x]
F[38,x] = F[2,x]+F[39,x]
F[39,x] = F[40,x]
F[40,x] = F[38,x]*F[4,x]
F[41,x] = F[35,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[39,x]
F[46,x] = F[42,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[31,x]+F[49,x]
F[49,x] = F[35,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = F[29,x]
F[54,x] = F[50,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{19}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)+F_{47}\! \left(x \right)
F_{21}\! \left(x \right) = 0
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{28}\! \left(x \right)
F_{24}\! \left(x \right) = F_{11}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{7}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{2}\! \left(x \right)+F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{41}\! \left(x \right)
F_{38}\! \left(x \right) = F_{2}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{41}\! \left(x \right) = F_{35}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{39}\! \left(x \right)
F_{46}\! \left(x \right) = F_{42}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{31}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{35}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{29}\! \left(x \right)
F_{54}\! \left(x \right) = F_{50}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_19(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_7(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_11(x))
Eq(F_18(x), F_14(x))
Eq(F_19(x), F_2(x) + F_20(x))
Eq(F_20(x), F_21(x) + F_22(x) + F_47(x))
Eq(F_21(x), 0)
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_24(x) + F_28(x))
Eq(F_24(x), F_11(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_7(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_21(x) + F_22(x) + F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_2(x) + F_29(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_41(x))
Eq(F_38(x), F_2(x) + F_39(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_38(x)*F_4(x))
Eq(F_41(x), F_35(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_39(x))
Eq(F_46(x), F_42(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_31(x) + F_49(x))
Eq(F_49(x), F_35(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), F_29(x))
Eq(F_54(x), F_50(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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