0123_0213_0321_2103
Counting sequence:
1, 1, 2, 6, 20, 62, 172, 471, 1337, 3846, 11030, 31442, 89470, 254934, 727203, 2074435, 5915652, 16866988, 48093810, 137141828, 391072846, 1115164897, 3179915535, 9067592160, 25856510664, 73730732368, 210245631360, 599521974384, 1709555338705, 4874850377793, 13900789573274, 39638539791222, 113030541781260, 322310136422902, 919077471943572, 2620778282482175, 7473231610979089, 21310154692010038, 60766575435582302, 173277798479801170, 494107085073158750, 1408961873371613110, 4017699038254993875, 11456595005008739667, 32668840512235510748, 93156224861562742668, 265637901269232115754, 757474819267709231596, 2159963239735830997270, 6159203023425430911385, 17563160884367239386567, 50081904927834825557792, 142810124994842950698608, 407227557147157568642944, 1161222170388884316644256, 3311261493326219301640704, 9442166156295131402214593, 26924633376970009178980257, 76776437788157744428018578, 218930423932188810085169286, 624286980536635654359972452, 1780173934109159324229233806, 5076221889102355201194564252, 14475006162977441999630434439, 41275934739583645434607951753, 117699624403885153588290676870, 335624175980935701371539640646, 957042879902035174441076026610, 2729037833148254864470674023710, 7781937101414806075817882132598, 22190438078505902681100289266915, 63276731191579592119774122637251, 180435586540750709491789318595668, 514517742576392566495738839334348, 1467163504168946262542823726561026, 4183662816342433235174027782119348, 11929845931357625535346762024441918, 34018330394597719163541219783201905, 97004337649842175753051721711779551, 276610915754375708530555508675885504, 788764714735401543588864897075861496, 2249187359489726083315802496700244624, 6413628403478219089433437432161870176, 18288662847204866517346605378171259568, 52150696563171646555763965680050357713, 148709349324555210406382760529190972449, 424049380620346875304837021924438649834, 1209190128403096294608906544078566210870, 3448043632297053260877549302315227595036, 9832204721953313318732277109399302944262, 28036840598214505524434848959002511495876, 79947931614418800707026049961224269077359, 227974038195688551702835089497033327194529, 650075130672623416922363167993379373129718, 1853709654238254328462965142325620110078414, 5285911304837458849112724832850304004525490, 15072942118376243353505157709008961632815294, 42980967897815812952206186464436417093564950, 122561580010371833324195141642221724936635091, 349488195108843143307649470652278309875722899, 996576565919764467468204564251901730381465196
Generating function in Maple syntax:
-(x^3+x^2+x-1)/(x+1)/(7*x^8+7*x^7+8*x^6-8*x^5-4*x^3+2*x^2-3*x+1)
Generating function in latex syntax:
-\frac{x^{3}+x^{2}+x -1}{\left(x +1\right) \left(7 x^{8}+7 x^{7}+8 x^{6}-8 x^{5}-4 x^{3}+2 x^{2}-3 x +1\right)}
Generating function in sympy syntax:
(-x**3 - x**2 - x + 1)/((x + 1)*(7*x**8 + 7*x**7 + 8*x**6 - 8*x**5 - 4*x**3 + 2*x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
(x+1)*(7*x^8+7*x^7+8*x^6-8*x^5-4*x^3+2*x^2-3*x+1)*F(x)+x^3+x^2+x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x +1\right) \left(7 x^{8}+7 x^{7}+8 x^{6}-8 x^{5}-4 x^{3}+2 x^{2}-3 x +1\right) F \! \left(x \right)+x^{3}+x^{2}+x -1 = 0
Explicit closed form in Maple syntax:
-827572547366719/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n+7)-827572547366719/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n+7)-827572547366719/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n+7)-827572547366719/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n+7)-827572547366719/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n+7)-827572547366719/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n+7)-827572547366719/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 7)^(-n+7)-827572547366719/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 8)^(-n+7)-2583105803268235/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n+6)-2583105803268235/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n+6)-2583105803268235/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n+6)-2583105803268235/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n+6)-2583105803268235/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n+6)-2583105803268235/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n+6)-2583105803268235/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 7)^(-n+6)-2583105803268235/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 8)^(-n+6)-1788050310971779/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n+5)-1788050310971779/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n+5)-1788050310971779/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n+5)-1788050310971779/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n+5)-1788050310971779/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n+5)-1788050310971779/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n+5)-1788050310971779/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 7)^(-n+5)-1788050310971779/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 8)^(-n+5)-1194584782389937/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n+4)-1194584782389937/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n+4)-1194584782389937/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n+4)-1194584782389937/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n+4)-1194584782389937/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n+4)-1194584782389937/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n+4)-1194584782389937/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 7)^(-n+4)-1194584782389937/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 8)^(-n+4)-18280248420497/478931552634782*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n+3)-18280248420497/478931552634782*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n+3)-18280248420497/478931552634782*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n+3)-18280248420497/478931552634782*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n+3)-18280248420497/478931552634782*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n+3)-18280248420497/478931552634782*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n+3)-18280248420497/478931552634782*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 7)^(-n+3)-18280248420497/478931552634782*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 8)^(-n+3)+202633550511943/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n+2)+202633550511943/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n+2)+202633550511943/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n+2)+202633550511943/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n+2)+202633550511943/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n+2)+202633550511943/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n+2)+202633550511943/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 7)^(-n+2)+202633550511943/6226110184252166*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 8)^(-n+2)+244876768743349/3113055092126083*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n+1)+244876768743349/3113055092126083*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n+1)+244876768743349/3113055092126083*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n+1)+244876768743349/3113055092126083*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n+1)+244876768743349/3113055092126083*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n+1)+244876768743349/3113055092126083*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n+1)+244876768743349/3113055092126083*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 7)^(-n+1)+244876768743349/3113055092126083*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 8)^(-n+1)+497581031739549/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n-1)+497581031739549/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n-1)+497581031739549/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n-1)+497581031739549/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n-1)+497581031739549/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n-1)+497581031739549/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n-1)+497581031739549/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 7)^(-n-1)+497581031739549/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 8)^(-n-1)+2122999850763533/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 3)^(-n)+2122999850763533/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 4)^(-n)+2122999850763533/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 5)^(-n)+1/13*(-1)^(-n)+2122999850763533/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 6)^(-n)+2122999850763533/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 7)^(-n)+2122999850763533/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 8)^(-n)+2122999850763533/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 1)^(-n)+2122999850763533/12452220368504332*RootOf(7*_Z^8+7*_Z^7+8*_Z^6-8*_Z^5-4*_Z^3+2*_Z^2-3*_Z+1,index = 2)^(-n)
Explicit closed form in latex syntax:
-\frac{827572547366719 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +7}}{12452220368504332}-\frac{827572547366719 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +7}}{12452220368504332}-\frac{827572547366719 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +7}}{12452220368504332}-\frac{827572547366719 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +7}}{12452220368504332}-\frac{827572547366719 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +7}}{12452220368504332}-\frac{827572547366719 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +7}}{12452220368504332}-\frac{827572547366719 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +7}}{12452220368504332}-\frac{827572547366719 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +7}}{12452220368504332}-\frac{2583105803268235 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +6}}{12452220368504332}-\frac{2583105803268235 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +6}}{12452220368504332}-\frac{2583105803268235 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +6}}{12452220368504332}-\frac{2583105803268235 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +6}}{12452220368504332}-\frac{2583105803268235 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +6}}{12452220368504332}-\frac{2583105803268235 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +6}}{12452220368504332}-\frac{2583105803268235 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +6}}{12452220368504332}-\frac{2583105803268235 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +6}}{12452220368504332}-\frac{1788050310971779 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +5}}{6226110184252166}-\frac{1788050310971779 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +5}}{6226110184252166}-\frac{1788050310971779 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +5}}{6226110184252166}-\frac{1788050310971779 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +5}}{6226110184252166}-\frac{1788050310971779 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +5}}{6226110184252166}-\frac{1788050310971779 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +5}}{6226110184252166}-\frac{1788050310971779 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +5}}{6226110184252166}-\frac{1788050310971779 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +5}}{6226110184252166}-\frac{1194584782389937 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{6226110184252166}-\frac{1194584782389937 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +4}}{6226110184252166}-\frac{1194584782389937 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +4}}{6226110184252166}-\frac{1194584782389937 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +4}}{6226110184252166}-\frac{1194584782389937 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +4}}{6226110184252166}-\frac{1194584782389937 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +4}}{6226110184252166}-\frac{1194584782389937 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +4}}{6226110184252166}-\frac{1194584782389937 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +4}}{6226110184252166}-\frac{18280248420497 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{478931552634782}-\frac{18280248420497 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{478931552634782}-\frac{18280248420497 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{478931552634782}-\frac{18280248420497 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{478931552634782}-\frac{18280248420497 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{478931552634782}-\frac{18280248420497 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +3}}{478931552634782}-\frac{18280248420497 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +3}}{478931552634782}-\frac{18280248420497 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +3}}{478931552634782}+\frac{202633550511943 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{6226110184252166}+\frac{202633550511943 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{6226110184252166}+\frac{202633550511943 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{6226110184252166}+\frac{202633550511943 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{6226110184252166}+\frac{202633550511943 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{6226110184252166}+\frac{202633550511943 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{6226110184252166}+\frac{202633550511943 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +2}}{6226110184252166}+\frac{202633550511943 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +2}}{6226110184252166}+\frac{244876768743349 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{3113055092126083}+\frac{244876768743349 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{3113055092126083}+\frac{244876768743349 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{3113055092126083}+\frac{244876768743349 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{3113055092126083}+\frac{244876768743349 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{3113055092126083}+\frac{244876768743349 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{3113055092126083}+\frac{244876768743349 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +1}}{3113055092126083}+\frac{244876768743349 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =8\right)^{-n +1}}{3113055092126083}+\frac{497581031739549 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{12452220368504332}+\frac{497581031739549 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{12452220368504332}+\frac{497581031739549 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{12452220368504332}+\frac{497581031739549 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{12452220368504332}+\frac{497581031739549 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{12452220368504332}+\frac{497581031739549 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{12452220368504332}+\frac{497581031739549 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =7\right)^{-n -1}}{12452220368504332}+\frac{497581031739549 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =8\right)^{-n -1}}{12452220368504332}+\frac{2122999850763533 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{12452220368504332}+\frac{2122999850763533 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{12452220368504332}+\frac{2122999850763533 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{12452220368504332}+\frac{\left(-1\right)^{-n}}{13}+\frac{2122999850763533 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{12452220368504332}+\frac{2122999850763533 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =7\right)^{-n}}{12452220368504332}+\frac{2122999850763533 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =8\right)^{-n}}{12452220368504332}+\frac{2122999850763533 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{12452220368504332}+\frac{2122999850763533 \mathit{RootOf}\! \left(7 \textit{\_Z}^{8}+7 \textit{\_Z}^{7}+8 \textit{\_Z}^{6}-8 \textit{\_Z}^{5}-4 \textit{\_Z}^{3}+2 \textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{12452220368504332}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 62
a(6) = 172
a(7) = 471
a(8) = 1337
a(n+2) = -7/15*a(n)-14/15*a(n+1)+8/15*a(n+4)+4/15*a(n+5)+2/15*a(n+6)+1/15*a(n+7)+2/15*a(n+8)-1/15*a(n+9), n >= 9
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 20
a \! \left(5\right) = 62
a \! \left(6\right) = 172
a \! \left(7\right) = 471
a \! \left(8\right) = 1337
a \! \left(n +2\right) = -\frac{7 a \! \left(n \right)}{15}-\frac{14 a \! \left(n +1\right)}{15}+\frac{8 a \! \left(n +4\right)}{15}+\frac{4 a \! \left(n +5\right)}{15}+\frac{2 a \! \left(n +6\right)}{15}+\frac{a \! \left(n +7\right)}{15}+\frac{2 a \! \left(n +8\right)}{15}-\frac{a \! \left(n +9\right)}{15}, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14911/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[3,x]
F[3,x] = F[4,x]*F[5,x]
F[4,x] = x
F[5,x] = F[20,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[4,x]
F[14,x] = F[15,x]+F[17,x]
F[15,x] = F[16,x]
F[16,x] = F[13,x]*F[4,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[4,x]
F[19,x] = F[15,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[116,x]+F[22,x]+F[23,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[43,x]
F[25,x] = F[26,x]+F[7,x]
F[26,x] = F[22,x]+F[27,x]+F[34,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[33,x]
F[29,x] = F[11,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[4,x]
F[33,x] = F[17,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[14,x]+F[36,x]
F[36,x] = F[37,x]+F[40,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[4,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[37,x]
F[43,x] = F[44,x]+F[59,x]
F[44,x] = F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]+F[53,x]
F[47,x] = F[2,x]+F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[2,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[2,x]*F[4,x]
F[53,x] = F[54,x]+F[56,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[50,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[54,x]
F[59,x] = 2*F[22,x]+F[106,x]+F[60,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[102,x]+F[62,x]
F[62,x] = F[48,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[22,x]+F[52,x]+F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[79,x]
F[69,x] = F[4,x]+F[70,x]
F[70,x] = F[22,x]+F[71,x]+F[78,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[73,x]+F[76,x]
F[73,x] = F[4,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = x^2
F[76,x] = F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[15,x]*F[4,x]
F[79,x] = F[51,x]+F[80,x]
F[80,x] = 2*F[22,x]+F[81,x]+F[88,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[83,x]+F[86,x]
F[83,x] = F[51,x]+F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[4,x]*F[66,x]
F[86,x] = F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[100,x]+F[22,x]+F[90,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[92,x]+F[96,x]
F[92,x] = F[15,x]+F[93,x]
F[93,x] = F[22,x]+F[71,x]+F[94,x]
F[94,x] = F[4,x]*F[95,x]
F[95,x] = F[15,x]+F[77,x]
F[96,x] = F[54,x]+F[97,x]
F[97,x] = 2*F[22,x]+F[81,x]+F[98,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[87,x]+F[89,x]
F[100,x] = F[101,x]*F[4,x]
F[101,x] = F[2,x]+F[66,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[4,x]
F[105,x] = F[89,x]
F[106,x] = F[107,x]*F[4,x]
F[107,x] = F[108,x]+F[109,x]
F[108,x] = F[103,x]+F[89,x]
F[109,x] = F[110,x]+F[113,x]
F[110,x] = F[111,x]
F[111,x] = F[112,x]*F[4,x]
F[112,x] = F[51,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[4,x]
F[115,x] = F[110,x]
F[116,x] = F[117,x]*F[4,x]
F[117,x] = F[118,x]+F[133,x]
F[118,x] = F[119,x]+F[2,x]
F[119,x] = F[120,x]+F[132,x]+F[22,x]
F[120,x] = F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[127,x]
F[122,x] = F[11,x]+F[123,x]
F[123,x] = F[124,x]+F[22,x]+F[27,x]
F[124,x] = F[125,x]*F[4,x]
F[125,x] = F[126,x]+F[15,x]
F[126,x] = F[38,x]
F[127,x] = F[128,x]+F[48,x]
F[128,x] = 2*F[22,x]+F[129,x]+F[60,x]
F[129,x] = F[130,x]*F[4,x]
F[130,x] = F[131,x]+F[89,x]
F[131,x] = F[111,x]
F[132,x] = F[101,x]*F[4,x]
F[133,x] = F[134,x]+F[89,x]
F[134,x] = 2*F[22,x]+F[135,x]+F[151,x]
F[135,x] = F[136,x]*F[4,x]
F[136,x] = F[137,x]+F[143,x]
F[137,x] = F[138,x]+F[17,x]
F[138,x] = 2*F[22,x]+F[139,x]+F[141,x]
F[139,x] = F[140,x]*F[4,x]
F[140,x] = F[31,x]
F[141,x] = F[142,x]*F[4,x]
F[142,x] = F[37,x]
F[143,x] = F[144,x]+F[56,x]
F[144,x] = 3*F[22,x]+F[145,x]+F[149,x]
F[145,x] = F[146,x]*F[4,x]
F[146,x] = F[147,x]
F[147,x] = F[148,x]*F[4,x]
F[148,x] = F[51,x]
F[149,x] = F[150,x]*F[4,x]
F[150,x] = F[110,x]
F[151,x] = F[152,x]*F[4,x]
F[152,x] = F[89,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{20}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \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_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{15}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{116}\! \left(x \right)+F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{43}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{7}\! \left(x \right)
F_{26}\! \left(x \right) = F_{22}\! \left(x \right)+F_{27}\! \left(x \right)+F_{34}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{33}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{17}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{14}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{37}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{59}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{53}\! \left(x \right)
F_{47}\! \left(x \right) = F_{2}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{2}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{56}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{54}\! \left(x \right)
F_{59}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{106}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{102}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{48}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{22}\! \left(x \right)+F_{52}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{79}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{22}\! \left(x \right)+F_{71}\! \left(x \right)+F_{78}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{76}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = x^{2}
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{79}\! \left(x \right) = F_{51}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{81}\! \left(x \right)+F_{88}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{86}\! \left(x \right)
F_{83}\! \left(x \right) = F_{51}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{100}\! \left(x \right)+F_{22}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{96}\! \left(x \right)
F_{92}\! \left(x \right) = F_{15}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{22}\! \left(x \right)+F_{71}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{15}\! \left(x \right)+F_{77}\! \left(x \right)
F_{96}\! \left(x \right) = F_{54}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{81}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{87}\! \left(x \right)+F_{89}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = F_{2}\! \left(x \right)+F_{66}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{4}\! \left(x \right)
F_{105}\! \left(x \right) = F_{89}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{109}\! \left(x \right)
F_{108}\! \left(x \right) = F_{103}\! \left(x \right)+F_{89}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{113}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{4}\! \left(x \right)
F_{112}\! \left(x \right) = F_{51}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{4}\! \left(x \right)
F_{115}\! \left(x \right) = F_{110}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{4}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{133}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{2}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{132}\! \left(x \right)+F_{22}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{127}\! \left(x \right)
F_{122}\! \left(x \right) = F_{11}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{22}\! \left(x \right)+F_{27}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right) F_{4}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{15}\! \left(x \right)
F_{126}\! \left(x \right) = F_{38}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{48}\! \left(x \right)
F_{128}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{129}\! \left(x \right)+F_{60}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{4}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{89}\! \left(x \right)
F_{131}\! \left(x \right) = F_{111}\! \left(x \right)
F_{132}\! \left(x \right) = F_{101}\! \left(x \right) F_{4}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{89}\! \left(x \right)
F_{134}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{135}\! \left(x \right)+F_{151}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{143}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{17}\! \left(x \right)
F_{138}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{139}\! \left(x \right)+F_{141}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right) F_{4}\! \left(x \right)
F_{140}\! \left(x \right) = F_{31}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right) F_{4}\! \left(x \right)
F_{142}\! \left(x \right) = F_{37}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{56}\! \left(x \right)
F_{144}\! \left(x \right) = 3 F_{22}\! \left(x \right)+F_{145}\! \left(x \right)+F_{149}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right) F_{4}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{4}\! \left(x \right)
F_{148}\! \left(x \right) = F_{51}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{4}\! \left(x \right)
F_{150}\! \left(x \right) = F_{110}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{4}\! \left(x \right)
F_{152}\! \left(x \right) = F_{89}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_20(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_4(x))
Eq(F_14(x), F_15(x) + F_17(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_13(x)*F_4(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_4(x))
Eq(F_19(x), F_15(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_116(x) + F_22(x) + F_23(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_43(x))
Eq(F_25(x), F_26(x) + F_7(x))
Eq(F_26(x), F_22(x) + F_27(x) + F_34(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_33(x))
Eq(F_29(x), F_11(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_4(x))
Eq(F_33(x), F_17(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_14(x) + F_36(x))
Eq(F_36(x), F_37(x) + F_40(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_4(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_37(x))
Eq(F_43(x), F_44(x) + F_59(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_53(x))
Eq(F_47(x), F_2(x) + F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_2(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_2(x)*F_4(x))
Eq(F_53(x), F_54(x) + F_56(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_50(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_54(x))
Eq(F_59(x), F_106(x) + 2*F_22(x) + F_60(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_102(x) + F_62(x))
Eq(F_62(x), F_48(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_22(x) + F_52(x) + F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_79(x))
Eq(F_69(x), F_4(x) + F_70(x))
Eq(F_70(x), F_22(x) + F_71(x) + F_78(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_76(x))
Eq(F_73(x), F_4(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), x**2)
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_15(x)*F_4(x))
Eq(F_79(x), F_51(x) + F_80(x))
Eq(F_80(x), 2*F_22(x) + F_81(x) + F_88(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_86(x))
Eq(F_83(x), F_51(x) + F_84(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_4(x)*F_66(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_100(x) + F_22(x) + F_90(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_92(x) + F_96(x))
Eq(F_92(x), F_15(x) + F_93(x))
Eq(F_93(x), F_22(x) + F_71(x) + F_94(x))
Eq(F_94(x), F_4(x)*F_95(x))
Eq(F_95(x), F_15(x) + F_77(x))
Eq(F_96(x), F_54(x) + F_97(x))
Eq(F_97(x), 2*F_22(x) + F_81(x) + F_98(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_87(x) + F_89(x))
Eq(F_100(x), F_101(x)*F_4(x))
Eq(F_101(x), F_2(x) + F_66(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_4(x))
Eq(F_105(x), F_89(x))
Eq(F_106(x), F_107(x)*F_4(x))
Eq(F_107(x), F_108(x) + F_109(x))
Eq(F_108(x), F_103(x) + F_89(x))
Eq(F_109(x), F_110(x) + F_113(x))
Eq(F_110(x), F_111(x))
Eq(F_111(x), F_112(x)*F_4(x))
Eq(F_112(x), F_51(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_4(x))
Eq(F_115(x), F_110(x))
Eq(F_116(x), F_117(x)*F_4(x))
Eq(F_117(x), F_118(x) + F_133(x))
Eq(F_118(x), F_119(x) + F_2(x))
Eq(F_119(x), F_120(x) + F_132(x) + F_22(x))
Eq(F_120(x), F_121(x)*F_4(x))
Eq(F_121(x), F_122(x) + F_127(x))
Eq(F_122(x), F_11(x) + F_123(x))
Eq(F_123(x), F_124(x) + F_22(x) + F_27(x))
Eq(F_124(x), F_125(x)*F_4(x))
Eq(F_125(x), F_126(x) + F_15(x))
Eq(F_126(x), F_38(x))
Eq(F_127(x), F_128(x) + F_48(x))
Eq(F_128(x), F_129(x) + 2*F_22(x) + F_60(x))
Eq(F_129(x), F_130(x)*F_4(x))
Eq(F_130(x), F_131(x) + F_89(x))
Eq(F_131(x), F_111(x))
Eq(F_132(x), F_101(x)*F_4(x))
Eq(F_133(x), F_134(x) + F_89(x))
Eq(F_134(x), F_135(x) + F_151(x) + 2*F_22(x))
Eq(F_135(x), F_136(x)*F_4(x))
Eq(F_136(x), F_137(x) + F_143(x))
Eq(F_137(x), F_138(x) + F_17(x))
Eq(F_138(x), F_139(x) + F_141(x) + 2*F_22(x))
Eq(F_139(x), F_140(x)*F_4(x))
Eq(F_140(x), F_31(x))
Eq(F_141(x), F_142(x)*F_4(x))
Eq(F_142(x), F_37(x))
Eq(F_143(x), F_144(x) + F_56(x))
Eq(F_144(x), F_145(x) + F_149(x) + 3*F_22(x))
Eq(F_145(x), F_146(x)*F_4(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_148(x)*F_4(x))
Eq(F_148(x), F_51(x))
Eq(F_149(x), F_150(x)*F_4(x))
Eq(F_150(x), F_110(x))
Eq(F_151(x), F_152(x)*F_4(x))
Eq(F_152(x), F_89(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 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, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [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, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 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, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [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, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 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, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [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, 1], [0, 0], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": 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