0123_0132_2103
Counting sequence:
1, 1, 2, 6, 21, 73, 250, 861, 2967, 10220, 35203, 121263, 417710, 1438865, 4956391, 17073052, 58810751, 202582667, 697827126, 2403772765, 8280164651, 28522299468, 98249443251, 338435304271, 1165792409470, 4015751089881, 13832871688719, 47649452088476, 164135859525367, 565391189223075, 1947576829191782, 6708727652471717, 23109243260876131, 79603339374432940, 274205934310672235, 944544475169818343, 3253628583264049710, 11207623607061559681, 38606381676039499559, 132985613933086813308, 458089381739083422159, 1577959265335887979483, 5435523158398797867862, 18723494740658369428269, 64495954683179508485019, 222166226343516323774732, 765285704664373442706787, 2636144203386198073129407, 9080603778028683570787934, 31279535037434636653936745, 107747164844417957031307519, 371151665717417128004021596, 1278488943664766218204986983, 4403951618844494329540021715, 15170088061558214189525221830, 52255699361159833420463046133, 180002786051291868853986360467, 620047255750822335925062597228, 2135848048788389554811020200987, 7357256798095458309687045477463, 25343201555854089488881355735566, 87298551991131922148245180365201, 300713276613939127881140862591639, 1035853088847080705659808439209276, 3568155133541254172537682449994943, 12291058639587013300057374802906251, 42338440126014191639732933376401846, 145841262731484218308569258106918397, 502372639421946711754235840424550987, 1730499750982270228505667281233385164, 5960972300552551807288261450732730771, 20533485051231790690599457447527875759, 70730744430749495899480829839569291582, 243642917665741488580109998186852110073, 839265468028473002563998404732714602991, 2890978866011554384456490349162669040668, 9958420931292155551712490533699370193623, 34303311107083468052922997100047070244355, 118163026149234185502234242535792214787878, 407030700481313389657922708965357025789253, 1402079792075318181812935382933632094563011, 4829679287143151994997772361770438998666796, 16636572432253234010016251891975569001653195, 57307230115755022017667930318492825763176647, 197403559952841977273699742153064210236938222, 679986895254636785495173789795769330288171681, 2342319347373976073804561427453816974630472967, 8068478912417742493436225052679397536650160636, 27793115414904967081068248304446562593630944943, 95737656731974911929702693336620590846330064955, 329783069645155914286058430840075591545345117718, 1135988457802504636802405359610832856720366362061, 3913086798691784163565807446240456548325804012539, 13479228762338359021909808063403460559601206745228, 46431274687847920679040636968999262758877496842435, 159939660283975377557591217001202010749794615062175, 550936736148845762122029093380190550414023022795294, 1897786244508824936954628156187291274412967069107849, 6537216332718594610057276379817661474033311046752735, 22518446165586604450012434208462658271823191261271772, 77568247997928107078888652883577814816829229738659399
Generating function in Maple syntax:
(2*x^5-x^4-3*x^3-2*x^2-2*x+1)/(2*x^5-2*x^3-x^2-3*x+1)
Generating function in latex syntax:
\frac{2 x^{5}-x^{4}-3 x^{3}-2 x^{2}-2 x +1}{2 x^{5}-2 x^{3}-x^{2}-3 x +1}
Generating function in sympy syntax:
(2*x**5 - x**4 - 3*x**3 - 2*x**2 - 2*x + 1)/(2*x**5 - 2*x**3 - x**2 - 3*x + 1)
Implicit equation for the generating function in Maple syntax:
(2*x^5-2*x^3-x^2-3*x+1)*F(x)-2*x^5+x^4+3*x^3+2*x^2+2*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{5}-2 x^{3}-x^{2}-3 x +1\right) F \! \left(x \right)-2 x^{5}+x^{4}+3 x^{3}+2 x^{2}+2 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,7337/41583*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^(-n+1)+5657/41583*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^(-n+2)-296/41583*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^(-n+3)-3640/41583*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^(-n+4)+1/41583*(3640*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^3-3640*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)+5517)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 2)^(-n+1)+1/41583*(3640*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^2+2017)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 2)^(-n+2)+1/41583*(3640*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)-296)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 2)^(-n+3)+1/41583*((-3640*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)+296)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 2)^2+(-3640*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^2+296*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1))*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 2)+296*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^2+5221)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 3)^(-n+1)+1/41583*((-3640*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)+296)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 2)+296*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)+2017)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 3)^(-n+2)+1/41583*(((3640*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)-296)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 3)-296*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)-2017)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 2)+(-296*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)-2017)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 3)-2017*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)+5221)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 4)^(-n+1)+3650/41583*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^(-n)+1/41583*(3640*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^4-3640*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^2-1820*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)-1810)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 2)^(-n)+1/41583*((-3640*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)+296)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 2)^3+(-3640*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^2+296*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1))*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 2)^2+(-3640*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^3+296*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^2+3640*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)-296)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 2)+296*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^3-296*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)-1958)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 3)^(-n)+1/41583*(((3640*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)-296)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 3)-296*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)-2017)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 2)^2+((3640*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)-296)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 3)^2+(3640*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^2-592*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)-2017)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 3)-296*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^2-2017*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1))*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 2)+(-296*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)-2017)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 3)^2+(-296*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^2-2017*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1))*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 3)-2017*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)^2+59)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 4)^(-n)+1/41583*((((-3640*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 4)+296)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)+296*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 4)+2017)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 3)+(296*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 4)+2017)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)+2017*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 4)-5221)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 2)+((296*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 4)+2017)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)+2017*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 4)-5221)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 3)+(2017*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 4)-5221)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 1)-5221*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 4)+59)*RootOf(2*_Z^5-2*_Z^3-_Z^2-3*_Z+1,index = 5)^(-n))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{7337 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{41583}\\+\\\frac{5657 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{41583}\\-\\\frac{296 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{41583}\\-\\\frac{3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{41583}\\+\\\frac{\left(3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}-3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+5517\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{41583}\\+\\\frac{\left(3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+2017\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{41583}\\+\\\frac{\left(3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-296\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{41583}\\+\\\frac{\left(\left(-3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+296\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+296 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+296 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+5221\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{41583}\\+\\\frac{\left(\left(-3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+296\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+296 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+2017\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{41583}\\+\\\frac{\left(\left(\left(3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-296\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-296 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-2017\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-296 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-2017\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-2017 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+5221\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{41583}\\+\\\frac{3650 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{41583}\\+\\\frac{\left(3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{4}-3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}-1820 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-1810\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{41583}\\+\\\frac{\left(\left(-3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+296\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{3}+\left(-3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+296 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(-3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}+296 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-296\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+296 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{3}-296 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-1958\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{41583}\\+\\\frac{\left(\left(\left(3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-296\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-296 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-2017\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)^{2}+\left(\left(3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-296\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}+\left(3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}-592 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-2017\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-296 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}-2017 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(-296 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-2017\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)^{2}+\left(-296 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}-2017 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)-2017 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)^{2}+59\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{41583}\\+\\\frac{\left(\left(\left(\left(-3640 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+296\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+296 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+2017\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)+\left(296 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+2017\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+2017 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-5221\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =2\right)+\left(\left(296 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+2017\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)+2017 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-5221\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =3\right)+\left(2017 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)-5221\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =1\right)-5221 \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =4\right)+59\right) \mathit{RootOf}\left(2 \textit{\_Z}^{5}-2 \textit{\_Z}^{3}-\textit{\_Z}^{2}-3 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{41583} & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 73
a(n) = a(n+2)+1/2*a(n+3)+3/2*a(4+n)-1/2*a(n+5), n >= 6
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 21
a \! \left(5\right) = 73
a \! \left(n \right) = a \! \left(n +2\right)+\frac{a \! \left(n +3\right)}{2}+\frac{3 a \! \left(4+n \right)}{2}-\frac{a \! \left(n +5\right)}{2}, \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14625/
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[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[7,x]
F[12,x] = F[13,x]+F[14,x]+F[18,x]
F[13,x] = 0
F[14,x] = F[15,x]*F[4,x]
F[15,x] = F[16,x]+F[17,x]
F[16,x] = F[4,x]
F[17,x] = F[18,x]
F[18,x] = F[4,x]*F[7,x]
F[19,x] = F[2,x]+F[20,x]
F[20,x] = F[13,x]+F[21,x]+F[66,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[34,x]
F[23,x] = F[24,x]+F[7,x]
F[24,x] = F[13,x]+F[14,x]+F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[11,x]+F[27,x]
F[27,x] = F[24,x]+F[28,x]
F[28,x] = F[13,x]+F[29,x]+F[30,x]+F[33,x]
F[29,x] = 0
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[17,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[24,x]*F[4,x]
F[34,x] = F[35,x]+F[48,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[2,x]*F[4,x]
F[41,x] = F[35,x]+F[42,x]
F[42,x] = 2*F[13,x]+F[43,x]+F[47,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[47,x]
F[47,x] = F[35,x]*F[4,x]
F[48,x] = 2*F[13,x]+F[49,x]+F[54,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[39,x]
F[52,x] = F[53,x]
F[53,x] = F[20,x]*F[4,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[56,x]+F[58,x]
F[56,x] = F[20,x]+F[57,x]
F[57,x] = 2*F[13,x]+F[49,x]+F[53,x]
F[58,x] = F[48,x]+F[59,x]
F[59,x] = 2*F[13,x]+F[60,x]+F[61,x]+F[65,x]
F[60,x] = 0
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = F[53,x]
F[64,x] = F[65,x]
F[65,x] = F[4,x]*F[48,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[74,x]
F[68,x] = F[2,x]+F[69,x]
F[69,x] = F[13,x]+F[40,x]+F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[12,x]+F[4,x]
F[73,x] = F[39,x]+F[57,x]
F[74,x] = F[20,x]+F[75,x]
F[75,x] = F[13,x]+F[49,x]+F[53,x]+F[76,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[12,x]+F[28,x]
F[79,x] = F[42,x]+F[59,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_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{7}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{13}\! \left(x \right) = 0
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{19}\! \left(x \right) = F_{2}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{13}\! \left(x \right)+F_{21}\! \left(x \right)+F_{66}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{34}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{7}\! \left(x \right)
F_{24}\! \left(x \right) = F_{13}\! \left(x \right)+F_{14}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{11}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{24}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{13}\! \left(x \right)+F_{29}\! \left(x \right)+F_{30}\! \left(x \right)+F_{33}\! \left(x \right)
F_{29}\! \left(x \right) = 0
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{17}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{48}\! \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_{2}\! \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) = 2 F_{13}\! \left(x \right)+F_{43}\! \left(x \right)+F_{47}\! \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_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{48}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{49}\! \left(x \right)+F_{54}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{39}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{58}\! \left(x \right)
F_{56}\! \left(x \right) = F_{20}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{49}\! \left(x \right)+F_{53}\! \left(x \right)
F_{58}\! \left(x \right) = F_{48}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{60}\! \left(x \right)+F_{61}\! \left(x \right)+F_{65}\! \left(x \right)
F_{60}\! \left(x \right) = 0
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = F_{53}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{74}\! \left(x \right)
F_{68}\! \left(x \right) = F_{2}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{13}\! \left(x \right)+F_{40}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right)+F_{4}\! \left(x \right)
F_{73}\! \left(x \right) = F_{39}\! \left(x \right)+F_{57}\! \left(x \right)
F_{74}\! \left(x \right) = F_{20}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{13}\! \left(x \right)+F_{49}\! \left(x \right)+F_{53}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right)+F_{28}\! \left(x \right)
F_{79}\! \left(x \right) = F_{42}\! \left(x \right)+F_{59}\! \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_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_7(x))
Eq(F_12(x), F_13(x) + F_14(x) + F_18(x))
Eq(F_13(x), 0)
Eq(F_14(x), F_15(x)*F_4(x))
Eq(F_15(x), F_16(x) + F_17(x))
Eq(F_16(x), F_4(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_4(x)*F_7(x))
Eq(F_19(x), F_2(x) + F_20(x))
Eq(F_20(x), F_13(x) + F_21(x) + F_66(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_34(x))
Eq(F_23(x), F_24(x) + F_7(x))
Eq(F_24(x), F_13(x) + F_14(x) + F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_11(x) + F_27(x))
Eq(F_27(x), F_24(x) + F_28(x))
Eq(F_28(x), F_13(x) + F_29(x) + F_30(x) + F_33(x))
Eq(F_29(x), 0)
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_17(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_24(x)*F_4(x))
Eq(F_34(x), F_35(x) + F_48(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_2(x)*F_4(x))
Eq(F_41(x), F_35(x) + F_42(x))
Eq(F_42(x), 2*F_13(x) + F_43(x) + F_47(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_47(x))
Eq(F_47(x), F_35(x)*F_4(x))
Eq(F_48(x), 2*F_13(x) + F_49(x) + F_54(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_39(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_20(x)*F_4(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_58(x))
Eq(F_56(x), F_20(x) + F_57(x))
Eq(F_57(x), 2*F_13(x) + F_49(x) + F_53(x))
Eq(F_58(x), F_48(x) + F_59(x))
Eq(F_59(x), 2*F_13(x) + F_60(x) + F_61(x) + F_65(x))
Eq(F_60(x), 0)
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), F_53(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_4(x)*F_48(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_74(x))
Eq(F_68(x), F_2(x) + F_69(x))
Eq(F_69(x), F_13(x) + F_40(x) + F_70(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_12(x) + F_4(x))
Eq(F_73(x), F_39(x) + F_57(x))
Eq(F_74(x), F_20(x) + F_75(x))
Eq(F_75(x), F_13(x) + F_49(x) + F_53(x) + F_76(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_12(x) + F_28(x))
Eq(F_79(x), F_42(x) + F_59(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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{"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"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], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": 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