0132_0321_1203_2103
Counting sequence:
1, 1, 2, 6, 20, 62, 181, 521, 1509, 4401, 12865, 37593, 109774, 320462, 935553, 2731477, 7975248, 23285846, 67988700, 198508792, 579592425, 1692256111, 4940942043, 14426251263, 42120857431, 122981813861, 359074514924, 1048403050460, 3061060925869, 8937492142965, 26095124455762, 76190894406586, 222457355972784, 649516922201614, 1896418441410245, 5537042657817197, 16166707054572885, 47202529064906865, 137818959829410133, 402395084856712225, 1174887726026559010, 3430362896360253330, 10015756688965010981, 29243373101723744025, 85382951775268493104, 249295743979299910074, 727877950738617759336, 2125212018121987007088, 6205059677088786961201, 18117140910137409137051, 52897282514415915044707, 154446140883314268458327, 450942076792845729366915, 1316632163544164916636013, 3844219342776779654973392, 11224108573801696948654968, 32771442533112511000291145, 95683985827422757441940953, 279372051888522433973467746, 815692852899891696639871342, 2381608417070510232650562524, 6953669671244773710922659950, 20302885037779003758209176085, 59279080017541514781140830289, 173079309723092350074770228261, 505346025028687951349189020401, 1475477371737074067248621582809, 4308005538154883087550170558489, 12578242182680040383610322173702, 36725156224825503189481020884134, 107227789078113027748951728760185, 313076918725481240490003696418765, 914102191990905420215071479306864, 2668937783098764948548545327994750, 7792595786842857148274212091455876, 22752328466277295520664997982529912, 66430810066064482452464439342508953, 193960478927438397305267116397066503, 566313542591879633512897531394007307, 1653486474649014948914758011549832399, 4827745261634205207087326037280250527, 14095745365065000845852019362182749189, 41155866067691882180684435985615265892, 120164295531311996594338247357440305668, 350848112314947259079804251856820823797, 1024384134827190278110834668096395877613, 2990932026858577782863219732791631156210, 8732734220642202374496651514088637447522, 25497285221982497535153255508473106619352, 74445361242577478883490553739090962398110, 217360858706625068067612006531551793697445, 634636491906230482839782842985253902452597, 1852971502116958129342054338873008816210197, 5410189031747148536901697120371479914379185, 15796327858144058840761623019525530991173709, 46121119306139590358649331182849298735785729, 134661527992689176886586124910202677759697146, 393176215021127422600939316127635569435647114, 1147971052777096353819071288482270141251714365, 3351773295704931213402785548398423616803613169, 9786295742060054593378163325302230601456282192
Generating function in Maple syntax:
-(2*x-1)*(x-1)^3/(2*x^7-x^6-2*x^5-6*x^4+14*x^3-13*x^2+6*x-1)
Generating function in latex syntax:
-\frac{\left(2 x -1\right) \left(x -1\right)^{3}}{2 x^{7}-x^{6}-2 x^{5}-6 x^{4}+14 x^{3}-13 x^{2}+6 x -1}
Generating function in sympy syntax:
(1 - 2*x)*(x - 1)**3/(2*x**7 - x**6 - 2*x**5 - 6*x**4 + 14*x**3 - 13*x**2 + 6*x - 1)
Implicit equation for the generating function in Maple syntax:
(2*x^7-x^6-2*x^5-6*x^4+14*x^3-13*x^2+6*x-1)*F(x)+(2*x-1)*(x-1)^3 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{7}-x^{6}-2 x^{5}-6 x^{4}+14 x^{3}-13 x^{2}+6 x -1\right) F \! \left(x \right)+\left(2 x -1\right) \left(x -1\right)^{3} = 0
Explicit closed form in Maple syntax:
204922/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+5)+204922/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+5)+204922/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+5)+204922/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+5)+204922/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+5)+204922/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+5)+204922/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+5)+9722/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+4)+9722/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+4)+9722/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+4)+9722/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+4)+9722/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+4)+9722/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+4)+9722/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+4)-435059/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+3)-435059/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+3)-435059/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+3)-435059/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+3)-435059/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+3)-435059/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+3)-435059/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+3)-757563/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+2)-757563/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+2)-757563/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+2)-757563/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+2)-757563/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+2)-757563/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+2)-757563/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+2)+1013736/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+1)+1013736/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+1)+1013736/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+1)+1013736/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+1)+1013736/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+1)+1013736/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+1)+1013736/798901*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+1)+403803/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n-1)+403803/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n-1)+403803/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n-1)+403803/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n-1)+403803/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n-1)+403803/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n-1)+403803/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n-1)-1223543/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n)-1223543/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n)-1223543/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n)-1223543/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n)-1223543/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n)-1223543/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n)-1223543/1597802*RootOf(2*_Z^7-_Z^6-2*_Z^5-6*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n)
Explicit closed form in latex syntax:
\frac{204922 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +5}}{798901}+\frac{204922 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +5}}{798901}+\frac{204922 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +5}}{798901}+\frac{204922 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +5}}{798901}+\frac{204922 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +5}}{798901}+\frac{204922 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +5}}{798901}+\frac{204922 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +5}}{798901}+\frac{9722 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}}{798901}+\frac{9722 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +4}}{798901}+\frac{9722 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +4}}{798901}+\frac{9722 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +4}}{798901}+\frac{9722 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +4}}{798901}+\frac{9722 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +4}}{798901}+\frac{9722 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +4}}{798901}-\frac{435059 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{1597802}-\frac{435059 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{1597802}-\frac{435059 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{1597802}-\frac{435059 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{1597802}-\frac{435059 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{1597802}-\frac{435059 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +3}}{1597802}-\frac{435059 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +3}}{1597802}-\frac{757563 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{798901}-\frac{757563 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{798901}-\frac{757563 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{798901}-\frac{757563 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{798901}-\frac{757563 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{798901}-\frac{757563 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +2}}{798901}-\frac{757563 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +2}}{798901}+\frac{1013736 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{798901}+\frac{1013736 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{798901}+\frac{1013736 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{798901}+\frac{1013736 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{798901}+\frac{1013736 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{798901}+\frac{1013736 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =6\right)^{-n +1}}{798901}+\frac{1013736 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =7\right)^{-n +1}}{798901}+\frac{403803 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{1597802}+\frac{403803 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{1597802}+\frac{403803 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{1597802}+\frac{403803 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{1597802}+\frac{403803 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{1597802}+\frac{403803 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =6\right)^{-n -1}}{1597802}+\frac{403803 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =7\right)^{-n -1}}{1597802}-\frac{1223543 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{1597802}-\frac{1223543 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{1597802}-\frac{1223543 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{1597802}-\frac{1223543 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{1597802}-\frac{1223543 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{1597802}-\frac{1223543 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =6\right)^{-n}}{1597802}-\frac{1223543 \mathit{RootOf}\! \left(2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-6 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =7\right)^{-n}}{1597802}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 62
a(6) = 181
a(n+7) = 2*a(n)-a(n+1)-2*a(n+2)-6*a(n+3)+14*a(n+4)-13*a(n+5)+6*a(n+6), n >= 7
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) = 181
a \! \left(n +7\right) = 2 a \! \left(n \right)-a \! \left(n +1\right)-2 a \! \left(n +2\right)-6 a \! \left(n +3\right)+14 a \! \left(n +4\right)-13 a \! \left(n +5\right)+6 a \! \left(n +6\right), \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15432/
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[22,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[11,x]+F[14,x]
F[14,x] = F[15,x]+F[16,x]+F[19,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[11,x]+F[18,x]
F[18,x] = F[16,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[11,x]+F[21,x]
F[21,x] = F[19,x]
F[22,x] = F[2,x]+F[23,x]
F[23,x] = F[15,x]+F[24,x]+F[83,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[26,x]+F[42,x]
F[26,x] = F[27,x]+F[7,x]
F[27,x] = F[15,x]+F[28,x]+F[35,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[17,x]+F[30,x]
F[30,x] = F[21,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[21,x]+F[34,x]
F[34,x] = F[32,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[20,x]+F[37,x]
F[37,x] = F[18,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[18,x]+F[41,x]
F[41,x] = F[39,x]
F[42,x] = F[43,x]+F[57,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[49,x]
F[46,x] = F[2,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[46,x]
F[49,x] = F[47,x]+F[50,x]
F[50,x] = 2*F[15,x]+F[51,x]+F[54,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[47,x]+F[53,x]
F[53,x] = F[51,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[47,x]+F[56,x]
F[56,x] = F[54,x]
F[57,x] = 2*F[15,x]+F[58,x]+F[75,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[52,x]+F[60,x]
F[60,x] = F[61,x]+F[71,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[61,x]+F[64,x]
F[64,x] = F[15,x]+F[48,x]+F[65,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]+F[69,x]
F[67,x] = F[11,x]+F[68,x]
F[68,x] = F[15,x]+F[19,x]+F[28,x]
F[69,x] = F[47,x]+F[70,x]
F[70,x] = 2*F[15,x]+F[58,x]+F[62,x]
F[71,x] = F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[61,x]+F[74,x]
F[74,x] = F[72,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[63,x]+F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[51,x]
F[79,x] = F[80,x]
F[80,x] = F[4,x]*F[81,x]
F[81,x] = F[78,x]+F[82,x]
F[82,x] = F[80,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[46,x]+F[85,x]
F[85,x] = F[64,x]+F[86,x]
F[86,x] = 2*F[15,x]+F[51,x]+F[62,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_{22}\! \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_{11}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{16}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{11}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{2}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{15}\! \left(x \right)+F_{24}\! \left(x \right)+F_{83}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{42}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{7}\! \left(x \right)
F_{27}\! \left(x \right) = F_{15}\! \left(x \right)+F_{28}\! \left(x \right)+F_{35}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{17}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{21}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{21}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{32}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{20}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{18}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{18}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{57}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{49}\! \left(x \right)
F_{46}\! \left(x \right) = F_{2}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{49}\! \left(x \right) = F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{51}\! \left(x \right)+F_{54}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{47}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{51}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{47}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{54}\! \left(x \right)
F_{57}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{58}\! \left(x \right)+F_{75}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{52}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{71}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{61}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{15}\! \left(x \right)+F_{48}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{69}\! \left(x \right)
F_{67}\! \left(x \right) = F_{11}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{15}\! \left(x \right)+F_{19}\! \left(x \right)+F_{28}\! \left(x \right)
F_{69}\! \left(x \right) = F_{47}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{58}\! \left(x \right)+F_{62}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{61}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{63}\! \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_{51}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{78}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{80}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{46}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{64}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{51}\! \left(x \right)+F_{62}\! \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_22(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_11(x) + F_14(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_19(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_11(x) + F_18(x))
Eq(F_18(x), F_16(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_11(x) + F_21(x))
Eq(F_21(x), F_19(x))
Eq(F_22(x), F_2(x) + F_23(x))
Eq(F_23(x), F_15(x) + F_24(x) + F_83(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_26(x) + F_42(x))
Eq(F_26(x), F_27(x) + F_7(x))
Eq(F_27(x), F_15(x) + F_28(x) + F_35(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_17(x) + F_30(x))
Eq(F_30(x), F_21(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_21(x) + F_34(x))
Eq(F_34(x), F_32(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_20(x) + F_37(x))
Eq(F_37(x), F_18(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_18(x) + F_41(x))
Eq(F_41(x), F_39(x))
Eq(F_42(x), F_43(x) + F_57(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_49(x))
Eq(F_46(x), F_2(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_4(x)*F_46(x))
Eq(F_49(x), F_47(x) + F_50(x))
Eq(F_50(x), 2*F_15(x) + F_51(x) + F_54(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_47(x) + F_53(x))
Eq(F_53(x), F_51(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_47(x) + F_56(x))
Eq(F_56(x), F_54(x))
Eq(F_57(x), 2*F_15(x) + F_58(x) + F_75(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_52(x) + F_60(x))
Eq(F_60(x), F_61(x) + F_71(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_61(x) + F_64(x))
Eq(F_64(x), F_15(x) + F_48(x) + F_65(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_69(x))
Eq(F_67(x), F_11(x) + F_68(x))
Eq(F_68(x), F_15(x) + F_19(x) + F_28(x))
Eq(F_69(x), F_47(x) + F_70(x))
Eq(F_70(x), 2*F_15(x) + F_58(x) + F_62(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_61(x) + F_74(x))
Eq(F_74(x), F_72(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_63(x) + F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_51(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_4(x)*F_81(x))
Eq(F_81(x), F_78(x) + F_82(x))
Eq(F_82(x), F_80(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_46(x) + F_85(x))
Eq(F_85(x), F_64(x) + F_86(x))
Eq(F_86(x), 2*F_15(x) + F_51(x) + F_62(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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