0132_1023_1302_2031
Counting sequence:
1, 1, 2, 6, 20, 65, 208, 664, 2122, 6786, 21701, 69381, 221769, 708745, 2264817, 7236808, 23122921, 73880026, 236050283, 754185052, 2409621950, 7698719635, 24597291879, 78587889828, 251086696240, 802216577826, 2563064186217, 8188932434892, 26163453516396, 83591638439164, 267073377743060, 853293341511969, 2726252723231825, 8710315118889411, 27829257622339287, 88913841665173629, 284077690627721878, 907621724457773909, 2899830651357531136, 9264892608539238065, 29601119984838819096, 94574901337147542080, 302164646726048610443, 965409135406434670095, 3084460107510054872386, 9854779498040004084964, 31485795105132675338038, 100596395241494867856453, 321403182031599492010330, 1026875815699586277656578, 3280844745230576987733382, 10482223924004199578951728, 33490465695671503948648627, 107001271928992741418248517, 341866616560728227712434219, 1092256020996074675066559439, 3489733005826428324146093713, 11149617139073793634021721582, 35622771753705708501668547987, 113813941015918074904502936926, 363632938479228950626125132765, 1161798921702791464441274894398, 3711920983051620866852940286346, 11859502644592450024719827018857, 37890839707871917788655921611453, 121060366255939345150946003398964, 386785101386323651634906203453994, 1235769552672148842927455581522240, 3948255457198229543269108261444665, 12614585884226998102918951159590682, 40303313388809869064244265027136302, 128768164490257373821312761930662480, 411411340458021172016052172259759870, 1314449823273453600669598855913817659, 4199637122253583691554447017263893869, 13417744554666984265788095415481179601, 42869386971626195305855641565182300981, 136966710898055686111438977126970293933, 437605508719966056220058172290612514104, 1398139591777104653351260774772811873339, 4467024018533476000811317992061261231520, 14272039572809791191111707296998270995207, 45598840015801052319426492873177246386210, 145687250948202672266563185931360517780644, 465467434730570013190092707059131472150589, 1487157808144023911243761005056104579837777, 4751435183868269004099350408205089892156830, 15180726741216762409475650311159611560579434, 48502074736053671799643127558623034183906364, 154963019478814667077679803171207847779061189, 495103303037492578401078056210602795200474948, 1581843729575410692434688373203035122280449056, 5053954537256559658747089273435566122938458598, 16147269156297837272384079808967014822614849726, 51590155646208480488461771864476252660443727749, 164829367358501497801563429042996786739904405881, 526626058857423742010611752778946876057491104981, 1682558213455391693971680277400626049861977559449, 5375735009787374803063969238648661107245990115229, 17175350406513486112299826996924287115023145801308, 54874851727148423710400203623681162564293896670865
Generating function in Maple syntax:
-(2*x-1)*(x^2-3*x+1)*(x-1)^2/(x^7-3*x^6-7*x^5+26*x^4-35*x^3+24*x^2-8*x+1)
Generating function in latex syntax:
-\frac{\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x -1\right)^{2}}{x^{7}-3 x^{6}-7 x^{5}+26 x^{4}-35 x^{3}+24 x^{2}-8 x +1}
Generating function in sympy syntax:
(1 - 2*x)*(x - 1)**2*(x**2 - 3*x + 1)/(x**7 - 3*x**6 - 7*x**5 + 26*x**4 - 35*x**3 + 24*x**2 - 8*x + 1)
Implicit equation for the generating function in Maple syntax:
(x^7-3*x^6-7*x^5+26*x^4-35*x^3+24*x^2-8*x+1)*F(x)+(2*x-1)*(x^2-3*x+1)*(x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{7}-3 x^{6}-7 x^{5}+26 x^{4}-35 x^{3}+24 x^{2}-8 x +1\right) F \! \left(x \right)+\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x -1\right)^{2} = 0
Explicit closed form in Maple syntax:
513043/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 1)^(-n+5)+513043/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 2)^(-n+5)+513043/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 3)^(-n+5)+513043/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 4)^(-n+5)+513043/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 5)^(-n+5)+513043/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 6)^(-n+5)+513043/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 7)^(-n+5)-603683/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 1)^(-n+4)-603683/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 2)^(-n+4)-603683/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 3)^(-n+4)-603683/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 4)^(-n+4)-603683/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 5)^(-n+4)-603683/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 6)^(-n+4)-603683/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 7)^(-n+4)-2187105/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 1)^(-n+3)-2187105/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 2)^(-n+3)-2187105/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 3)^(-n+3)-2187105/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 4)^(-n+3)-2187105/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 5)^(-n+3)-2187105/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 6)^(-n+3)-2187105/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 7)^(-n+3)+5252441/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 1)^(-n+2)+5252441/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 2)^(-n+2)+5252441/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 3)^(-n+2)+5252441/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 4)^(-n+2)+5252441/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 5)^(-n+2)+5252441/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 6)^(-n+2)+5252441/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 7)^(-n+2)-11148413/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 1)^(-n+1)-11148413/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 2)^(-n+1)-11148413/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 3)^(-n+1)-11148413/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 4)^(-n+1)-11148413/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 5)^(-n+1)-11148413/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 6)^(-n+1)-11148413/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 7)^(-n+1)-394111/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 1)^(-n-1)-394111/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 2)^(-n-1)-394111/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 3)^(-n-1)-394111/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 4)^(-n-1)-394111/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 5)^(-n-1)-394111/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 6)^(-n-1)-394111/325571*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 7)^(-n-1)+5250503/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 1)^(-n)+5250503/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 2)^(-n)+5250503/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 3)^(-n)+5250503/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 4)^(-n)+5250503/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 5)^(-n)+5250503/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 6)^(-n)+5250503/651142*RootOf(_Z^7-3*_Z^6-7*_Z^5+26*_Z^4-35*_Z^3+24*_Z^2-8*_Z+1,index = 7)^(-n)
Explicit closed form in latex syntax:
\frac{513043 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +5}}{651142}+\frac{513043 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +5}}{651142}+\frac{513043 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +5}}{651142}+\frac{513043 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +5}}{651142}+\frac{513043 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +5}}{651142}+\frac{513043 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +5}}{651142}+\frac{513043 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +5}}{651142}-\frac{603683 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{325571}-\frac{603683 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +4}}{325571}-\frac{603683 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +4}}{325571}-\frac{603683 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +4}}{325571}-\frac{603683 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +4}}{325571}-\frac{603683 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +4}}{325571}-\frac{603683 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +4}}{325571}-\frac{2187105 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{325571}-\frac{2187105 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{325571}-\frac{2187105 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{325571}-\frac{2187105 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{325571}-\frac{2187105 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{325571}-\frac{2187105 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +3}}{325571}-\frac{2187105 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +3}}{325571}+\frac{5252441 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{325571}+\frac{5252441 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{325571}+\frac{5252441 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{325571}+\frac{5252441 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{325571}+\frac{5252441 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{325571}+\frac{5252441 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{325571}+\frac{5252441 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +2}}{325571}-\frac{11148413 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{651142}-\frac{11148413 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{651142}-\frac{11148413 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{651142}-\frac{11148413 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{651142}-\frac{11148413 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{651142}-\frac{11148413 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{651142}-\frac{11148413 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +1}}{651142}-\frac{394111 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{325571}-\frac{394111 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{325571}-\frac{394111 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{325571}-\frac{394111 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{325571}-\frac{394111 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{325571}-\frac{394111 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{325571}-\frac{394111 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n -1}}{325571}+\frac{5250503 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{651142}+\frac{5250503 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{651142}+\frac{5250503 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{651142}+\frac{5250503 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{651142}+\frac{5250503 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{651142}+\frac{5250503 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{651142}+\frac{5250503 \mathit{RootOf}\! \left(\textit{\_Z}^{7}-3 \textit{\_Z}^{6}-7 \textit{\_Z}^{5}+26 \textit{\_Z}^{4}-35 \textit{\_Z}^{3}+24 \textit{\_Z}^{2}-8 \textit{\_Z} +1, \mathit{index} =7\right)^{-n}}{651142}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 65
a(6) = 208
a(n+7) = -a(n)+3*a(n+1)+7*a(n+2)-26*a(n+3)+35*a(n+4)-24*a(n+5)+8*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) = 65
a \! \left(6\right) = 208
a \! \left(n +7\right) = -a \! \left(n \right)+3 a \! \left(n +1\right)+7 a \! \left(n +2\right)-26 a \! \left(n +3\right)+35 a \! \left(n +4\right)-24 a \! \left(n +5\right)+8 a \! \left(n +6\right), \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15484/
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[27,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[7,x]
F[14,x] = F[15,x]+F[16,x]+F[26,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[19,x]+F[4,x]
F[19,x] = F[20,x]
F[20,x] = F[18,x]*F[4,x]
F[21,x] = F[22,x]+F[24,x]
F[22,x] = F[15,x]+F[16,x]+F[23,x]
F[23,x] = F[4,x]*F[7,x]
F[24,x] = F[25,x]
F[25,x] = F[21,x]*F[4,x]
F[26,x] = F[13,x]*F[4,x]
F[27,x] = F[2,x]+F[28,x]
F[28,x] = F[15,x]+F[29,x]+F[72,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[31,x]+F[42,x]
F[31,x] = F[32,x]+F[35,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[1,x]+F[32,x]
F[35,x] = F[36,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[18,x]+F[38,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[36,x]
F[40,x] = F[41,x]
F[41,x] = F[38,x]*F[4,x]
F[42,x] = F[43,x]+F[47,x]
F[43,x] = F[15,x]+F[29,x]+F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[2,x]+F[46,x]
F[46,x] = F[44,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[60,x]
F[50,x] = F[51,x]+F[58,x]
F[51,x] = F[15,x]+F[52,x]+F[57,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]+F[55,x]
F[54,x] = F[39,x]+F[4,x]
F[55,x] = F[51,x]+F[56,x]
F[56,x] = F[48,x]
F[57,x] = F[2,x]*F[4,x]
F[58,x] = F[59,x]
F[59,x] = F[4,x]*F[50,x]
F[60,x] = F[61,x]+F[70,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[67,x]
F[64,x] = F[51,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[4,x]*F[64,x]
F[67,x] = F[61,x]+F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[4,x]*F[67,x]
F[70,x] = F[71,x]
F[71,x] = F[4,x]*F[60,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]+F[77,x]
F[74,x] = F[2,x]+F[75,x]
F[75,x] = F[15,x]+F[52,x]+F[76,x]
F[76,x] = F[4,x]*F[74,x]
F[77,x] = F[78,x]+F[98,x]
F[78,x] = F[79,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[81,x]+F[84,x]
F[81,x] = F[2,x]+F[82,x]
F[82,x] = F[83,x]
F[83,x] = F[4,x]*F[81,x]
F[84,x] = F[78,x]+F[85,x]
F[85,x] = 2*F[15,x]+F[86,x]+F[97,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[88,x]+F[92,x]
F[88,x] = F[89,x]+F[90,x]
F[89,x] = F[57,x]
F[90,x] = F[91,x]
F[91,x] = F[4,x]*F[88,x]
F[92,x] = F[93,x]+F[95,x]
F[93,x] = 2*F[15,x]+F[86,x]+F[94,x]
F[94,x] = F[4,x]*F[78,x]
F[95,x] = F[96,x]
F[96,x] = F[4,x]*F[92,x]
F[97,x] = F[4,x]*F[84,x]
F[98,x] = 2*F[15,x]+F[105,x]+F[99,x]
F[99,x] = F[100,x]*F[4,x]
F[100,x] = F[101,x]+F[64,x]
F[101,x] = F[102,x]+F[103,x]
F[102,x] = 2*F[15,x]+F[94,x]+F[99,x]
F[103,x] = F[104,x]
F[104,x] = F[101,x]*F[4,x]
F[105,x] = F[4,x]*F[77,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_{27}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{26}\! \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_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{24}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{2}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{15}\! \left(x \right)+F_{29}\! \left(x \right)+F_{72}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{42}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{1}\! \left(x \right)+F_{32}\! \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_{18}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{36}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{47}\! \left(x \right)
F_{43}\! \left(x \right) = F_{15}\! \left(x \right)+F_{29}\! \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_{2}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{60}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{58}\! \left(x \right)
F_{51}\! \left(x \right) = F_{15}\! \left(x \right)+F_{52}\! \left(x \right)+F_{57}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{55}\! \left(x \right)
F_{54}\! \left(x \right) = F_{39}\! \left(x \right)+F_{4}\! \left(x \right)
F_{55}\! \left(x \right) = F_{51}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{48}\! \left(x \right)
F_{57}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{70}\! \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_{64}\! \left(x \right)+F_{67}\! \left(x \right)
F_{64}\! \left(x \right) = F_{51}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{67}\! \left(x \right) = F_{61}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{77}\! \left(x \right)
F_{74}\! \left(x \right) = F_{2}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{15}\! \left(x \right)+F_{52}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{98}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{84}\! \left(x \right)
F_{81}\! \left(x \right) = F_{2}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{84}\! \left(x \right) = F_{78}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{86}\! \left(x \right)+F_{97}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{92}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{57}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{95}\! \left(x \right)
F_{93}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{86}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{98}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{105}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{4}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{64}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{103}\! \left(x \right)
F_{102}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{94}\! \left(x \right)+F_{99}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{101}\! \left(x \right) F_{4}\! \left(x \right)
F_{105}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \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_27(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_7(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_26(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_19(x) + F_4(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_18(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_24(x))
Eq(F_22(x), F_15(x) + F_16(x) + F_23(x))
Eq(F_23(x), F_4(x)*F_7(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_21(x)*F_4(x))
Eq(F_26(x), F_13(x)*F_4(x))
Eq(F_27(x), F_2(x) + F_28(x))
Eq(F_28(x), F_15(x) + F_29(x) + F_72(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_31(x) + F_42(x))
Eq(F_31(x), F_32(x) + F_35(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_1(x) + F_32(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_18(x) + F_38(x))
Eq(F_38(x), F_39(x) + F_40(x))
Eq(F_39(x), F_36(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_38(x)*F_4(x))
Eq(F_42(x), F_43(x) + F_47(x))
Eq(F_43(x), F_15(x) + F_29(x) + F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_2(x) + F_46(x))
Eq(F_46(x), F_44(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_60(x))
Eq(F_50(x), F_51(x) + F_58(x))
Eq(F_51(x), F_15(x) + F_52(x) + F_57(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_55(x))
Eq(F_54(x), F_39(x) + F_4(x))
Eq(F_55(x), F_51(x) + F_56(x))
Eq(F_56(x), F_48(x))
Eq(F_57(x), F_2(x)*F_4(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_4(x)*F_50(x))
Eq(F_60(x), F_61(x) + F_70(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_67(x))
Eq(F_64(x), F_51(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_4(x)*F_64(x))
Eq(F_67(x), F_61(x) + F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_4(x)*F_67(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_4(x)*F_60(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_77(x))
Eq(F_74(x), F_2(x) + F_75(x))
Eq(F_75(x), F_15(x) + F_52(x) + F_76(x))
Eq(F_76(x), F_4(x)*F_74(x))
Eq(F_77(x), F_78(x) + F_98(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_84(x))
Eq(F_81(x), F_2(x) + F_82(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_4(x)*F_81(x))
Eq(F_84(x), F_78(x) + F_85(x))
Eq(F_85(x), 2*F_15(x) + F_86(x) + F_97(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_92(x))
Eq(F_88(x), F_89(x) + F_90(x))
Eq(F_89(x), F_57(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_4(x)*F_88(x))
Eq(F_92(x), F_93(x) + F_95(x))
Eq(F_93(x), 2*F_15(x) + F_86(x) + F_94(x))
Eq(F_94(x), F_4(x)*F_78(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_4(x)*F_92(x))
Eq(F_97(x), F_4(x)*F_84(x))
Eq(F_98(x), F_105(x) + 2*F_15(x) + F_99(x))
Eq(F_99(x), F_100(x)*F_4(x))
Eq(F_100(x), F_101(x) + F_64(x))
Eq(F_101(x), F_102(x) + F_103(x))
Eq(F_102(x), 2*F_15(x) + F_94(x) + F_99(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_101(x)*F_4(x))
Eq(F_105(x), F_4(x)*F_77(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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [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, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 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