0123_0321_1032_2103
Counting sequence:
1, 1, 2, 6, 20, 59, 165, 466, 1334, 3828, 10959, 31335, 89608, 256330, 733300, 2097699, 6000559, 17164882, 49101296, 140457812, 401789357, 1149345637, 3287780920, 9404921096, 26903418240, 76959061359, 220146636187, 629744444862, 1801426876254, 5153104280710, 14740805785097, 42167078963357, 120621801422942, 345046878684260, 987030098116624, 2823466823689161, 8076719159441589, 23104005272200600, 66090580727281916, 189056607692536712, 540809303215160785, 1547021847126670411, 4425361363532148768, 12659047597949134246, 36212067879410034160, 103587086623755325357, 296317916748922214205, 847637583488955740718, 2424725041354119134736, 6936091132214810910430, 19841161110589942099333, 56756992766137526235041, 162357243605871108756138, 464433953714035707496354, 1328544957846593006753138, 3800393340979506384916421, 10871284001989419800988273, 31098048346082607939201694, 88958085425632910582981080, 254470662419915615463155640, 727930662205682676542891683, 2082295239617113153478806493, 5956547360972317552909188198, 17039109434851482245064346548, 48741533096020334585714880626, 139428475275307322838688405873, 398844650193907292080795051675, 1140922287747865072148945729068, 3263685913919040229714224158870, 9335995850987785692683113102130, 26706252019514424630025755338521, 76395052902080750575880287263853, 218533252200539627627814701359224, 625129252525773431970152347036650, 1788224805279620660240715377543512, 5115338854000433115847801039811533, 14632775204767858099775051605486351, 41858050132068709706025110226698056, 119737803413250308814255173300699352, 342518142173231868566097114853215690, 979796475077307737491131046487508035, 2802774552269956694775066073057548201, 8017527507671671609858614696202088074, 22934683520731693480106590684297852392, 65606224324495612721012913111928212776, 187671073212120003782268594148399095203, 536845887463128060609859549330490654911, 1535684226414180592895746988308852231832, 4392929327263024076946497753656036086236, 12566273549210017517375986237350914280222, 35946681394021089803648660561069114150257, 102827930506454259382680681915548466645671, 294146298968195178835733448864471850458058, 841425522915255807402026860733539449040416, 2406955018970898048865337719728164549948942, 6885258772846473165327665481722411058505607, 19695751684353560560437231196894277769215571, 56341039198348511987532314616994840012756774, 161167380094030084192187461533305566684667134, 461030268095142813603872744525863317484074608, 1318808483303951364095796249347441643973278495
Generating function in Maple syntax:
(x^5+x^3+x^2+x-1)/(x^9+x^8+x^6+6*x^5+4*x^4+2*x^3+x^2+2*x-1)
Generating function in latex syntax:
\frac{x^{5}+x^{3}+x^{2}+x -1}{x^{9}+x^{8}+x^{6}+6 x^{5}+4 x^{4}+2 x^{3}+x^{2}+2 x -1}
Generating function in sympy syntax:
(x**5 + x**3 + x**2 + x - 1)/(x**9 + x**8 + x**6 + 6*x**5 + 4*x**4 + 2*x**3 + x**2 + 2*x - 1)
Implicit equation for the generating function in Maple syntax:
(x^9+x^8+x^6+6*x^5+4*x^4+2*x^3+x^2+2*x-1)*F(x)-x^5-x^3-x^2-x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{9}+x^{8}+x^{6}+6 x^{5}+4 x^{4}+2 x^{3}+x^{2}+2 x -1\right) F \! \left(x \right)-x^{5}-x^{3}-x^{2}-x +1 = 0
Explicit closed form in Maple syntax:
-15096011956/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 1)^(-n+7)-15096011956/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 2)^(-n+7)-15096011956/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 3)^(-n+7)-15096011956/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 4)^(-n+7)-15096011956/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 5)^(-n+7)-15096011956/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 6)^(-n+7)-15096011956/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 7)^(-n+7)-15096011956/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 8)^(-n+7)-15096011956/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 9)^(-n+7)-3650272553/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 1)^(-n+6)-3650272553/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 2)^(-n+6)-3650272553/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 3)^(-n+6)-3650272553/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 4)^(-n+6)-3650272553/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 5)^(-n+6)-3650272553/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 6)^(-n+6)-3650272553/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 7)^(-n+6)-3650272553/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 8)^(-n+6)-3650272553/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 9)^(-n+6)+12864084588/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 1)^(-n+5)+12864084588/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 2)^(-n+5)+12864084588/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 3)^(-n+5)+12864084588/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 4)^(-n+5)+12864084588/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 5)^(-n+5)+12864084588/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 6)^(-n+5)+12864084588/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 7)^(-n+5)+12864084588/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 8)^(-n+5)+12864084588/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 9)^(-n+5)+27005976409/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 1)^(-n+4)+27005976409/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 2)^(-n+4)+27005976409/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 3)^(-n+4)+27005976409/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 4)^(-n+4)+27005976409/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 5)^(-n+4)+27005976409/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 6)^(-n+4)+27005976409/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 7)^(-n+4)+27005976409/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 8)^(-n+4)+27005976409/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 9)^(-n+4)-19719062589/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 1)^(-n+3)-19719062589/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 2)^(-n+3)-19719062589/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 3)^(-n+3)-19719062589/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 4)^(-n+3)-19719062589/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 5)^(-n+3)-19719062589/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 6)^(-n+3)-19719062589/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 7)^(-n+3)-19719062589/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 8)^(-n+3)-19719062589/388486311961*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 9)^(-n+3)+2493295711/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 1)^(-n+2)+2493295711/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 2)^(-n+2)+2493295711/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 3)^(-n+2)+2493295711/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 4)^(-n+2)+2493295711/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 5)^(-n+2)+2493295711/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 6)^(-n+2)+2493295711/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 7)^(-n+2)+2493295711/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 8)^(-n+2)+2493295711/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 9)^(-n+2)+246512553577/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 1)^(-n+1)+246512553577/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 2)^(-n+1)+246512553577/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 3)^(-n+1)+246512553577/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 4)^(-n+1)+246512553577/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 5)^(-n+1)+246512553577/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 6)^(-n+1)+246512553577/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 7)^(-n+1)+246512553577/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 8)^(-n+1)+246512553577/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 9)^(-n+1)+82322837216/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 1)^(-n-1)+82322837216/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 2)^(-n-1)+82322837216/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 3)^(-n-1)+82322837216/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 4)^(-n-1)+82322837216/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 5)^(-n-1)+82322837216/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 6)^(-n-1)+82322837216/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 7)^(-n-1)+82322837216/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 8)^(-n-1)+82322837216/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 9)^(-n-1)+261371694072/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 1)^(-n)+261371694072/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 2)^(-n)+261371694072/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 3)^(-n)+261371694072/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 4)^(-n)+261371694072/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 5)^(-n)+261371694072/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 6)^(-n)+261371694072/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 7)^(-n)+261371694072/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 8)^(-n)+261371694072/1942431559805*RootOf(_Z^9+_Z^8+_Z^6+6*_Z^5+4*_Z^4+2*_Z^3+_Z^2+2*_Z-1,index = 9)^(-n)
Explicit closed form in latex syntax:
-\frac{15096011956 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+\textit{\_Z}^{8}+\textit{\_Z}^{6}+6 \textit{\_Z}^{5}+4 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +7}}{1942431559805}-\frac{15096011956 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+\textit{\_Z}^{8}+\textit{\_Z}^{6}+6 \textit{\_Z}^{5}+4 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +7}}{1942431559805}-\frac{15096011956 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+\textit{\_Z}^{8}+\textit{\_Z}^{6}+6 \textit{\_Z}^{5}+4 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +7}}{1942431559805}-\frac{15096011956 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+\textit{\_Z}^{8}+\textit{\_Z}^{6}+6 \textit{\_Z}^{5}+4 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +7}}{1942431559805}-\frac{15096011956 \mathit{RootOf}\! \left(\textit{\_Z}^{9}+\textit{\_Z}^{8}+\textit{\_Z}^{6}+6 \textit{\_Z}^{5}+4 \textit{\_Z}^{4}+2 \textit{\_Z}^{3}+\textit{\_Z}^{2}+2 \textit{\_Z} -1, \mathit{index} =5\right)^{-n +7}}{1942431559805}-\frac{15096011956 \mathit{RootOf}\! 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Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 59
a(6) = 165
a(7) = 466
a(8) = 1334
a(n+1) = -a(n)-a(n+3)-6*a(n+4)-4*a(n+5)-2*a(n+6)-a(n+7)-2*a(n+8)+a(n+9), n >= 9
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 20
a \! \left(5\right) = 59
a \! \left(6\right) = 165
a \! \left(7\right) = 466
a \! \left(8\right) = 1334
a \! \left(n +1\right) = -a \! \left(n \right)-a \! \left(n +3\right)-6 a \! \left(n +4\right)-4 a \! \left(n +5\right)-2 a \! \left(n +6\right)-a \! \left(n +7\right)-2 a \! \left(n +8\right)+a \! \left(n +9\right), \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15095/
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[28,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[4,x]*F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[1,x]+F[4,x]
F[14,x] = F[15,x]+F[17,x]
F[15,x] = F[16,x]
F[16,x] = F[13,x]*F[4,x]
F[17,x] = F[18,x]+F[19,x]+F[23,x]
F[18,x] = 0
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[21,x]+F[4,x]
F[21,x] = F[22,x]
F[22,x] = x^2
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[15,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[4,x]
F[28,x] = F[2,x]+F[29,x]
F[29,x] = F[18,x]+F[30,x]+F[95,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[46,x]
F[32,x] = F[15,x]+F[33,x]
F[33,x] = F[18,x]+F[34,x]+F[43,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[36,x]+F[38,x]
F[36,x] = F[37,x]+F[4,x]
F[37,x] = F[22,x]
F[38,x] = F[39,x]+F[41,x]
F[39,x] = F[40,x]
F[40,x] = F[15,x]*F[4,x]
F[41,x] = F[42,x]
F[42,x] = F[25,x]*F[4,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[15,x]+F[45,x]
F[45,x] = F[18,x]+F[19,x]+F[40,x]
F[46,x] = F[47,x]+F[52,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[2,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[2,x]*F[4,x]
F[52,x] = 2*F[18,x]+F[53,x]+F[89,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[69,x]
F[55,x] = F[50,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[18,x]+F[51,x]+F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[63,x]
F[61,x] = F[4,x]+F[62,x]
F[62,x] = F[18,x]+F[34,x]+F[40,x]
F[63,x] = F[50,x]+F[64,x]
F[64,x] = 2*F[18,x]+F[53,x]+F[65,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[18,x]+F[30,x]+F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[2,x]+F[58,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[65,x]
F[71,x] = F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = 2*F[18,x]+F[74,x]+F[87,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]+F[80,x]
F[76,x] = F[25,x]+F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[39,x]
F[80,x] = F[81,x]+F[84,x]
F[81,x] = F[82,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[50,x]
F[84,x] = F[85,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[70,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[50,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[66,x]+F[91,x]
F[91,x] = 2*F[18,x]+F[65,x]+F[92,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[50,x]+F[94,x]
F[94,x] = F[57,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[100,x]+F[97,x]
F[97,x] = F[2,x]+F[98,x]
F[98,x] = F[18,x]+F[59,x]+F[99,x]
F[99,x] = F[4,x]*F[68,x]
F[100,x] = F[101,x]+F[66,x]
F[101,x] = F[102,x]+F[18,x]+F[74,x]+F[92,x]
F[102,x] = F[103,x]*F[4,x]
F[103,x] = F[66,x]+F[73,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_{28}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{1}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{23}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = x^{2}
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{15}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{2}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{18}\! \left(x \right)+F_{30}\! \left(x \right)+F_{95}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{46}\! \left(x \right)
F_{32}\! \left(x \right) = F_{15}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18}\! \left(x \right)+F_{34}\! \left(x \right)+F_{43}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{38}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{22}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{41}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{15}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{40}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{52}\! \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_{2}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{52}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{53}\! \left(x \right)+F_{89}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{69}\! \left(x \right)
F_{55}\! \left(x \right) = F_{50}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{18}\! \left(x \right)+F_{51}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{63}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{18}\! \left(x \right)+F_{34}\! \left(x \right)+F_{40}\! \left(x \right)
F_{63}\! \left(x \right) = F_{50}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{53}\! \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_{18}\! \left(x \right)+F_{30}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{2}\! \left(x \right)+F_{58}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{65}\! \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) = 2 F_{18}\! \left(x \right)+F_{74}\! \left(x \right)+F_{87}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{80}\! \left(x \right)
F_{76}\! \left(x \right) = F_{25}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{39}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{84}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{50}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{70}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{50}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{66}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{65}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{50}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{57}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{100}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{2}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{18}\! \left(x \right)+F_{59}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{66}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{18}\! \left(x \right)+F_{74}\! \left(x \right)+F_{92}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{4}\! \left(x \right)
F_{103}\! \left(x \right) = F_{66}\! \left(x \right)+F_{73}\! \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_28(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_8(x))
Eq(F_8(x), F_4(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_1(x) + F_4(x))
Eq(F_14(x), F_15(x) + F_17(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_13(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_23(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_21(x) + F_4(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), x**2)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_15(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_4(x))
Eq(F_28(x), F_2(x) + F_29(x))
Eq(F_29(x), F_18(x) + F_30(x) + F_95(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_46(x))
Eq(F_32(x), F_15(x) + F_33(x))
Eq(F_33(x), F_18(x) + F_34(x) + F_43(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_38(x))
Eq(F_36(x), F_37(x) + F_4(x))
Eq(F_37(x), F_22(x))
Eq(F_38(x), F_39(x) + F_41(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_15(x)*F_4(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_25(x)*F_4(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_15(x) + F_45(x))
Eq(F_45(x), F_18(x) + F_19(x) + F_40(x))
Eq(F_46(x), F_47(x) + F_52(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_2(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_2(x)*F_4(x))
Eq(F_52(x), 2*F_18(x) + F_53(x) + F_89(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_69(x))
Eq(F_55(x), F_50(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_18(x) + F_51(x) + F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_63(x))
Eq(F_61(x), F_4(x) + F_62(x))
Eq(F_62(x), F_18(x) + F_34(x) + F_40(x))
Eq(F_63(x), F_50(x) + F_64(x))
Eq(F_64(x), 2*F_18(x) + F_53(x) + F_65(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_18(x) + F_30(x) + F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_2(x) + F_58(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_65(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), 2*F_18(x) + F_74(x) + F_87(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_80(x))
Eq(F_76(x), F_25(x) + F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_39(x))
Eq(F_80(x), F_81(x) + F_84(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_50(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_70(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_50(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_66(x) + F_91(x))
Eq(F_91(x), 2*F_18(x) + F_65(x) + F_92(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_50(x) + F_94(x))
Eq(F_94(x), F_57(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(x), F_100(x) + F_97(x))
Eq(F_97(x), F_2(x) + F_98(x))
Eq(F_98(x), F_18(x) + F_59(x) + F_99(x))
Eq(F_99(x), F_4(x)*F_68(x))
Eq(F_100(x), F_101(x) + F_66(x))
Eq(F_101(x), F_102(x) + F_18(x) + F_74(x) + F_92(x))
Eq(F_102(x), F_103(x)*F_4(x))
Eq(F_103(x), F_66(x) + F_73(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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