0132_0213_0231_0312_2103
Counting sequence:
1, 1, 2, 6, 19, 56, 159, 450, 1279, 3646, 10402, 29676, 84654, 241479, 688843, 1965037, 5605655, 15991309, 45618649, 130137128, 371244725, 1059057530, 3021196180, 8618632528, 24586563730, 70138637415, 200086056466, 570789967393, 1628305316860, 4645103048313, 13251189542951, 37801965369729, 107838513849929, 307633345552119, 877592540399609, 2503527911474912, 7141870190989926, 20373773183778378, 58120719455282685, 165802279213917708, 472987878512945840, 1349303123467884066, 3849187266130316954, 10980662797020162074, 31324782902341246501, 89360910358314308661, 254921872083351890301, 727221338792539605930, 2074560614486440722388, 5918145568066742171060, 16882826522521069236301, 48162017664370553723615, 137392867385620191870005, 391943712574306890326851, 1118106614627722963812861, 3189647802902967405078456, 9099179786134397938234322, 25957434142115409011948280, 74049354236191472258017078, 211242252711735299772679210, 602615509493789792500533773, 1719094772095685905328847338, 4904100191396042837771600000, 13990036545764130376799124431, 39909690853216505249889968867, 113851269708196175551896164510, 324786069174067582125034213592, 926524499901543525169191275812, 2643117209740065258448092333818, 7540079712049144730322796850731, 21509754412157244359909597707102, 61361358571841906488111106196800, 175046923067334883017609134850969, 499360281266694291689677449287158, 1424536267974450776287930559962062, 4063806543898476828752174606714699, 11592912021618162678912565001814026, 33071359989506534169528619885737120, 94343409966020827513649851258308872, 269135560401533012411340780223153710, 767769046070471496791287664607557805, 2190231967951434376630459217561652356, 6248123830973121080736487565839807146, 17824162909871230822875172324656870486, 50847389077458248183706875721157937296, 145053486610726830336235183797338285573, 413797332757367174596033116137932243907, 1180448926792282851612287588892950184202, 3367493114273205641999960006588964998487, 9606523092441163119494273876673944005412, 27404743764568302912251461954257254483893, 78178126838895644510155533385074203567542, 223020494865580539268359751264338035542174, 636215564905840404884916721009515920407388, 1814946403344776639432502936002268573929439, 5177538288459911478597662256762475237293741, 14770079534616434145562953777849788614696944, 42134936972873020057025796042479936695020385, 120199279194611741010364718099099197237408293, 342895178132245304327163391066371414563254714, 978184760958324874739352672690815224110153537
Generating function in Maple syntax:
-(2*x-1)*(x-1)^3/(x^9-2*x^8+x^7+x^6-x^5-7*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}}{x^{9}-2 x^{8}+x^{7}+x^{6}-x^{5}-7 x^{4}+14 x^{3}-13 x^{2}+6 x -1}
Generating function in sympy syntax:
(1 - 2*x)*(x - 1)**3/(x**9 - 2*x**8 + x**7 + x**6 - x**5 - 7*x**4 + 14*x**3 - 13*x**2 + 6*x - 1)
Implicit equation for the generating function in Maple syntax:
(x^9-2*x^8+x^7+x^6-x^5-7*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(x^{9}-2 x^{8}+x^{7}+x^{6}-x^{5}-7 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:
7492119475/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+7)+7492119475/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+7)+7492119475/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+7)+7492119475/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+7)+7492119475/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+7)+7492119475/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+7)+7492119475/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+7)+7492119475/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 8)^(-n+7)+7492119475/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 9)^(-n+7)-67002693/419982361*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+6)-67002693/419982361*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+6)-67002693/419982361*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+6)-67002693/419982361*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+6)-67002693/419982361*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+6)-67002693/419982361*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+6)-67002693/419982361*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+6)-67002693/419982361*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 8)^(-n+6)-67002693/419982361*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 9)^(-n+6)-1772391333/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+5)-1772391333/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+5)-1772391333/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+5)-1772391333/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+5)-1772391333/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+5)-1772391333/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+5)-1772391333/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+5)-1772391333/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 8)^(-n+5)-1772391333/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 9)^(-n+5)+5005336178/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+4)+5005336178/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+4)+5005336178/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+4)+5005336178/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+4)+5005336178/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+4)+5005336178/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+4)+5005336178/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+4)+5005336178/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 8)^(-n+4)+5005336178/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 9)^(-n+4)+104988217/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+3)+104988217/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+3)+104988217/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+3)+104988217/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+3)+104988217/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+3)+104988217/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+3)+104988217/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+3)+104988217/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 8)^(-n+3)+104988217/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 9)^(-n+3)-50683082993/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+2)-50683082993/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+2)-50683082993/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+2)-50683082993/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+2)-50683082993/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+2)-50683082993/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+2)-50683082993/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+2)-50683082993/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 8)^(-n+2)-50683082993/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 9)^(-n+2)+54896873856/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n+1)+54896873856/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n+1)+54896873856/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n+1)+54896873856/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n+1)+54896873856/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n+1)+54896873856/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n+1)+54896873856/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n+1)+54896873856/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 8)^(-n+1)+54896873856/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 9)^(-n+1)+12331756168/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n-1)+12331756168/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n-1)+12331756168/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n-1)+12331756168/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n-1)+12331756168/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n-1)+12331756168/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n-1)+12331756168/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n-1)+12331756168/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 8)^(-n-1)+12331756168/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 9)^(-n-1)-33692734657/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 1)^(-n)-33692734657/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 2)^(-n)-33692734657/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 3)^(-n)-33692734657/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 4)^(-n)-33692734657/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 5)^(-n)-33692734657/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 6)^(-n)-33692734657/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 7)^(-n)-33692734657/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 8)^(-n)-33692734657/49977900959*RootOf(_Z^9-2*_Z^8+_Z^7+_Z^6-_Z^5-7*_Z^4+14*_Z^3-13*_Z^2+6*_Z-1,index = 9)^(-n)
Explicit closed form in latex syntax:
\frac{7492119475 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n +7}}{49977900959}+\frac{7492119475 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n +7}}{49977900959}+\frac{7492119475 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n +7}}{49977900959}+\frac{7492119475 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n +7}}{49977900959}+\frac{7492119475 \mathit{RootOf}\! 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\left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{49977900959}+\frac{12331756168 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{49977900959}+\frac{12331756168 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =6\right)^{-n -1}}{49977900959}+\frac{12331756168 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =7\right)^{-n -1}}{49977900959}+\frac{12331756168 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =8\right)^{-n -1}}{49977900959}+\frac{12331756168 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =9\right)^{-n -1}}{49977900959}-\frac{33692734657 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{49977900959}-\frac{33692734657 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{49977900959}-\frac{33692734657 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{49977900959}-\frac{33692734657 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{49977900959}-\frac{33692734657 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{49977900959}-\frac{33692734657 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =6\right)^{-n}}{49977900959}-\frac{33692734657 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =7\right)^{-n}}{49977900959}-\frac{33692734657 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =8\right)^{-n}}{49977900959}-\frac{33692734657 \mathit{RootOf}\! \left(\textit{\_Z}^{9}-2 \textit{\_Z}^{8}+\textit{\_Z}^{7}+\textit{\_Z}^{6}-\textit{\_Z}^{5}-7 \textit{\_Z}^{4}+14 \textit{\_Z}^{3}-13 \textit{\_Z}^{2}+6 \textit{\_Z} -1, \mathit{index} =9\right)^{-n}}{49977900959}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 56
a(6) = 159
a(7) = 450
a(8) = 1279
a(n+9) = a(n)-2*a(n+1)+a(n+2)+a(n+3)-a(n+4)-7*a(n+5)+14*a(n+6)-13*a(n+7)+6*a(n+8), 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) = 19
a \! \left(5\right) = 56
a \! \left(6\right) = 159
a \! \left(7\right) = 450
a \! \left(8\right) = 1279
a \! \left(n +9\right) = a \! \left(n \right)-2 a \! \left(n +1\right)+a \! \left(n +2\right)+a \! \left(n +3\right)-a \! \left(n +4\right)-7 a \! \left(n +5\right)+14 a \! \left(n +6\right)-13 a \! \left(n +7\right)+6 a \! \left(n +8\right), \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18122/
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[17,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[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[1,x]+F[14,x]
F[17,x] = F[18,x]+F[2,x]
F[18,x] = F[19,x]+F[20,x]+F[80,x]
F[19,x] = 0
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[35,x]
F[22,x] = F[23,x]+F[7,x]
F[23,x] = F[19,x]+F[24,x]+F[29,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[26,x]
F[26,x] = F[11,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[26,x]*F[4,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[13,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[14,x]+F[32,x]
F[35,x] = F[36,x]+F[46,x]
F[36,x] = F[37,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[39,x]+F[42,x]
F[39,x] = F[2,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[39,x]*F[4,x]
F[42,x] = F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[2,x]+F[43,x]
F[46,x] = 2*F[19,x]+F[47,x]+F[52,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[40,x]+F[50,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[49,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]+F[79,x]
F[54,x] = F[55,x]
F[55,x] = F[19,x]+F[56,x]+F[77,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[65,x]
F[58,x] = F[14,x]+F[59,x]
F[59,x] = F[19,x]+F[33,x]+F[60,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = F[4,x]*F[62,x]
F[65,x] = F[43,x]+F[66,x]
F[66,x] = 2*F[19,x]+F[67,x]+F[74,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]
F[69,x] = F[70,x]+F[72,x]
F[70,x] = F[71,x]
F[71,x] = F[2,x]*F[4,x]
F[72,x] = F[73,x]
F[73,x] = F[4,x]*F[69,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[55,x]+F[76,x]
F[76,x] = F[74,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[2,x]+F[55,x]
F[79,x] = F[76,x]
F[80,x] = F[4,x]*F[81,x]
F[81,x] = F[82,x]+F[93,x]
F[82,x] = F[2,x]+F[83,x]
F[83,x] = F[19,x]+F[84,x]+F[92,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[86,x]+F[89,x]
F[86,x] = F[11,x]+F[87,x]
F[87,x] = F[19,x]+F[24,x]+F[88,x]
F[88,x] = F[13,x]*F[4,x]
F[89,x] = F[40,x]+F[90,x]
F[90,x] = 2*F[19,x]+F[47,x]+F[91,x]
F[91,x] = F[4,x]*F[54,x]
F[92,x] = F[4,x]*F[82,x]
F[93,x] = F[55,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_{17}\! \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_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{2}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{80}\! \left(x \right)
F_{19}\! \left(x \right) = 0
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_{35}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{7}\! \left(x \right)
F_{23}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)+F_{29}\! \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_{26}\! \left(x \right) = F_{11}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{13}\! \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_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{14}\! \left(x \right)+F_{32}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{46}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{42}\! \left(x \right)
F_{39}\! \left(x \right) = F_{2}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \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_{2}\! \left(x \right)+F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{47}\! \left(x \right)+F_{52}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{40}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \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_{79}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{19}\! \left(x \right)+F_{56}\! \left(x \right)+F_{77}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{65}\! \left(x \right)
F_{58}\! \left(x \right) = F_{14}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{19}\! \left(x \right)+F_{33}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{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_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{43}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{67}\! \left(x \right)+F_{74}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{72}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{55}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{74}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{2}\! \left(x \right)+F_{55}\! \left(x \right)
F_{79}\! \left(x \right) = F_{76}\! \left(x \right)
F_{80}\! \left(x \right) = F_{4}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{93}\! \left(x \right)
F_{82}\! \left(x \right) = F_{2}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{19}\! \left(x \right)+F_{84}\! \left(x \right)+F_{92}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{89}\! \left(x \right)
F_{86}\! \left(x \right) = F_{11}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{89}\! \left(x \right) = F_{40}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{47}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{93}\! \left(x \right) = F_{55}\! \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_17(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))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_1(x) + F_14(x))
Eq(F_17(x), F_18(x) + F_2(x))
Eq(F_18(x), F_19(x) + F_20(x) + F_80(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_35(x))
Eq(F_22(x), F_23(x) + F_7(x))
Eq(F_23(x), F_19(x) + F_24(x) + F_29(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_11(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_26(x)*F_4(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_13(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_14(x) + F_32(x))
Eq(F_35(x), F_36(x) + F_46(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_39(x) + F_42(x))
Eq(F_39(x), F_2(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_39(x)*F_4(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_2(x) + F_43(x))
Eq(F_46(x), 2*F_19(x) + F_47(x) + F_52(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_40(x) + F_50(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_49(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_79(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_19(x) + F_56(x) + F_77(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_65(x))
Eq(F_58(x), F_14(x) + F_59(x))
Eq(F_59(x), F_19(x) + F_33(x) + F_60(x))
Eq(F_60(x), F_4(x)*F_61(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))
Eq(F_64(x), F_4(x)*F_62(x))
Eq(F_65(x), F_43(x) + F_66(x))
Eq(F_66(x), 2*F_19(x) + F_67(x) + F_74(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_70(x) + F_72(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_2(x)*F_4(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_4(x)*F_69(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_55(x) + F_76(x))
Eq(F_76(x), F_74(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_2(x) + F_55(x))
Eq(F_79(x), F_76(x))
Eq(F_80(x), F_4(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_93(x))
Eq(F_82(x), F_2(x) + F_83(x))
Eq(F_83(x), F_19(x) + F_84(x) + F_92(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_89(x))
Eq(F_86(x), F_11(x) + F_87(x))
Eq(F_87(x), F_19(x) + F_24(x) + F_88(x))
Eq(F_88(x), F_13(x)*F_4(x))
Eq(F_89(x), F_40(x) + F_90(x))
Eq(F_90(x), 2*F_19(x) + F_47(x) + F_91(x))
Eq(F_91(x), F_4(x)*F_54(x))
Eq(F_92(x), F_4(x)*F_82(x))
Eq(F_93(x), F_55(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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3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": 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