0123_0321_1302_2103
Counting sequence:
1, 1, 2, 6, 20, 57, 140, 355, 965, 2641, 7069, 18687, 49641, 132789, 355338, 948353, 2528219, 6744569, 18005251, 48065382, 128273466, 342294447, 913483184, 2437988961, 6506665122, 17364853567, 46342618888, 123678611797, 330074210331, 880902364602, 2350944942691, 6274179401026, 16744490780589, 44687621005057, 119262087232013, 318285914492080, 849439448915184, 2266978984992217, 6050100476540175, 16146472756255088, 43091610440439050, 115002633820532453, 306918350431032918, 819101886287650684, 2186014280471247961, 5834021990279160419, 15569803412222260580, 41552599409866843759, 110895331986332122740, 295956807132513349828, 789847778874384294024, 2107941087423793787753, 5625660725655300762864, 15013730122596939086910, 40068554285772813650396, 106934721044583926790907, 285386752002576705755949, 761638478358872453445365, 2032656273098339389997416, 5424741057512783950954001, 14477516897690371770986831, 38637511597545449273386922, 103115562772474114352444686, 275194204964229338430991730, 734436669011198295501159618, 1960060244939543931636248427, 5230997206288531333408385303, 13960454451770010340844396103, 37257578395500388250718109397, 99432805192150057541625804856, 265365683282677372310676292649, 708206368391221370550090047786, 1890056973552285963794745563984, 5044172889024654826245683226209, 13461858817171376454251542044558, 35926929310405870485011695037990, 95881576772182928173913502625602, 255888185847747509326968568675186, 682912879207551281236404257686734, 1822553858993065921770740523345847, 4864020975537909808136471777012744, 12981070454369919960131138420967547, 34643804167123367294337027409921026, 92457179967462836005367281753079820, 246749175878557017804585234195780995, 658522743373457068685041942414026771, 1757461608518341693328132413364303243, 4690303161882216245554207027109783556, 12517453379200074641462447323457572020, 33406505654864556433393169946212801210, 89155085004983258182287906007809552186, 237936564343668036616646446382962048824, 635003697753236311496437699063706052160, 1694694118462059045218309959872905043111, 4522789655102064730441209998880331106553, 12070394321579287366024044886247763965866, 32213397082055025017893027334479675327632, 85970923891936150627113893857464266924966, 229438693969669832503620366334660423421533, 612324631484453565974586953411544551253418, 1634168360338280444457042585456435624067587
Generating function in Maple syntax:
-1/(x^7+11*x^6+16*x^5+9*x^4+3*x^3+x^2+x-1)
Generating function in latex syntax:
-\frac{1}{x^{7}+11 x^{6}+16 x^{5}+9 x^{4}+3 x^{3}+x^{2}+x -1}
Generating function in sympy syntax:
-1/(x**7 + 11*x**6 + 16*x**5 + 9*x**4 + 3*x**3 + x**2 + x - 1)
Implicit equation for the generating function in Maple syntax:
(x^7+11*x^6+16*x^5+9*x^4+3*x^3+x^2+x-1)*F(x)+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{7}+11 x^{6}+16 x^{5}+9 x^{4}+3 x^{3}+x^{2}+x -1\right) F \! \left(x \right)+1 = 0
Explicit closed form in Maple syntax:
1011882922/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 1)^(-n+5)+1011882922/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 2)^(-n+5)+1011882922/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 3)^(-n+5)+1011882922/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 4)^(-n+5)+1011882922/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 5)^(-n+5)+1011882922/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 6)^(-n+5)+1011882922/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 7)^(-n+5)+16205286681/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 1)^(-n+4)+16205286681/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 2)^(-n+4)+16205286681/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 3)^(-n+4)+16205286681/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 4)^(-n+4)+16205286681/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 5)^(-n+4)+16205286681/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 6)^(-n+4)+16205286681/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 7)^(-n+4)+72580036121/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 1)^(-n+3)+72580036121/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 2)^(-n+3)+72580036121/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 3)^(-n+3)+72580036121/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 4)^(-n+3)+72580036121/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 5)^(-n+3)+72580036121/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 6)^(-n+3)+72580036121/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 7)^(-n+3)+99275530671/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 1)^(-n+2)+99275530671/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 2)^(-n+2)+99275530671/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 3)^(-n+2)+99275530671/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 4)^(-n+2)+99275530671/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 5)^(-n+2)+99275530671/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 6)^(-n+2)+99275530671/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 7)^(-n+2)+94288491620/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 1)^(-n+1)+94288491620/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 2)^(-n+1)+94288491620/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 3)^(-n+1)+94288491620/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 4)^(-n+1)+94288491620/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 5)^(-n+1)+94288491620/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 6)^(-n+1)+94288491620/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 7)^(-n+1)+29325756146/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 1)^(-n-1)+29325756146/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 2)^(-n-1)+29325756146/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 3)^(-n-1)+29325756146/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 4)^(-n-1)+29325756146/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 5)^(-n-1)+29325756146/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 6)^(-n-1)+29325756146/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 7)^(-n-1)+127130177931/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 1)^(-n)+127130177931/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 2)^(-n)+127130177931/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 3)^(-n)+127130177931/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 4)^(-n)+127130177931/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 5)^(-n)+127130177931/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 6)^(-n)+127130177931/677934931013*RootOf(_Z^7+11*_Z^6+16*_Z^5+9*_Z^4+3*_Z^3+_Z^2+_Z-1,index = 7)^(-n)
Explicit closed form in latex syntax:
\frac{1011882922 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n +5}}{677934931013}+\frac{1011882922 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{-n +5}}{677934931013}+\frac{1011882922 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{-n +5}}{677934931013}+\frac{1011882922 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)^{-n +5}}{677934931013}+\frac{1011882922 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =5\right)^{-n +5}}{677934931013}+\frac{1011882922 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =6\right)^{-n +5}}{677934931013}+\frac{1011882922 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =7\right)^{-n +5}}{677934931013}+\frac{16205286681 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n +4}}{677934931013}+\frac{16205286681 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{-n +4}}{677934931013}+\frac{16205286681 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{-n +4}}{677934931013}+\frac{16205286681 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)^{-n +4}}{677934931013}+\frac{16205286681 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =5\right)^{-n +4}}{677934931013}+\frac{16205286681 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =6\right)^{-n +4}}{677934931013}+\frac{16205286681 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =7\right)^{-n +4}}{677934931013}+\frac{72580036121 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n +3}}{677934931013}+\frac{72580036121 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{-n +3}}{677934931013}+\frac{72580036121 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{-n +3}}{677934931013}+\frac{72580036121 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)^{-n +3}}{677934931013}+\frac{72580036121 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =5\right)^{-n +3}}{677934931013}+\frac{72580036121 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =6\right)^{-n +3}}{677934931013}+\frac{72580036121 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =7\right)^{-n +3}}{677934931013}+\frac{99275530671 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n +2}}{677934931013}+\frac{99275530671 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{-n +2}}{677934931013}+\frac{99275530671 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{-n +2}}{677934931013}+\frac{99275530671 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)^{-n +2}}{677934931013}+\frac{99275530671 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =5\right)^{-n +2}}{677934931013}+\frac{99275530671 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =6\right)^{-n +2}}{677934931013}+\frac{99275530671 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =7\right)^{-n +2}}{677934931013}+\frac{94288491620 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n +1}}{677934931013}+\frac{94288491620 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{-n +1}}{677934931013}+\frac{94288491620 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{-n +1}}{677934931013}+\frac{94288491620 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)^{-n +1}}{677934931013}+\frac{94288491620 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =5\right)^{-n +1}}{677934931013}+\frac{94288491620 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =6\right)^{-n +1}}{677934931013}+\frac{94288491620 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =7\right)^{-n +1}}{677934931013}+\frac{29325756146 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n -1}}{677934931013}+\frac{29325756146 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{-n -1}}{677934931013}+\frac{29325756146 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{-n -1}}{677934931013}+\frac{29325756146 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)^{-n -1}}{677934931013}+\frac{29325756146 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =5\right)^{-n -1}}{677934931013}+\frac{29325756146 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =6\right)^{-n -1}}{677934931013}+\frac{29325756146 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =7\right)^{-n -1}}{677934931013}+\frac{127130177931 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =1\right)^{-n}}{677934931013}+\frac{127130177931 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =2\right)^{-n}}{677934931013}+\frac{127130177931 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =3\right)^{-n}}{677934931013}+\frac{127130177931 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =4\right)^{-n}}{677934931013}+\frac{127130177931 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =5\right)^{-n}}{677934931013}+\frac{127130177931 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =6\right)^{-n}}{677934931013}+\frac{127130177931 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+11 \textit{\_Z}^{6}+16 \textit{\_Z}^{5}+9 \textit{\_Z}^{4}+3 \textit{\_Z}^{3}+\textit{\_Z}^{2}+\textit{\_Z} -1, \mathit{index} =7\right)^{-n}}{677934931013}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 57
a(6) = 140
a(n+7) = a(n)+11*a(n+1)+16*a(n+2)+9*a(n+3)+3*a(n+4)+a(n+5)+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) = 57
a \! \left(6\right) = 140
a \! \left(n +7\right) = a \! \left(n \right)+11 a \! \left(n +1\right)+16 a \! \left(n +2\right)+9 a \! \left(n +3\right)+3 a \! \left(n +4\right)+a \! \left(n +5\right)+a \! \left(n +6\right), \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15116/
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[26,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[24,x]
F[18,x] = 0
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[11,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[4,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[15,x]
F[26,x] = F[2,x]+F[27,x]
F[27,x] = F[18,x]+F[28,x]+F[68,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]+F[39,x]
F[30,x] = F[31,x]+F[7,x]
F[31,x] = F[18,x]+F[32,x]+F[37,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[36,x]
F[34,x] = F[11,x]+F[35,x]
F[35,x] = F[22,x]
F[36,x] = F[24,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[14,x]
F[39,x] = F[40,x]+F[60,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]+F[49,x]
F[43,x] = F[2,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[2,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[2,x]*F[4,x]
F[49,x] = F[50,x]+F[52,x]
F[50,x] = F[51,x]
F[51,x] = F[4,x]*F[46,x]
F[52,x] = 2*F[18,x]+F[53,x]+F[58,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[44,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[47,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[50,x]
F[60,x] = 2*F[18,x]+F[61,x]+F[66,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[63,x]+F[65,x]
F[63,x] = F[44,x]+F[64,x]
F[64,x] = F[56,x]
F[65,x] = F[58,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[49,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]+F[78,x]
F[70,x] = F[2,x]+F[71,x]
F[71,x] = F[18,x]+F[45,x]+F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]+F[76,x]
F[74,x] = F[11,x]+F[75,x]
F[75,x] = F[18,x]+F[24,x]+F[32,x]
F[76,x] = F[44,x]+F[77,x]
F[77,x] = 2*F[18,x]+F[58,x]+F[61,x]
F[78,x] = F[50,x]+F[79,x]
F[79,x] = 2*F[18,x]+F[53,x]+F[58,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_{26}\! \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_{24}\! \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_{11}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{15}\! \left(x \right)
F_{26}\! \left(x \right) = F_{2}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{18}\! \left(x \right)+F_{28}\! \left(x \right)+F_{68}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{39}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{7}\! \left(x \right)
F_{31}\! \left(x \right) = F_{18}\! \left(x \right)+F_{32}\! \left(x \right)+F_{37}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{36}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{22}\! \left(x \right)
F_{36}\! \left(x \right) = F_{24}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{14}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{60}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{49}\! \left(x \right)
F_{43}\! \left(x \right) = F_{2}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{2}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{52}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{52}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{53}\! \left(x \right)+F_{58}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{44}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{47}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{50}\! \left(x \right)
F_{60}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{61}\! \left(x \right)+F_{66}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{65}\! \left(x \right)
F_{63}\! \left(x \right) = F_{44}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{56}\! \left(x \right)
F_{65}\! \left(x \right) = F_{58}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{49}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{78}\! \left(x \right)
F_{70}\! \left(x \right) = F_{2}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{18}\! \left(x \right)+F_{45}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{76}\! \left(x \right)
F_{74}\! \left(x \right) = F_{11}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{18}\! \left(x \right)+F_{24}\! \left(x \right)+F_{32}\! \left(x \right)
F_{76}\! \left(x \right) = F_{44}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{58}\! \left(x \right)+F_{61}\! \left(x \right)
F_{78}\! \left(x \right) = F_{50}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{53}\! \left(x \right)+F_{58}\! \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_26(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_24(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_11(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_4(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_15(x))
Eq(F_26(x), F_2(x) + F_27(x))
Eq(F_27(x), F_18(x) + F_28(x) + F_68(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_39(x))
Eq(F_30(x), F_31(x) + F_7(x))
Eq(F_31(x), F_18(x) + F_32(x) + F_37(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_36(x))
Eq(F_34(x), F_11(x) + F_35(x))
Eq(F_35(x), F_22(x))
Eq(F_36(x), F_24(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_14(x))
Eq(F_39(x), F_40(x) + F_60(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_49(x))
Eq(F_43(x), F_2(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_2(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_2(x)*F_4(x))
Eq(F_49(x), F_50(x) + F_52(x))
Eq(F_50(x), F_51(x))
Eq(F_51(x), F_4(x)*F_46(x))
Eq(F_52(x), 2*F_18(x) + F_53(x) + F_58(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_44(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_47(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_50(x))
Eq(F_60(x), 2*F_18(x) + F_61(x) + F_66(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_65(x))
Eq(F_63(x), F_44(x) + F_64(x))
Eq(F_64(x), F_56(x))
Eq(F_65(x), F_58(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_49(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_78(x))
Eq(F_70(x), F_2(x) + F_71(x))
Eq(F_71(x), F_18(x) + F_45(x) + F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_76(x))
Eq(F_74(x), F_11(x) + F_75(x))
Eq(F_75(x), F_18(x) + F_24(x) + F_32(x))
Eq(F_76(x), F_44(x) + F_77(x))
Eq(F_77(x), 2*F_18(x) + F_58(x) + F_61(x))
Eq(F_78(x), F_50(x) + F_79(x))
Eq(F_79(x), 2*F_18(x) + F_53(x) + F_58(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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