0123_0231_1032_1302_2031
Counting sequence:
1, 1, 2, 6, 19, 55, 155, 440, 1260, 3618, 10390, 29837, 85701, 246212, 707433, 2032760, 5841171, 16785030, 48233620, 138605671, 398303516, 1144586068, 3289148468, 9451895903, 27161555862, 78053164283, 224298556713, 644558738671, 1852245535745, 5322732408983, 15295748086752, 43954851680569, 126311507969063, 362976930540966, 1043074021685902, 2997445087131467, 8613652411904325, 24752749684370955, 71131105359606238, 204406953397672026, 587397066215131276, 1687982271153318324, 4850695231207413895, 13939272129269872193, 40056795621461103750, 115109803482012755635, 330786990127668276320, 950570929046811710503, 2731622216469326611988, 7849766603955827897778, 22557597959608791729649, 64822975176264232772220, 186279501843607826117944, 535304846973719692329580, 1538286694765678348971023, 4420520323458798111715788, 12703093640870341456246393, 36504433017166711210364689, 104901504120026106036758981, 301451759611471032380320445, 866271309788633730102081237, 2489373368163821470966763532, 7153624616328734465754048085, 20557119235629589383526048985, 59074269888761622718329435906, 169759649826897123031330909454, 487832329770920894998236045363, 1401866593223959302567911913731, 4028494679965540577879422967703, 11576543349384166295148538675416, 33267105101729250055556562455776, 95598508850949287110730919603826, 274718069593917659543126698361474, 789447645873601665262642346538733, 2268607909543821393345492459648701, 6519218689352841156056702211949760, 18734049255851112948724124994149409, 53835377864198582390825470926113864, 154704830237160142271432800357923531, 444569824680747137529251038987404658, 1277544655287669910201009751561697260, 3671235103340951341609641845044510427, 10549899080410584283563550986076899504, 30316873606258801668619701878732489488, 87120532457463207962862046103840593304, 250355207276550333893857211420796279987, 719436946061905911923133494844482869558, 2067420626035294931994991095485315195879, 5941073874997216532701646919491070710205, 17072654854886730661519766152832376968655, 49061087259115089578732720137849224691777, 140985119391525019148657182768714222154715, 405143974589548876435443946330889074833700, 1164247977762708516016392474348525793122957, 3345658429445447102197863795757310260386343, 9614300853697310404538703944029538919794462, 27628277917398212472094671220145940944592318, 79394409671239685790320367372163009493138275, 228152920203368331186223445921376922215857321, 655635015272124710800412473178047240938805783, 1884075263501856389133385725029642754667465238
Generating function in Maple syntax:
-(x^3+2*x-1)*(x-1)^2/(x^7+x^6+x^5+4*x^4-7*x^3+8*x^2-5*x+1)
Generating function in latex syntax:
-\frac{\left(x^{3}+2 x -1\right) \left(x -1\right)^{2}}{x^{7}+x^{6}+x^{5}+4 x^{4}-7 x^{3}+8 x^{2}-5 x +1}
Generating function in sympy syntax:
(x - 1)**2*(-x**3 - 2*x + 1)/(x**7 + x**6 + x**5 + 4*x**4 - 7*x**3 + 8*x**2 - 5*x + 1)
Implicit equation for the generating function in Maple syntax:
(x^7+x^6+x^5+4*x^4-7*x^3+8*x^2-5*x+1)*F(x)+(x^3+2*x-1)*(x-1)^2 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{7}+x^{6}+x^{5}+4 x^{4}-7 x^{3}+8 x^{2}-5 x +1\right) F \! \left(x \right)+\left(x^{3}+2 x -1\right) \left(x -1\right)^{2} = 0
Explicit closed form in Maple syntax:
-1167731/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n+5)-1167731/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 2)^(-n+5)-1167731/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 3)^(-n+5)-1167731/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 4)^(-n+5)-1167731/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 5)^(-n+5)-1167731/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 6)^(-n+5)-1167731/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 7)^(-n+5)-2294431/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n+4)-2294431/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 2)^(-n+4)-2294431/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 3)^(-n+4)-2294431/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 4)^(-n+4)-2294431/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 5)^(-n+4)-2294431/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 6)^(-n+4)-2294431/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 7)^(-n+4)-2847210/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n+3)-2847210/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 2)^(-n+3)-2847210/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 3)^(-n+3)-2847210/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 4)^(-n+3)-2847210/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 5)^(-n+3)-2847210/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 6)^(-n+3)-2847210/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 7)^(-n+3)-5624240/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n+2)-5624240/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 2)^(-n+2)-5624240/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 3)^(-n+2)-5624240/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 4)^(-n+2)-5624240/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 5)^(-n+2)-5624240/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 6)^(-n+2)-5624240/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 7)^(-n+2)+3807213/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n+1)+3807213/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 2)^(-n+1)+3807213/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 3)^(-n+1)+3807213/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 4)^(-n+1)+3807213/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 5)^(-n+1)+3807213/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 6)^(-n+1)+3807213/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 7)^(-n+1)+2160189/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n-1)+2160189/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 2)^(-n-1)+2160189/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 3)^(-n-1)+2160189/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 4)^(-n-1)+2160189/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 5)^(-n-1)+2160189/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 6)^(-n-1)+2160189/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 7)^(-n-1)-1940788/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n)-1940788/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 2)^(-n)-1940788/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 3)^(-n)-1940788/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 4)^(-n)-1940788/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 5)^(-n)-1940788/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 6)^(-n)-1940788/17591579*RootOf(_Z^7+_Z^6+_Z^5+4*_Z^4-7*_Z^3+8*_Z^2-5*_Z+1,index = 7)^(-n)
Explicit closed form in latex syntax:
-\frac{1167731 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +5}}{17591579}-\frac{1167731 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +5}}{17591579}-\frac{1167731 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +5}}{17591579}-\frac{1167731 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +5}}{17591579}-\frac{1167731 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +5}}{17591579}-\frac{1167731 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +5}}{17591579}-\frac{1167731 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +5}}{17591579}-\frac{2294431 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{17591579}-\frac{2294431 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +4}}{17591579}-\frac{2294431 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +4}}{17591579}-\frac{2294431 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +4}}{17591579}-\frac{2294431 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +4}}{17591579}-\frac{2294431 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +4}}{17591579}-\frac{2294431 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +4}}{17591579}-\frac{2847210 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{17591579}-\frac{2847210 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{17591579}-\frac{2847210 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{17591579}-\frac{2847210 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{17591579}-\frac{2847210 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{17591579}-\frac{2847210 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +3}}{17591579}-\frac{2847210 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +3}}{17591579}-\frac{5624240 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{17591579}-\frac{5624240 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{17591579}-\frac{5624240 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{17591579}-\frac{5624240 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{17591579}-\frac{5624240 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{17591579}-\frac{5624240 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{17591579}-\frac{5624240 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +2}}{17591579}+\frac{3807213 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{17591579}+\frac{3807213 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{17591579}+\frac{3807213 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{17591579}+\frac{3807213 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{17591579}+\frac{3807213 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{17591579}+\frac{3807213 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{17591579}+\frac{3807213 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +1}}{17591579}+\frac{2160189 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{17591579}+\frac{2160189 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{17591579}+\frac{2160189 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{17591579}+\frac{2160189 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{17591579}+\frac{2160189 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{17591579}+\frac{2160189 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{17591579}+\frac{2160189 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =7\right)^{-n -1}}{17591579}-\frac{1940788 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{17591579}-\frac{1940788 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{17591579}-\frac{1940788 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{17591579}-\frac{1940788 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{17591579}-\frac{1940788 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{17591579}-\frac{1940788 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{17591579}-\frac{1940788 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+\textit{\_Z}^{6}+\textit{\_Z}^{5}+4 \textit{\_Z}^{4}-7 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =7\right)^{-n}}{17591579}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 55
a(6) = 155
a(n+7) = -a(n)-a(n+1)-a(n+2)-4*a(n+3)+7*a(n+4)-8*a(n+5)+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) = 19
a \! \left(5\right) = 55
a \! \left(6\right) = 155
a \! \left(n +7\right) = -a \! \left(n \right)-a \! \left(n +1\right)-a \! \left(n +2\right)-4 a \! \left(n +3\right)+7 a \! \left(n +4\right)-8 a \! \left(n +5\right)+5 a \! \left(n +6\right), \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/17229/
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[20,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[15,x] = F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[4,x]
F[18,x] = F[19,x]
F[19,x] = F[15,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[22,x]+F[23,x]+F[64,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[30,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[1,x]+F[4,x]
F[29,x] = F[15,x]
F[30,x] = F[31,x]+F[58,x]
F[31,x] = F[22,x]+F[23,x]+F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[2,x]+F[34,x]
F[34,x] = F[22,x]+F[35,x]+F[57,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[19,x]+F[4,x]
F[38,x] = F[34,x]+F[39,x]
F[39,x] = 2*F[22,x]+F[40,x]+F[49,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[45,x]
F[42,x] = F[43,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[4,x]
F[45,x] = F[46,x]
F[46,x] = 2*F[22,x]+F[40,x]+F[47,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[34,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[34,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[34,x]
F[56,x] = F[53,x]
F[57,x] = F[2,x]*F[4,x]
F[58,x] = 2*F[22,x]+F[49,x]+F[59,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[43,x]
F[62,x] = F[63,x]
F[63,x] = 2*F[22,x]+F[47,x]+F[59,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]+F[71,x]
F[66,x] = F[2,x]+F[67,x]
F[67,x] = F[22,x]+F[35,x]+F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[2,x]+F[70,x]
F[70,x] = F[68,x]
F[71,x] = F[72,x]+F[81,x]
F[72,x] = F[73,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[69,x]+F[75,x]
F[75,x] = F[72,x]+F[76,x]
F[76,x] = F[77,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = F[57,x]
F[80,x] = F[77,x]
F[81,x] = F[53,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_{20}\! \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_{15}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{15}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{64}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{30}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{15}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{58}\! \left(x \right)
F_{31}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{2}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{22}\! \left(x \right)+F_{35}\! \left(x \right)+F_{57}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{19}\! \left(x \right)+F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{34}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{40}\! \left(x \right)+F_{49}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{45}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{40}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{34}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{34}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \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_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{34}\! \left(x \right)
F_{56}\! \left(x \right) = F_{53}\! \left(x \right)
F_{57}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{58}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{49}\! \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_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{43}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = 2 F_{22}\! \left(x \right)+F_{47}\! \left(x \right)+F_{59}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{71}\! \left(x \right)
F_{66}\! \left(x \right) = F_{2}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{22}\! \left(x \right)+F_{35}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{2}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{81}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{69}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{72}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{57}\! \left(x \right)
F_{80}\! \left(x \right) = F_{77}\! \left(x \right)
F_{81}\! \left(x \right) = F_{53}\! \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_20(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))
Eq(F_15(x), F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_4(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_15(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_64(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_30(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_1(x) + F_4(x))
Eq(F_29(x), F_15(x))
Eq(F_30(x), F_31(x) + F_58(x))
Eq(F_31(x), F_22(x) + F_23(x) + F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_2(x) + F_34(x))
Eq(F_34(x), F_22(x) + F_35(x) + F_57(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_19(x) + F_4(x))
Eq(F_38(x), F_34(x) + F_39(x))
Eq(F_39(x), 2*F_22(x) + F_40(x) + F_49(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_45(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_4(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), 2*F_22(x) + F_40(x) + F_47(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_34(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_34(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_34(x))
Eq(F_56(x), F_53(x))
Eq(F_57(x), F_2(x)*F_4(x))
Eq(F_58(x), 2*F_22(x) + F_49(x) + F_59(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_43(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), 2*F_22(x) + F_47(x) + F_59(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_71(x))
Eq(F_66(x), F_2(x) + F_67(x))
Eq(F_67(x), F_22(x) + F_35(x) + F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_2(x) + F_70(x))
Eq(F_70(x), F_68(x))
Eq(F_71(x), F_72(x) + F_81(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_69(x) + F_75(x))
Eq(F_75(x), F_72(x) + F_76(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), F_57(x))
Eq(F_80(x), F_77(x))
Eq(F_81(x), F_53(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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