0132_0231_0321_2103
Counting sequence:
1, 1, 2, 6, 20, 63, 186, 535, 1539, 4460, 12986, 37846, 110219, 320764, 933263, 2715419, 7901498, 22993410, 66911374, 194711801, 566606010, 1648804147, 4797967137, 13961945522, 40628877718, 118228919534, 344042868685, 1001155096594, 2913333189327, 8477717784575, 24669921037724, 71788778825596, 208903334370358, 607902847159513, 1768980243246880, 5147682915415225, 14979612973672913, 43590253820955714, 126846416633167180, 369119516454370404, 1074127445152412941, 3125680753760708446, 9095643369429964069, 26468067221674242813, 77021333620741881280, 224129921653748262768, 652211788851426048248, 1897918021734912551895, 5522888237836477966148, 16071449945846460351589, 46767468802344916139303, 136092023155857508818668, 396023972238708612620356, 1152418657250116269253236, 3353505986192287488275623, 9758608409085058729822776, 28397276901835592107949945, 82635279707379091178667633, 240466347386829251601860266, 699750329766230861693224622, 2036253843122032660433156172, 5925441600026730758893517103, 17242868944814141057792314482, 50176265250288633575788024303, 146011525258650061012906597659, 424889445278806745067583139564, 1236416374594628339827739893234, 3597936988909186027038334277038, 10469895774718366411344545511139, 30467103195906564183509414068188, 88658416198511695790661246678407, 257993505726025207052437358676851, 750753869184524767582639461074210, 2184672713018132253369594866572114, 6357336350714058637420773510182486, 18499670561763868037067270886054385, 53833522722980101078643915081439682, 156654041978210114631250606122137363, 455858870585021809122373884039447129, 1326536534052257272879701809560732410, 3860184126541364914172289796797990638, 11233027593505323679381968685541131342, 32687795395269696461209048833828389205, 95120568244735023502781782318040989914, 276798187023363233412148129934794235703, 805474964597486801285278894461853715391, 2343909566642361387887375303462824700804, 6820711130783572665067167984578022508212, 19848078181718246141789530943993845339198, 57757351096372087287999807040770438204345, 168072272545875492900497838759606824344120, 489085601443197293902995064316326934537569, 1423225389385764773604098706085492234332569, 4141545985028374998019631326712590725961106, 12051782714126033422669190171744593873065540, 35070349843649493979499096307094330338134156, 102053734898020656872254432235825366148444405, 296973507623033060231165451475584192183942830, 864184581956325764508124765085398381460940285, 2514752907316595491953418731847983736284331877, 7317860462797369691692830792050643919612689816
Generating function in Maple syntax:
(x^2+x-1)*(x-1)^3/(x^7+2*x^6+3*x^5-3*x^4-5*x^3+8*x^2-5*x+1)
Generating function in latex syntax:
\frac{\left(x^{2}+x -1\right) \left(x -1\right)^{3}}{x^{7}+2 x^{6}+3 x^{5}-3 x^{4}-5 x^{3}+8 x^{2}-5 x +1}
Generating function in sympy syntax:
(x - 1)**3*(x**2 + x - 1)/(x**7 + 2*x**6 + 3*x**5 - 3*x**4 - 5*x**3 + 8*x**2 - 5*x + 1)
Implicit equation for the generating function in Maple syntax:
(x^7+2*x^6+3*x^5-3*x^4-5*x^3+8*x^2-5*x+1)*F(x)-(x^2+x-1)*(x-1)^3 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{7}+2 x^{6}+3 x^{5}-3 x^{4}-5 x^{3}+8 x^{2}-5 x +1\right) F \! \left(x \right)-\left(x^{2}+x -1\right) \left(x -1\right)^{3} = 0
Explicit closed form in Maple syntax:
-7248725/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n+5)-7248725/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 2)^(-n+5)-7248725/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 3)^(-n+5)-7248725/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 4)^(-n+5)-7248725/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 5)^(-n+5)-7248725/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 6)^(-n+5)-7248725/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 7)^(-n+5)-20683503/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n+4)-20683503/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 2)^(-n+4)-20683503/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 3)^(-n+4)-20683503/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 4)^(-n+4)-20683503/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 5)^(-n+4)-20683503/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 6)^(-n+4)-20683503/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 7)^(-n+4)-18625293/76342861*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n+3)-18625293/76342861*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 2)^(-n+3)-18625293/76342861*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 3)^(-n+3)-18625293/76342861*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 4)^(-n+3)-18625293/76342861*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 5)^(-n+3)-18625293/76342861*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 6)^(-n+3)-18625293/76342861*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 7)^(-n+3)-8988891/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n+2)-8988891/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 2)^(-n+2)-8988891/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 3)^(-n+2)-8988891/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 4)^(-n+2)-8988891/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 5)^(-n+2)-8988891/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 6)^(-n+2)-8988891/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 7)^(-n+2)+2437208/10906123*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n+1)+2437208/10906123*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 2)^(-n+1)+2437208/10906123*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 3)^(-n+1)+2437208/10906123*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 4)^(-n+1)+2437208/10906123*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 5)^(-n+1)+2437208/10906123*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 6)^(-n+1)+2437208/10906123*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 7)^(-n+1)+18047609/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n-1)+18047609/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 2)^(-n-1)+18047609/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 3)^(-n-1)+18047609/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 4)^(-n-1)+18047609/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 5)^(-n-1)+18047609/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 6)^(-n-1)+18047609/152685722*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 7)^(-n-1)-7855859/76342861*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 1)^(-n)-7855859/76342861*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 2)^(-n)-7855859/76342861*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 3)^(-n)-7855859/76342861*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 4)^(-n)-7855859/76342861*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 5)^(-n)-7855859/76342861*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 6)^(-n)-7855859/76342861*RootOf(_Z^7+2*_Z^6+3*_Z^5-3*_Z^4-5*_Z^3+8*_Z^2-5*_Z+1,index = 7)^(-n)
Explicit closed form in latex syntax:
-\frac{7248725 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +5}}{152685722}-\frac{7248725 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +5}}{152685722}-\frac{7248725 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +5}}{152685722}-\frac{7248725 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +5}}{152685722}-\frac{7248725 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +5}}{152685722}-\frac{7248725 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +5}}{152685722}-\frac{7248725 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +5}}{152685722}-\frac{20683503 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +4}}{152685722}-\frac{20683503 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +4}}{152685722}-\frac{20683503 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +4}}{152685722}-\frac{20683503 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +4}}{152685722}-\frac{20683503 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +4}}{152685722}-\frac{20683503 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +4}}{152685722}-\frac{20683503 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +4}}{152685722}-\frac{18625293 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +3}}{76342861}-\frac{18625293 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +3}}{76342861}-\frac{18625293 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +3}}{76342861}-\frac{18625293 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +3}}{76342861}-\frac{18625293 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +3}}{76342861}-\frac{18625293 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +3}}{76342861}-\frac{18625293 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +3}}{76342861}-\frac{8988891 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +2}}{152685722}-\frac{8988891 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +2}}{152685722}-\frac{8988891 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +2}}{152685722}-\frac{8988891 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +2}}{152685722}-\frac{8988891 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +2}}{152685722}-\frac{8988891 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +2}}{152685722}-\frac{8988891 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +2}}{152685722}+\frac{2437208 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n +1}}{10906123}+\frac{2437208 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n +1}}{10906123}+\frac{2437208 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n +1}}{10906123}+\frac{2437208 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)^{-n +1}}{10906123}+\frac{2437208 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =5\right)^{-n +1}}{10906123}+\frac{2437208 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =6\right)^{-n +1}}{10906123}+\frac{2437208 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =7\right)^{-n +1}}{10906123}+\frac{18047609 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n -1}}{152685722}+\frac{18047609 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n -1}}{152685722}+\frac{18047609 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n -1}}{152685722}+\frac{18047609 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)^{-n -1}}{152685722}+\frac{18047609 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =5\right)^{-n -1}}{152685722}+\frac{18047609 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =6\right)^{-n -1}}{152685722}+\frac{18047609 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =7\right)^{-n -1}}{152685722}-\frac{7855859 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =1\right)^{-n}}{76342861}-\frac{7855859 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =2\right)^{-n}}{76342861}-\frac{7855859 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =3\right)^{-n}}{76342861}-\frac{7855859 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =4\right)^{-n}}{76342861}-\frac{7855859 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =5\right)^{-n}}{76342861}-\frac{7855859 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =6\right)^{-n}}{76342861}-\frac{7855859 \mathit{RootOf}\! \left(\textit{\_Z}^{7}+2 \textit{\_Z}^{6}+3 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-5 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}-5 \textit{\_Z} +1, \mathit{index} =7\right)^{-n}}{76342861}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 63
a(6) = 186
a(n+7) = -a(n)-2*a(n+1)-3*a(n+2)+3*a(n+3)+5*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) = 20
a \! \left(5\right) = 63
a \! \left(6\right) = 186
a \! \left(n +7\right) = -a \! \left(n \right)-2 a \! \left(n +1\right)-3 a \! \left(n +2\right)+3 a \! \left(n +3\right)+5 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/15314/
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[11,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[16,x]*F[4,x]
F[16,x] = F[11,x]+F[14,x]
F[17,x] = F[18,x]+F[2,x]
F[18,x] = F[19,x]+F[20,x]+F[67,x]
F[19,x] = 0
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[32,x]
F[22,x] = F[23,x]+F[7,x]
F[23,x] = F[19,x]+F[24,x]+F[26,x]
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[16,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[13,x]+F[28,x]
F[28,x] = F[14,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[14,x]+F[29,x]
F[32,x] = F[33,x]+F[43,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[2,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[36,x]*F[4,x]
F[39,x] = F[37,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[37,x]+F[40,x]
F[43,x] = 2*F[19,x]+F[44,x]+F[49,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]
F[46,x] = F[37,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[46,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[63,x]
F[51,x] = F[47,x]+F[52,x]
F[52,x] = F[19,x]+F[53,x]+F[61,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[58,x]
F[55,x] = F[11,x]+F[56,x]
F[56,x] = F[19,x]+F[24,x]+F[57,x]
F[57,x] = F[13,x]*F[4,x]
F[58,x] = F[37,x]+F[59,x]
F[59,x] = 2*F[19,x]+F[44,x]+F[60,x]
F[60,x] = F[4,x]*F[51,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[2,x]+F[52,x]
F[63,x] = F[47,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[40,x]+F[64,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[62,x]+F[69,x]
F[69,x] = F[52,x]+F[70,x]
F[70,x] = 2*F[19,x]+F[48,x]+F[71,x]
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[73,x]+F[77,x]
F[73,x] = F[14,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[4,x]*F[76,x]
F[76,x] = F[31,x]
F[77,x] = F[40,x]+F[78,x]
F[78,x] = F[79,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[66,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_{11}\! \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_{11}\! \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_{67}\! \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_{32}\! \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_{26}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{16}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{13}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{14}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{14}\! \left(x \right)+F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{43}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{37}\! \left(x \right)+F_{40}\! \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_{37}\! \left(x \right)+F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{44}\! \left(x \right)+F_{49}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{37}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \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_{63}\! \left(x \right)
F_{51}\! \left(x \right) = F_{47}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{19}\! \left(x \right)+F_{53}\! \left(x \right)+F_{61}\! \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_{58}\! \left(x \right)
F_{55}\! \left(x \right) = F_{11}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{19}\! \left(x \right)+F_{24}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{58}\! \left(x \right) = F_{37}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{44}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{2}\! \left(x \right)+F_{52}\! \left(x \right)
F_{63}\! \left(x \right) = F_{47}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{40}\! \left(x \right)+F_{64}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{62}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{52}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{48}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{77}\! \left(x \right)
F_{73}\! \left(x \right) = F_{14}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{31}\! \left(x \right)
F_{77}\! \left(x \right) = F_{40}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{66}\! \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_11(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_11(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_67(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_32(x))
Eq(F_22(x), F_23(x) + F_7(x))
Eq(F_23(x), F_19(x) + F_24(x) + F_26(x))
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_16(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_13(x) + F_28(x))
Eq(F_28(x), F_14(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_14(x) + F_29(x))
Eq(F_32(x), F_33(x) + F_43(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_2(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_36(x)*F_4(x))
Eq(F_39(x), F_37(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_37(x) + F_40(x))
Eq(F_43(x), 2*F_19(x) + F_44(x) + F_49(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_37(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_4(x)*F_46(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_63(x))
Eq(F_51(x), F_47(x) + F_52(x))
Eq(F_52(x), F_19(x) + F_53(x) + F_61(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_58(x))
Eq(F_55(x), F_11(x) + F_56(x))
Eq(F_56(x), F_19(x) + F_24(x) + F_57(x))
Eq(F_57(x), F_13(x)*F_4(x))
Eq(F_58(x), F_37(x) + F_59(x))
Eq(F_59(x), 2*F_19(x) + F_44(x) + F_60(x))
Eq(F_60(x), F_4(x)*F_51(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_2(x) + F_52(x))
Eq(F_63(x), F_47(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_40(x) + F_64(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_62(x) + F_69(x))
Eq(F_69(x), F_52(x) + F_70(x))
Eq(F_70(x), 2*F_19(x) + F_48(x) + F_71(x))
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_77(x))
Eq(F_73(x), F_14(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_4(x)*F_76(x))
Eq(F_76(x), F_31(x))
Eq(F_77(x), F_40(x) + F_78(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_66(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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