0123_0132_0321_1302_3102
Counting sequence:
1, 1, 2, 6, 19, 51, 124, 296, 695, 1598, 3623, 8136, 18130, 40143, 88430, 194001, 424170, 924821, 2011703, 4367437, 9466348, 20490079, 44299973, 95684074, 206498611, 445338607, 959853886, 2067760077, 4452542682, 9584217304, 20623829920, 44367611189, 95425360071, 205199855268, 441182305216, 948412809073, 2038562269541, 4381324739545, 9415607062361, 20232903327059, 43475026228698, 93410853473284, 200693891339286, 431174704161574, 926311915570108, 1989977952217796, 4274921879408541, 9183296403545124, 19726992947585096, 42375634563108824, 91026025327985057, 195528397629978747, 420000428472434489, 902164813378105714, 1937844088122249864, 4162450073461297680, 8940810577681330122, 19204488277603300677, 41250276416012212832, 88603221437959650866, 190314070811108963329, 408781473165206524811, 878032485440131241934, 1885945643122088027520, 4050858559984904995353, 8700904594241742163722, 18688792233263952785133, 40141873593052532541660, 86221123403645213183960, 185195062060087766997647, 397781756058647485194504, 854397737167581560514577, 1835165017765367921274564, 3941758261762912238299657, 8466515488070480303678949, 18185251202995060698043177, 39060140081745305913308106, 83897341243894918641486727, 180203209692949362560657159, 387058652253988660549470450, 831363553225944241527727589, 1785686164843105788589824523, 3835475781298883887605236852, 8238218759719337462341055153, 17694869537834644600982780624, 38006806842504835699550483400, 81634808828008825981007324330, 175343373255575571459363079141, 376619947112868484502630798737, 808941777165636671879489100808, 1737525549924050285681213191806, 3732029980717671831138749013533, 8016024567071598083390815553171, 17217613222397761830892704063025, 36981698119915068354562339350475, 79432959767745587434041146543467, 170613988792560091633653545279772, 366461642429172776375945032370864, 787122645961794991590837723613660, 1690660041336250127669167658400954, 3631367199573525264952765771558402
Generating function in Maple syntax:
(x^9+2*x^8+4*x^7+x^6-5*x^5-6*x^4-x^3+2*x-1)/(x-1)/(x^2+1)/(x^3+2*x^2+x-1)/(x^3+x^2+x-1)
Generating function in latex syntax:
\frac{x^{9}+2 x^{8}+4 x^{7}+x^{6}-5 x^{5}-6 x^{4}-x^{3}+2 x -1}{\left(x -1\right) \left(x^{2}+1\right) \left(x^{3}+2 x^{2}+x -1\right) \left(x^{3}+x^{2}+x -1\right)}
Generating function in sympy syntax:
(x**9 + 2*x**8 + 4*x**7 + x**6 - 5*x**5 - 6*x**4 - x**3 + 2*x - 1)/((x - 1)*(x**2 + 1)*(x**3 + x**2 + x - 1)*(x**3 + 2*x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
(x-1)*(x^2+1)*(x^3+2*x^2+x-1)*(x^3+x^2+x-1)*F(x)-x^9-2*x^8-4*x^7-x^6+5*x^5+6*x^4+x^3-2*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(x^{2}+1\right) \left(x^{3}+2 x^{2}+x -1\right) \left(x^{3}+x^{2}+x -1\right) F \! \left(x \right)-x^{9}-2 x^{8}-4 x^{7}-x^{6}+5 x^{5}+6 x^{4}+x^{3}-2 x +1 = 0
Explicit closed form in Maple syntax:
119671/24552*Sum(_alpha^(-n+7),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))+608329/49104*Sum(_alpha^(-n+6),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))+397429/24552*Sum(_alpha^(-n+5),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))+54623/16368*Sum(_alpha^(-n+4),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))-134927/16368*Sum(_alpha^(-n+3),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))-102161/5456*Sum(_alpha^(-n+2),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))-25965/2728*Sum(_alpha^(-n+1),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))-472943/49104*Sum(_alpha^(-n),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))+52269/5456*Sum(_alpha^(-n-1),_alpha = RootOf(_Z^9+2*_Z^8+2*_Z^7-_Z^6-2*_Z^5-3*_Z^4-_Z^2+3*_Z-1))+piecewise(n = 0,1,0)
Explicit closed form in latex syntax:
\frac{119671 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +7}\right)}{24552}+\frac{608329 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +6}\right)}{49104}+\frac{397429 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +5}\right)}{24552}+\frac{54623 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +4}\right)}{16368}-\frac{134927 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +3}\right)}{16368}-\frac{102161 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +2}\right)}{5456}-\frac{25965 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n +1}\right)}{2728}-\frac{472943 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{49104}+\frac{52269 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{9}+2 \textit{\_Z}^{8}+2 \textit{\_Z}^{7}-\textit{\_Z}^{6}-2 \textit{\_Z}^{5}-3 \textit{\_Z}^{4}-\textit{\_Z}^{2}+3 \textit{\_Z} -1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{5456}+\left(\left\{\begin{array}{cc}1 & n =0 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 51
a(6) = 124
a(7) = 296
a(8) = 695
a(9) = 1598
a(n+8) = -a(n)-3*a(n+1)-5*a(n+2)-4*a(n+3)-2*a(n+4)+a(n+5)+a(n+6)+2*a(n+7)+3, n >= 10
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) = 51
a \! \left(6\right) = 124
a \! \left(7\right) = 296
a \! \left(8\right) = 695
a \! \left(9\right) = 1598
a \! \left(n +8\right) = -a \! \left(n \right)-3 a \! \left(n +1\right)-5 a \! \left(n +2\right)-4 a \! \left(n +3\right)-2 a \! \left(n +4\right)+a \! \left(n +5\right)+a \! \left(n +6\right)+2 a \! \left(n +7\right)+3, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16266/
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[19,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[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[14,x]
F[12,x] = F[13,x]
F[13,x] = F[10,x]*F[4,x]
F[14,x] = F[15,x]+F[16,x]+F[18,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[4,x]
F[18,x] = F[12,x]*F[4,x]
F[19,x] = F[20,x]+F[41,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[29,x]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[10,x]+F[27,x]
F[27,x] = F[12,x]+F[28,x]
F[28,x] = F[18,x]
F[29,x] = F[20,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[36,x]
F[33,x] = F[20,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[20,x]*F[4,x]
F[36,x] = F[37,x]+F[39,x]
F[37,x] = F[38,x]
F[38,x] = F[33,x]*F[4,x]
F[39,x] = F[40,x]
F[40,x] = F[37,x]*F[4,x]
F[41,x] = F[15,x]+F[42,x]+F[69,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[44,x]+F[51,x]
F[44,x] = F[45,x]+F[7,x]
F[45,x] = F[15,x]+F[46,x]+F[49,x]
F[46,x] = F[4,x]*F[47,x]
F[47,x] = F[17,x]+F[48,x]
F[48,x] = F[14,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[11,x]
F[51,x] = F[41,x]+F[52,x]
F[52,x] = 2*F[15,x]+F[53,x]+F[66,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]+F[63,x]
F[55,x] = F[56,x]
F[56,x] = F[15,x]+F[35,x]+F[57,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[59,x]+F[61,x]
F[59,x] = F[4,x]+F[60,x]
F[60,x] = F[15,x]+F[18,x]+F[46,x]
F[61,x] = F[56,x]+F[62,x]
F[62,x] = 2*F[15,x]+F[40,x]+F[53,x]
F[63,x] = F[64,x]
F[64,x] = 2*F[15,x]+F[40,x]+F[65,x]
F[65,x] = F[4,x]*F[55,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[37,x]+F[64,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[68,x]+F[71,x]
F[71,x] = F[20,x]+F[56,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_{19}\! \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_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{14}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{18}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{41}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{29}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{10}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{18}\! \left(x \right)
F_{29}\! \left(x \right) = F_{20}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{36}\! \left(x \right)
F_{33}\! \left(x \right) = F_{20}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{39}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{41}\! \left(x \right) = F_{15}\! \left(x \right)+F_{42}\! \left(x \right)+F_{69}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{51}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{7}\! \left(x \right)
F_{45}\! \left(x \right) = F_{15}\! \left(x \right)+F_{46}\! \left(x \right)+F_{49}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{17}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{14}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right)
F_{51}\! \left(x \right) = F_{41}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{53}\! \left(x \right)+F_{66}\! \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_{63}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{15}\! \left(x \right)+F_{35}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{61}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)+F_{46}\! \left(x \right)
F_{61}\! \left(x \right) = F_{56}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{40}\! \left(x \right)+F_{53}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{40}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{37}\! \left(x \right)+F_{64}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{68}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{20}\! \left(x \right)+F_{56}\! \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_19(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_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_14(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_10(x)*F_4(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_18(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_4(x))
Eq(F_18(x), F_12(x)*F_4(x))
Eq(F_19(x), F_20(x) + F_41(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_23(x) + F_29(x))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_10(x) + F_27(x))
Eq(F_27(x), F_12(x) + F_28(x))
Eq(F_28(x), F_18(x))
Eq(F_29(x), F_20(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_36(x))
Eq(F_33(x), F_20(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_20(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_39(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_33(x)*F_4(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_37(x)*F_4(x))
Eq(F_41(x), F_15(x) + F_42(x) + F_69(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_51(x))
Eq(F_44(x), F_45(x) + F_7(x))
Eq(F_45(x), F_15(x) + F_46(x) + F_49(x))
Eq(F_46(x), F_4(x)*F_47(x))
Eq(F_47(x), F_17(x) + F_48(x))
Eq(F_48(x), F_14(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_11(x))
Eq(F_51(x), F_41(x) + F_52(x))
Eq(F_52(x), 2*F_15(x) + F_53(x) + F_66(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_63(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_15(x) + F_35(x) + F_57(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_61(x))
Eq(F_59(x), F_4(x) + F_60(x))
Eq(F_60(x), F_15(x) + F_18(x) + F_46(x))
Eq(F_61(x), F_56(x) + F_62(x))
Eq(F_62(x), 2*F_15(x) + F_40(x) + F_53(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), 2*F_15(x) + F_40(x) + F_65(x))
Eq(F_65(x), F_4(x)*F_55(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_37(x) + F_64(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_68(x) + F_71(x))
Eq(F_71(x), F_20(x) + F_56(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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"pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "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], 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