0123_0132_1320_2103_3021
Counting sequence:
1, 1, 2, 6, 19, 47, 85, 161, 333, 705, 1502, 3219, 6921, 14919, 32251, 69894, 151777, 330148, 719217, 1568793, 3425601, 7486892, 16375732, 35841189, 78487765, 171957780, 376886327, 826305801, 1812134438, 3975027445, 8721152824, 19137191166, 41999262311, 92183831083, 202352909435, 444220948755, 975254258725, 2141219447265, 4701376545806, 10323004074764, 22667393096846, 49774754912019, 109301670956712, 240023048451250, 527091717977944, 1157511684888528, 2541964939263505, 5582360772224410, 12259414769881465, 26923065247026230, 59126438499822814, 129849711518317194, 285168780059366831, 626274034965151107, 1375396900125582340, 3020596299924343704, 6633735890531544785, 14568819957494809702, 31995667065564877442, 70268140137057162807, 154321403586347284154, 338917675530150532239, 744324930487654359621, 1634674005019905604562, 3590045493672082954550, 7884404900347741623962, 17315619342117187552626, 38028330613132672788240, 83517328261325788204872, 183419712681593078755803, 402824146481188948327113, 884677621199783465896997, 1942918739087593631964684, 4267016025920325129809409, 9371172790876270407439553, 20580866073406737070978091, 45199473060648726924564713, 99266593238417118370468004, 218008225624605920076289009, 478787338787417487566822692, 1051507673422149084705107591, 2309310049084794994874599147, 5071682443114069469853759353, 11138375824078131576346912740, 24461984573233938374018792146, 53723155469003191651761559091, 117986235025473238431087842657, 259120143726550344166705479108, 569076971725506776277180943821, 1249800949101854389297928576587, 2744799908106446476330493774802, 6028101171255304546930960941749, 13238853492758565326812043811074, 29075033299219295195825363238640, 63854287968552026569812599150351, 140236128292054672948616174820743, 307985138286073976409951605611677, 676393784460683062932240733574149, 1485489055485167216049183231828925, 3262415750644671328613748316653293, 7164883846987897689526899027326528
Generating function in Maple syntax:
(4*x^15+27*x^14+79*x^13+131*x^12+127*x^11+58*x^10-20*x^9-55*x^8-49*x^7-21*x^6+7*x^5+5*x^4-x^2-x+1)/(x^3+x^2+x-1)/(x^5+3*x^4+2*x^3+x^2+x-1)
Generating function in latex syntax:
\frac{4 x^{15}+27 x^{14}+79 x^{13}+131 x^{12}+127 x^{11}+58 x^{10}-20 x^{9}-55 x^{8}-49 x^{7}-21 x^{6}+7 x^{5}+5 x^{4}-x^{2}-x +1}{\left(x^{3}+x^{2}+x -1\right) \left(x^{5}+3 x^{4}+2 x^{3}+x^{2}+x -1\right)}
Generating function in sympy syntax:
(4*x**15 + 27*x**14 + 79*x**13 + 131*x**12 + 127*x**11 + 58*x**10 - 20*x**9 - 55*x**8 - 49*x**7 - 21*x**6 + 7*x**5 + 5*x**4 - x**2 - x + 1)/((x**3 + x**2 + x - 1)*(x**5 + 3*x**4 + 2*x**3 + x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
-(x^3+x^2+x-1)*(x^5+3*x^4+2*x^3+x^2+x-1)*F(x)+4*x^15+27*x^14+79*x^13+131*x^12+127*x^11+58*x^10-20*x^9-55*x^8-49*x^7-21*x^6+7*x^5+5*x^4-x^2-x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{3}+x^{2}+x -1\right) \left(x^{5}+3 x^{4}+2 x^{3}+x^{2}+x -1\right) F \! \left(x \right)+4 x^{15}+27 x^{14}+79 x^{13}+131 x^{12}+127 x^{11}+58 x^{10}-20 x^{9}-55 x^{8}-49 x^{7}-21 x^{6}+7 x^{5}+5 x^{4}-x^{2}-x +1 = 0
Explicit closed form in Maple syntax:
56305/3079406*Sum(_alpha^(6-n),_alpha = RootOf(_Z^8+4*_Z^7+6*_Z^6+5*_Z^5+_Z^4-_Z^3-_Z^2-2*_Z+1))+400253/3079406*Sum(_alpha^(5-n),_alpha = RootOf(_Z^8+4*_Z^7+6*_Z^6+5*_Z^5+_Z^4-_Z^3-_Z^2-2*_Z+1))+701601/3079406*Sum(_alpha^(4-n),_alpha = RootOf(_Z^8+4*_Z^7+6*_Z^6+5*_Z^5+_Z^4-_Z^3-_Z^2-2*_Z+1))+233626/1539703*Sum(_alpha^(3-n),_alpha = RootOf(_Z^8+4*_Z^7+6*_Z^6+5*_Z^5+_Z^4-_Z^3-_Z^2-2*_Z+1))+606367/3079406*Sum(_alpha^(2-n),_alpha = RootOf(_Z^8+4*_Z^7+6*_Z^6+5*_Z^5+_Z^4-_Z^3-_Z^2-2*_Z+1))+243796/1539703*Sum(_alpha^(1-n),_alpha = RootOf(_Z^8+4*_Z^7+6*_Z^6+5*_Z^5+_Z^4-_Z^3-_Z^2-2*_Z+1))+612499/3079406*Sum(_alpha^(-n),_alpha = RootOf(_Z^8+4*_Z^7+6*_Z^6+5*_Z^5+_Z^4-_Z^3-_Z^2-2*_Z+1))+209105/3079406*Sum(_alpha^(-n-1),_alpha = RootOf(_Z^8+4*_Z^7+6*_Z^6+5*_Z^5+_Z^4-_Z^3-_Z^2-2*_Z+1))+piecewise(n = 1,-1,Or(n = 2,n = 3),-2,n = 4,1,Or(n = 5,n = 6),11,n = 7,4,0)
Explicit closed form in latex syntax:
\frac{56305 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{8}+4 \textit{\_Z}^{7}+6 \textit{\_Z}^{6}+5 \textit{\_Z}^{5}+\textit{\_Z}^{4}-\textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{6-n}\right)}{3079406}+\frac{400253 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{8}+4 \textit{\_Z}^{7}+6 \textit{\_Z}^{6}+5 \textit{\_Z}^{5}+\textit{\_Z}^{4}-\textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{5-n}\right)}{3079406}+\frac{701601 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{8}+4 \textit{\_Z}^{7}+6 \textit{\_Z}^{6}+5 \textit{\_Z}^{5}+\textit{\_Z}^{4}-\textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{4-n}\right)}{3079406}+\frac{233626 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{8}+4 \textit{\_Z}^{7}+6 \textit{\_Z}^{6}+5 \textit{\_Z}^{5}+\textit{\_Z}^{4}-\textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{3-n}\right)}{1539703}+\frac{606367 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{8}+4 \textit{\_Z}^{7}+6 \textit{\_Z}^{6}+5 \textit{\_Z}^{5}+\textit{\_Z}^{4}-\textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{2-n}\right)}{3079406}+\frac{243796 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{8}+4 \textit{\_Z}^{7}+6 \textit{\_Z}^{6}+5 \textit{\_Z}^{5}+\textit{\_Z}^{4}-\textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{1-n}\right)}{1539703}+\frac{612499 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{8}+4 \textit{\_Z}^{7}+6 \textit{\_Z}^{6}+5 \textit{\_Z}^{5}+\textit{\_Z}^{4}-\textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n}\right)}{3079406}+\frac{209105 \left(\munderset{\underline{\hspace{1.25 ex}}\alpha =\mathit{RootOf}\! \left(\textit{\_Z}^{8}+4 \textit{\_Z}^{7}+6 \textit{\_Z}^{6}+5 \textit{\_Z}^{5}+\textit{\_Z}^{4}-\textit{\_Z}^{3}-\textit{\_Z}^{2}-2 \textit{\_Z} +1\right)}{\textcolor{gray}{\sum}}\! \underline{\hspace{1.25 ex}}\alpha^{-n -1}\right)}{3079406}+\left(\left\{\begin{array}{cc}-1 & n =1 \\ -2 & n =2\text{ or } n =3 \\ 1 & n =4 \\ 11 & n =5\text{ or } n =6 \\ 4 & n =7 \\ 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) = 47
a(6) = 85
a(7) = 161
a(8) = 333
a(9) = 705
a(10) = 1502
a(11) = 3219
a(12) = 6921
a(13) = 14919
a(14) = 32251
a(15) = 69894
a(n+8) = -a(n)-4*a(n+1)-6*a(n+2)-5*a(n+3)-a(n+4)+a(n+5)+a(n+6)+2*a(n+7), n >= 16
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) = 47
a \! \left(6\right) = 85
a \! \left(7\right) = 161
a \! \left(8\right) = 333
a \! \left(9\right) = 705
a \! \left(10\right) = 1502
a \! \left(11\right) = 3219
a \! \left(12\right) = 6921
a \! \left(13\right) = 14919
a \! \left(14\right) = 32251
a \! \left(15\right) = 69894
a \! \left(n +8\right) = -a \! \left(n \right)-4 a \! \left(n +1\right)-6 a \! \left(n +2\right)-5 a \! \left(n +3\right)-a \! \left(n +4\right)+a \! \left(n +5\right)+a \! \left(n +6\right)+2 a \! \left(n +7\right), \quad n \geq 16
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16620/
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[7,x]
F[12,x] = F[13,x]+F[14,x]+F[18,x]
F[13,x] = 0
F[14,x] = F[15,x]*F[4,x]
F[15,x] = F[16,x]+F[17,x]
F[16,x] = F[4,x]
F[17,x] = F[18,x]
F[18,x] = F[4,x]*F[7,x]
F[19,x] = F[20,x]+F[51,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[10,x]*F[4,x]
F[26,x] = F[20,x]+F[27,x]
F[27,x] = F[13,x]+F[28,x]+F[42,x]
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]+F[33,x]
F[30,x] = F[24,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[16,x]*F[4,x]
F[33,x] = F[34,x]+F[39,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[20,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[20,x]*F[4,x]
F[39,x] = F[40,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[37,x]
F[42,x] = F[4,x]*F[43,x]
F[43,x] = F[20,x]+F[44,x]
F[44,x] = F[13,x]+F[38,x]+F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[47,x]+F[49,x]
F[47,x] = F[4,x]+F[48,x]
F[48,x] = F[32,x]
F[49,x] = F[37,x]+F[50,x]
F[50,x] = F[40,x]
F[51,x] = F[13,x]+F[52,x]+F[78,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[54,x]+F[65,x]
F[54,x] = F[55,x]+F[7,x]
F[55,x] = F[13,x]+F[32,x]+F[56,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[61,x]
F[58,x] = F[24,x]+F[59,x]
F[59,x] = F[13,x]+F[32,x]+F[60,x]
F[60,x] = F[24,x]*F[4,x]
F[61,x] = F[62,x]+F[63,x]
F[62,x] = F[32,x]
F[63,x] = F[64,x]
F[64,x] = F[4,x]*F[62,x]
F[65,x] = F[66,x]+F[69,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[36,x]
F[69,x] = 2*F[13,x]+F[40,x]+F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[73,x]+F[76,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[30,x]
F[76,x] = F[77,x]
F[77,x] = F[4,x]*F[73,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[87,x]
F[80,x] = F[20,x]+F[81,x]
F[81,x] = F[13,x]+F[38,x]+F[82,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[4,x]+F[59,x]
F[85,x] = F[37,x]+F[86,x]
F[86,x] = 2*F[13,x]+F[40,x]+F[77,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[74,x]
F[89,x] = 2*F[13,x]+F[90,x]+F[95,x]
F[90,x] = F[4,x]*F[91,x]
F[91,x] = F[92,x]
F[92,x] = F[59,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[31,x]*F[4,x]
F[95,x] = F[4,x]*F[88,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_{7}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{14}\! \left(x \right)+F_{18}\! \left(x \right)
F_{13}\! \left(x \right) = 0
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{51}\! \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_{26}\! \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_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{20}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{13}\! \left(x \right)+F_{28}\! \left(x \right)+F_{42}\! \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_{33}\! \left(x \right)
F_{30}\! \left(x \right) = F_{24}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{39}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{20}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{37}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{20}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{13}\! \left(x \right)+F_{38}\! \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_{47}\! \left(x \right)+F_{49}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{32}\! \left(x \right)
F_{49}\! \left(x \right) = F_{37}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{40}\! \left(x \right)
F_{51}\! \left(x \right) = F_{13}\! \left(x \right)+F_{52}\! \left(x \right)+F_{78}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{65}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{7}\! \left(x \right)
F_{55}\! \left(x \right) = F_{13}\! \left(x \right)+F_{32}\! \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_{58}\! \left(x \right)+F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = F_{24}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{13}\! \left(x \right)+F_{32}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{63}\! \left(x \right)
F_{62}\! \left(x \right) = F_{32}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{69}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{36}\! \left(x \right)
F_{69}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{40}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{76}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{30}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{87}\! \left(x \right)
F_{80}\! \left(x \right) = F_{20}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{13}\! \left(x \right)+F_{38}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right)+F_{59}\! \left(x \right)
F_{85}\! \left(x \right) = F_{37}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{40}\! \left(x \right)+F_{77}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{74}\! \left(x \right)
F_{89}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{90}\! \left(x \right)+F_{95}\! \left(x \right)
F_{90}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{59}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \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_7(x))
Eq(F_12(x), F_13(x) + F_14(x) + F_18(x))
Eq(F_13(x), 0)
Eq(F_14(x), F_15(x)*F_4(x))
Eq(F_15(x), F_16(x) + F_17(x))
Eq(F_16(x), F_4(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_4(x)*F_7(x))
Eq(F_19(x), F_20(x) + F_51(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_26(x))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_10(x)*F_4(x))
Eq(F_26(x), F_20(x) + F_27(x))
Eq(F_27(x), F_13(x) + F_28(x) + F_42(x))
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_33(x))
Eq(F_30(x), F_24(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_16(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_39(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_20(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_20(x)*F_4(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_37(x))
Eq(F_42(x), F_4(x)*F_43(x))
Eq(F_43(x), F_20(x) + F_44(x))
Eq(F_44(x), F_13(x) + F_38(x) + F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_49(x))
Eq(F_47(x), F_4(x) + F_48(x))
Eq(F_48(x), F_32(x))
Eq(F_49(x), F_37(x) + F_50(x))
Eq(F_50(x), F_40(x))
Eq(F_51(x), F_13(x) + F_52(x) + F_78(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_65(x))
Eq(F_54(x), F_55(x) + F_7(x))
Eq(F_55(x), F_13(x) + F_32(x) + F_56(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_61(x))
Eq(F_58(x), F_24(x) + F_59(x))
Eq(F_59(x), F_13(x) + F_32(x) + F_60(x))
Eq(F_60(x), F_24(x)*F_4(x))
Eq(F_61(x), F_62(x) + F_63(x))
Eq(F_62(x), F_32(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_4(x)*F_62(x))
Eq(F_65(x), F_66(x) + F_69(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_36(x))
Eq(F_69(x), 2*F_13(x) + F_40(x) + F_70(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_73(x) + F_76(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_30(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_4(x)*F_73(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_87(x))
Eq(F_80(x), F_20(x) + F_81(x))
Eq(F_81(x), F_13(x) + F_38(x) + F_82(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_4(x) + F_59(x))
Eq(F_85(x), F_37(x) + F_86(x))
Eq(F_86(x), 2*F_13(x) + F_40(x) + F_77(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_74(x))
Eq(F_89(x), 2*F_13(x) + F_90(x) + F_95(x))
Eq(F_90(x), F_4(x)*F_91(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_59(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_31(x)*F_4(x))
Eq(F_95(x), F_4(x)*F_88(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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 3], "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, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 3], "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, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 3], "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, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], 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