0123_0132_1302_2130
Counting sequence:
1, 1, 2, 6, 20, 61, 171, 455, 1172, 2958, 7368, 18193, 44655, 109151, 266008, 646878, 1570560, 3808585, 9227287, 22339667, 54055432, 130741362, 316108844, 764082685, 1846492795, 4461459035, 10778117324, 26034985170, 62882474180, 151868388709, 366755647683, 885651644159, 2138601509852, 5163937633206, 12468639190320, 30105535139017, 72688338491175, 175499455236599, 423721711036960, 1023011762367462, 2469882942639720, 5963052959048353, 14396539317959119, 34757232241497611, 83913204660521872, 202588042580267610, 489098090721606356, 1180801823988266869, 2850736935656498035, 6882346084410451763, 16615569874917037076, 40113767362537527834, 96843667636213085420, 233802228674454403837, 564450377010787012155, 1362707486661091094903, 3289874358123510672932, 7942474218263343948894, 19174858824995226290712, 46292263928352565240321, 111759530800941172165215, 269811613767168531602447, 651383334806640748651432, 1572579436319122315929966, 3796544513315672484240720, 9165673074681431282012281, 22127899886123295363289351, 53421491293789764748603715, 128970919367381364770309272, 311363403815836850648598978, 751697874573506109755799548, 1814759448111560765046073453, 4381217361093742968098526955, 10577195350892778903732408971, 25535610424065958665008858588, 61648420921396707043096224738, 148832461711601282884815527060, 359313363234079676625332810005, 867459225958715915820991324467, 2094231890709413123244012022127, 5055923158493330919928383818732, 12206078509927629061611168091782, 29468080782811659351109123722624, 71142241284477027073955501365945, 171752565769617772924419203356695, 414647377659416531272948245516455, 1001047330759858492475127458141104, 2416742058521948410036685961811830, 5834531486489384420283827343178680, 14085805108871974365987218204894929, 34006141858975845603044602861705663, 82098089136308687593581907774964219, 198202320750563260173172775729419552, 478502731875375279165742369123027626, 1155207786977193948756126918632046500, 2788918310781523417440660795832040677, 6733044418443761233222343054195867875, 16255007167476086731374427137164933219, 39243058793010016307328214304559624740, 94741124832724282433443037353645217322, 228725308616914907130115656392016959420
Generating function in Maple syntax:
-(2*x^8+4*x^7+x^5-7*x^4-5*x^3+12*x^2-6*x+1)/(2*x-1)/(x^2+x-1)/(x^2+2*x-1)/(x-1)^2
Generating function in latex syntax:
-\frac{2 x^{8}+4 x^{7}+x^{5}-7 x^{4}-5 x^{3}+12 x^{2}-6 x +1}{\left(2 x -1\right) \left(x^{2}+x -1\right) \left(x^{2}+2 x -1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(-2*x**8 - 4*x**7 - x**5 + 7*x**4 + 5*x**3 - 12*x**2 + 6*x - 1)/((x - 1)**2*(2*x - 1)*(x**2 + x - 1)*(x**2 + 2*x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x^2+x-1)*(x^2+2*x-1)*(x-1)^2*F(x)+2*x^8+4*x^7+x^5-7*x^4-5*x^3+12*x^2-6*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x^{2}+x -1\right) \left(x^{2}+2 x -1\right) \left(x -1\right)^{2} F \! \left(x \right)+2 x^{8}+4 x^{7}+x^{5}-7 x^{4}-5 x^{3}+12 x^{2}-6 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/10*(4*5^(1/2)-10)*(-1/2*5^(1/2)-1/2)^(-n)+1/10*(-4*5^(1/2)-10)*(1/2*5^(1/2)-1/2)^(-n)+1/10*(-5*2^(1/2)+5)*(-1-2^(1/2))^(-n)+1/10*(5*2^(1/2)+5)*(2^(1/2)-1)^(-n)-n-2^(-1+n)+4)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{\left(4 \sqrt{5}-10\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{10}+\frac{\left(-4 \sqrt{5}-10\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{10}+\\\frac{\left(-5 \sqrt{2}+5\right) \left(-1-\sqrt{2}\right)^{-n}}{10}+\frac{\left(5 \sqrt{2}+5\right) \left(\sqrt{2}-1\right)^{-n}}{10}-n -2^{-1+n}+4 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 61
a(6) = 171
a(7) = 455
a(8) = 1172
a(n+5) = 2*a(n)+5*a(n+1)-3*a(n+2)-6*a(n+3)+5*a(n+4)+2*n-12, n >= 9
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) = 61
a \! \left(6\right) = 171
a \! \left(7\right) = 455
a \! \left(8\right) = 1172
a \! \left(n +5\right) = 2 a \! \left(n \right)+5 a \! \left(n +1\right)-3 a \! \left(n +2\right)-6 a \! \left(n +3\right)+5 a \! \left(n +4\right)+2 n -12, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14859/
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[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[19,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[14,x]
F[19,x] = F[4,x]*F[7,x]
F[20,x] = F[2,x]+F[21,x]
F[21,x] = F[125,x]+F[13,x]+F[22,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[24,x]+F[42,x]
F[24,x] = F[25,x]+F[7,x]
F[25,x] = F[13,x]+F[14,x]+F[26,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[11,x]+F[28,x]
F[28,x] = F[29,x]+F[37,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[34,x]
F[32,x] = F[33,x]+F[7,x]
F[33,x] = F[19,x]
F[34,x] = F[29,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[29,x]*F[4,x]
F[37,x] = 2*F[13,x]+F[36,x]+F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[18,x]
F[41,x] = F[38,x]
F[42,x] = F[105,x]+F[43,x]
F[43,x] = F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[48,x]
F[46,x] = F[47,x]+F[7,x]
F[47,x] = F[14,x]
F[48,x] = F[43,x]+F[49,x]
F[49,x] = 2*F[13,x]+F[50,x]+F[72,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[57,x]
F[52,x] = F[47,x]+F[53,x]
F[53,x] = F[54,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[17,x]+F[56,x]
F[56,x] = F[38,x]
F[57,x] = F[58,x]+F[63,x]
F[58,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[47,x]
F[62,x] = F[58,x]
F[63,x] = F[64,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[53,x]
F[67,x] = F[68,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[53,x]
F[71,x] = F[68,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[100,x]+F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[18,x]+F[4,x]
F[79,x] = F[75,x]+F[80,x]
F[80,x] = 2*F[13,x]+F[72,x]+F[81,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[83,x]+F[85,x]
F[83,x] = F[18,x]+F[84,x]
F[84,x] = F[54,x]
F[85,x] = F[86,x]+F[91,x]
F[86,x] = F[87,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[89,x]+F[90,x]
F[89,x] = F[18,x]
F[90,x] = F[86,x]
F[91,x] = F[92,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[94,x]+F[95,x]
F[94,x] = F[84,x]
F[95,x] = F[96,x]
F[96,x] = F[4,x]*F[97,x]
F[97,x] = F[98,x]+F[99,x]
F[98,x] = F[84,x]
F[99,x] = F[96,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[4,x]
F[102,x] = F[103,x]+F[104,x]
F[103,x] = F[75,x]
F[104,x] = F[101,x]
F[105,x] = 2*F[13,x]+F[106,x]+F[72,x]
F[106,x] = F[107,x]*F[4,x]
F[107,x] = F[108,x]+F[110,x]
F[108,x] = F[109,x]+F[25,x]
F[109,x] = F[54,x]
F[110,x] = F[111,x]+F[116,x]
F[111,x] = F[112,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[114,x]+F[115,x]
F[114,x] = F[25,x]
F[115,x] = F[111,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[4,x]
F[118,x] = F[119,x]+F[120,x]
F[119,x] = F[109,x]
F[120,x] = F[121,x]
F[121,x] = F[122,x]*F[4,x]
F[122,x] = F[123,x]+F[124,x]
F[123,x] = F[109,x]
F[124,x] = F[121,x]
F[125,x] = F[126,x]*F[4,x]
F[126,x] = F[127,x]+F[154,x]
F[127,x] = F[128,x]+F[2,x]
F[128,x] = F[129,x]+F[13,x]+F[153,x]
F[129,x] = F[130,x]*F[4,x]
F[130,x] = F[131,x]+F[132,x]
F[131,x] = F[12,x]+F[4,x]
F[132,x] = F[133,x]+F[75,x]
F[133,x] = 2*F[13,x]+F[134,x]+F[72,x]
F[134,x] = F[135,x]*F[4,x]
F[135,x] = F[136,x]+F[138,x]
F[136,x] = F[12,x]+F[137,x]
F[137,x] = F[54,x]
F[138,x] = F[139,x]+F[144,x]
F[139,x] = F[140,x]
F[140,x] = F[141,x]*F[4,x]
F[141,x] = F[142,x]+F[143,x]
F[142,x] = F[12,x]
F[143,x] = F[139,x]
F[144,x] = F[145,x]
F[145,x] = F[146,x]*F[4,x]
F[146,x] = F[147,x]+F[148,x]
F[147,x] = F[137,x]
F[148,x] = F[149,x]
F[149,x] = F[150,x]*F[4,x]
F[150,x] = F[151,x]+F[152,x]
F[151,x] = F[137,x]
F[152,x] = F[149,x]
F[153,x] = F[2,x]*F[4,x]
F[154,x] = F[155,x]+F[163,x]
F[155,x] = F[156,x]
F[156,x] = F[157,x]*F[4,x]
F[157,x] = F[158,x]+F[160,x]
F[158,x] = F[159,x]+F[2,x]
F[159,x] = F[153,x]
F[160,x] = F[155,x]+F[161,x]
F[161,x] = F[162,x]
F[162,x] = F[155,x]*F[4,x]
F[163,x] = 2*F[13,x]+F[101,x]+F[162,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_{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_{19}\! \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_{14}\! \left(x \right)
F_{19}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{20}\! \left(x \right) = F_{2}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{125}\! \left(x \right)+F_{13}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{42}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{7}\! \left(x \right)
F_{25}\! \left(x \right) = F_{13}\! \left(x \right)+F_{14}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{37}\! \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_{32}\! \left(x \right)+F_{34}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{7}\! \left(x \right)
F_{33}\! \left(x \right) = F_{19}\! \left(x \right)
F_{34}\! \left(x \right) = F_{29}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{36}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{18}\! \left(x \right)
F_{41}\! \left(x \right) = F_{38}\! \left(x \right)
F_{42}\! \left(x \right) = F_{105}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \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_{48}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{7}\! \left(x \right)
F_{47}\! \left(x \right) = F_{14}\! \left(x \right)
F_{48}\! \left(x \right) = F_{43}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{50}\! \left(x \right)+F_{72}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{57}\! \left(x \right)
F_{52}\! \left(x \right) = F_{47}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{17}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{38}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{63}\! \left(x \right)
F_{58}\! \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_{47}\! \left(x \right)
F_{62}\! \left(x \right) = F_{58}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \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_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{53}\! \left(x \right)
F_{67}\! \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_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{53}\! \left(x \right)
F_{71}\! \left(x \right) = F_{68}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{100}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{18}\! \left(x \right)+F_{4}\! \left(x \right)
F_{79}\! \left(x \right) = F_{75}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{72}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{85}\! \left(x \right)
F_{83}\! \left(x \right) = F_{18}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{54}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{91}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{18}\! \left(x \right)
F_{90}\! \left(x \right) = F_{86}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{84}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{4}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)+F_{99}\! \left(x \right)
F_{98}\! \left(x \right) = F_{84}\! \left(x \right)
F_{99}\! \left(x \right) = F_{96}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{104}\! \left(x \right)
F_{103}\! \left(x \right) = F_{75}\! \left(x \right)
F_{104}\! \left(x \right) = F_{101}\! \left(x \right)
F_{105}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{106}\! \left(x \right)+F_{72}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{110}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{25}\! \left(x \right)
F_{109}\! \left(x \right) = F_{54}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{116}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{115}\! \left(x \right)
F_{114}\! \left(x \right) = F_{25}\! \left(x \right)
F_{115}\! \left(x \right) = F_{111}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{4}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{120}\! \left(x \right)
F_{119}\! \left(x \right) = F_{109}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{4}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{124}\! \left(x \right)
F_{123}\! \left(x \right) = F_{109}\! \left(x \right)
F_{124}\! \left(x \right) = F_{121}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right) F_{4}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{154}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{2}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{13}\! \left(x \right)+F_{153}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right) F_{4}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{132}\! \left(x \right)
F_{131}\! \left(x \right) = F_{12}\! \left(x \right)+F_{4}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{75}\! \left(x \right)
F_{133}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{134}\! \left(x \right)+F_{72}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{4}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)+F_{138}\! \left(x \right)
F_{136}\! \left(x \right) = F_{12}\! \left(x \right)+F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{54}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{144}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{4}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{143}\! \left(x \right)
F_{142}\! \left(x \right) = F_{12}\! \left(x \right)
F_{143}\! \left(x \right) = F_{139}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right) F_{4}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{148}\! \left(x \right)
F_{147}\! \left(x \right) = F_{137}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right) F_{4}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{152}\! \left(x \right)
F_{151}\! \left(x \right) = F_{137}\! \left(x \right)
F_{152}\! \left(x \right) = F_{149}\! \left(x \right)
F_{153}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)+F_{163}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{157}\! \left(x \right) F_{4}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)+F_{160}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{2}\! \left(x \right)
F_{159}\! \left(x \right) = F_{153}\! \left(x \right)
F_{160}\! \left(x \right) = F_{155}\! \left(x \right)+F_{161}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{155}\! \left(x \right) F_{4}\! \left(x \right)
F_{163}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{101}\! \left(x \right)+F_{162}\! \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_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_19(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_14(x))
Eq(F_19(x), F_4(x)*F_7(x))
Eq(F_20(x), F_2(x) + F_21(x))
Eq(F_21(x), F_125(x) + F_13(x) + F_22(x))
Eq(F_22(x), F_23(x)*F_4(x))
Eq(F_23(x), F_24(x) + F_42(x))
Eq(F_24(x), F_25(x) + F_7(x))
Eq(F_25(x), F_13(x) + F_14(x) + F_26(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_11(x) + F_28(x))
Eq(F_28(x), F_29(x) + F_37(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_34(x))
Eq(F_32(x), F_33(x) + F_7(x))
Eq(F_33(x), F_19(x))
Eq(F_34(x), F_29(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_29(x)*F_4(x))
Eq(F_37(x), 2*F_13(x) + F_36(x) + F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_18(x))
Eq(F_41(x), F_38(x))
Eq(F_42(x), F_105(x) + F_43(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_48(x))
Eq(F_46(x), F_47(x) + F_7(x))
Eq(F_47(x), F_14(x))
Eq(F_48(x), F_43(x) + F_49(x))
Eq(F_49(x), 2*F_13(x) + F_50(x) + F_72(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_57(x))
Eq(F_52(x), F_47(x) + F_53(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_17(x) + F_56(x))
Eq(F_56(x), F_38(x))
Eq(F_57(x), F_58(x) + F_63(x))
Eq(F_58(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_47(x))
Eq(F_62(x), F_58(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_53(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_53(x))
Eq(F_71(x), F_68(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_100(x) + F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_18(x) + F_4(x))
Eq(F_79(x), F_75(x) + F_80(x))
Eq(F_80(x), 2*F_13(x) + F_72(x) + F_81(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_85(x))
Eq(F_83(x), F_18(x) + F_84(x))
Eq(F_84(x), F_54(x))
Eq(F_85(x), F_86(x) + F_91(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_90(x))
Eq(F_89(x), F_18(x))
Eq(F_90(x), F_86(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_95(x))
Eq(F_94(x), F_84(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_4(x)*F_97(x))
Eq(F_97(x), F_98(x) + F_99(x))
Eq(F_98(x), F_84(x))
Eq(F_99(x), F_96(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_4(x))
Eq(F_102(x), F_103(x) + F_104(x))
Eq(F_103(x), F_75(x))
Eq(F_104(x), F_101(x))
Eq(F_105(x), F_106(x) + 2*F_13(x) + F_72(x))
Eq(F_106(x), F_107(x)*F_4(x))
Eq(F_107(x), F_108(x) + F_110(x))
Eq(F_108(x), F_109(x) + F_25(x))
Eq(F_109(x), F_54(x))
Eq(F_110(x), F_111(x) + F_116(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_114(x) + F_115(x))
Eq(F_114(x), F_25(x))
Eq(F_115(x), F_111(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_4(x))
Eq(F_118(x), F_119(x) + F_120(x))
Eq(F_119(x), F_109(x))
Eq(F_120(x), F_121(x))
Eq(F_121(x), F_122(x)*F_4(x))
Eq(F_122(x), F_123(x) + F_124(x))
Eq(F_123(x), F_109(x))
Eq(F_124(x), F_121(x))
Eq(F_125(x), F_126(x)*F_4(x))
Eq(F_126(x), F_127(x) + F_154(x))
Eq(F_127(x), F_128(x) + F_2(x))
Eq(F_128(x), F_129(x) + F_13(x) + F_153(x))
Eq(F_129(x), F_130(x)*F_4(x))
Eq(F_130(x), F_131(x) + F_132(x))
Eq(F_131(x), F_12(x) + F_4(x))
Eq(F_132(x), F_133(x) + F_75(x))
Eq(F_133(x), 2*F_13(x) + F_134(x) + F_72(x))
Eq(F_134(x), F_135(x)*F_4(x))
Eq(F_135(x), F_136(x) + F_138(x))
Eq(F_136(x), F_12(x) + F_137(x))
Eq(F_137(x), F_54(x))
Eq(F_138(x), F_139(x) + F_144(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_141(x)*F_4(x))
Eq(F_141(x), F_142(x) + F_143(x))
Eq(F_142(x), F_12(x))
Eq(F_143(x), F_139(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_146(x)*F_4(x))
Eq(F_146(x), F_147(x) + F_148(x))
Eq(F_147(x), F_137(x))
Eq(F_148(x), F_149(x))
Eq(F_149(x), F_150(x)*F_4(x))
Eq(F_150(x), F_151(x) + F_152(x))
Eq(F_151(x), F_137(x))
Eq(F_152(x), F_149(x))
Eq(F_153(x), F_2(x)*F_4(x))
Eq(F_154(x), F_155(x) + F_163(x))
Eq(F_155(x), F_156(x))
Eq(F_156(x), F_157(x)*F_4(x))
Eq(F_157(x), F_158(x) + F_160(x))
Eq(F_158(x), F_159(x) + F_2(x))
Eq(F_159(x), F_153(x))
Eq(F_160(x), F_155(x) + F_161(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_155(x)*F_4(x))
Eq(F_163(x), F_101(x) + 2*F_13(x) + F_162(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, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "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, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": 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