0123_0132_2130

Counting sequence:
1, 1, 2, 6, 21, 73, 238, 724, 2078, 5706, 15161, 39319, 100168, 251846, 627046, 1549898, 3810125, 9328073, 22766362, 55432684, 134725294, 326982110, 792733065, 1920267887, 4648446316, 11246721414, 27199650590, 65759222454, 158940539445, 384078470185, 927962430886, 2241713977348, 5414779171166, 13077995117106, 31584122848889, 76272792893959, 184182553081840, 444743152791494, 1073878637875894, 2592918769531874, 6260550825820541, 15115686326980169, 36495249637515730, 88112828501395996, 212734176770034094, 513607696246463174, 1240002554381061513, 2993718703360713695, 7227651638524650580, 17449445137444327686, 42127387899639866798, 101705912366131307598, 245542594591685277093, 592797863981452325545, 1431151844958162724894, 3455128594637761255348, 8341463108993261792798, 20138162951043766428954, 48618005269594676733497, 117374605977018993272695, 283368082147315280822296, 684112500036744474513350, 1651596541615373171526022, 3987312501833136739613306, 9626235382044763434918701, 23239810938842567207144393, 56105912604571474863522058, 135451746836025722711205964, 327009627650000040156886318, 789471444878333301481897646, 1905953402883968992465769481, 4601380021588853480298910799, 11108716987927079457909447868, 26818821081141347171577129606, 64746373317553095657770642366, 156311596050846558848531366118, 377369622088300365030835611285, 911050953565319358439214630953, 2199471755894295458672693986582, 5309994918703986672344926719844, 12819462500001377476948341003614, 30948921732103246135789134846210, 74717309590998069449066349412985, 180383548167675177556302866458087, 435484420433492456325264921820096, 1051352418048935771767716180360134, 2538189314559895068844642782372310, 6127731163225754790623984551486994, 14793651873125407921900713314389085, 35715035373704487910430922567742025, 86223723548990072076765971927155906, 208162484328595769266196419871407228, 502548695920003492889819009385534766, 1213259883596245877597393652268073366, 2929068477967780442193949624686777609, 7071396869242375429920055200265606079, 17071862275873665822485290132961640100, 41215121539831971508669893794539104774, 99502105593222130169280519877260360014, 240219333201645262173932980271318750334, 579940772947250694997694522450350080261

Generating function in Maple syntax:
(2*x^11+x^10-10*x^9-9*x^8+12*x^7+17*x^6-30*x^5+2*x^4+28*x^3-24*x^2+8*x-1)/(2*x-1)/(x^2+2*x-1)/(x^2+x-1)^2/(x-1)^3

Generating function in latex syntax:
\frac{2 x^{11}+x^{10}-10 x^{9}-9 x^{8}+12 x^{7}+17 x^{6}-30 x^{5}+2 x^{4}+28 x^{3}-24 x^{2}+8 x -1}{\left(2 x -1\right) \left(x^{2}+2 x -1\right) \left(x^{2}+x -1\right)^{2} \left(x -1\right)^{3}}

Generating function in sympy syntax:
(2*x**11 + x**10 - 10*x**9 - 9*x**8 + 12*x**7 + 17*x**6 - 30*x**5 + 2*x**4 + 28*x**3 - 24*x**2 + 8*x - 1)/((x - 1)**3*(2*x - 1)*(x**2 + x - 1)**2*(x**2 + 2*x - 1))

Implicit equation for the generating function in Maple syntax:
-(2*x-1)*(x^2+2*x-1)*(x^2+x-1)^2*(x-1)^3*F(x)+2*x^11+x^10-10*x^9-9*x^8+12*x^7+17*x^6-30*x^5+2*x^4+28*x^3-24*x^2+8*x-1 = 0

Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right) \left(x^{2}+2 x -1\right) \left(x^{2}+x -1\right)^{2} \left(x -1\right)^{3} F \! \left(x \right)+2 x^{11}+x^{10}-10 x^{9}-9 x^{8}+12 x^{7}+17 x^{6}-30 x^{5}+2 x^{4}+28 x^{3}-24 x^{2}+8 x -1 = 0

Explicit closed form in Maple syntax:
piecewise(n = 0,2,1/20*((8*n+6)*5^(1/2)-20*n-10)*(-1/2*5^(1/2)-1/2)^(-n)+1/20*((-8*n-6)*5^(1/2)-20*n-10)*(1/2*5^(1/2)-1/2)^(-n)+1/20*(-15*2^(1/2)+40)*(-1-2^(1/2))^(-n)+1/20*(15*2^(1/2)+40)*(2^(1/2)-1)^(-n)+n^2+2*n-3*2^n+1)

Explicit closed form in latex syntax:
\left\{\begin{array}{cc}2 & n =0 \\ \frac{\left(\left(8 n +6\right) \sqrt{5}-20 n -10\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{20}+\\\frac{\left(\left(-8 n -6\right) \sqrt{5}-20 n -10\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{20}+\\\frac{\left(-15 \sqrt{2}+40\right) \left(-1-\sqrt{2}\right)^{-n}}{20}+\frac{\left(15 \sqrt{2}+40\right) \left(\sqrt{2}-1\right)^{-n}}{20}+n^{2}+2 n \\-3 \,2^{n}+1 & \mathit{\text{otherwise}} \end{array}\right.

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 73
a(6) = 238
a(7) = 724
a(8) = 2078
a(9) = 5706
a(10) = 15161
a(11) = 39319
a(n+1) = 2/7*n^2+2*a(n+3)-2/7*a(n+4)-10/7*a(n+5)+6/7*a(n+6)-1/7*a(n+7)-2/7*a(n)-8/7*n-2, n >= 12

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) = 21
a \! \left(5\right) = 73
a \! \left(6\right) = 238
a \! \left(7\right) = 724
a \! \left(8\right) = 2078
a \! \left(9\right) = 5706
a \! \left(10\right) = 15161
a \! \left(11\right) = 39319
a \! \left(n +1\right) = \frac{2 n^{2}}{7}+2 a \! \left(n +3\right)-\frac{2 a \! \left(n +4\right)}{7}-\frac{10 a \! \left(n +5\right)}{7}+\frac{6 a \! \left(n +6\right)}{7}-\frac{a \! \left(n +7\right)}{7}-\frac{2 a \! \left(n \right)}{7}-\frac{8 n}{7}-2, \quad n \geq 12

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14626/
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[111,x]+F[13,x]+F[22,x]
F[22,x] = F[23,x]*F[4,x]
F[23,x] = F[24,x]+F[36,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[25,x]+F[29,x]
F[29,x] = F[13,x]+F[30,x]+F[31,x]+F[35,x]
F[30,x] = 0
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[17,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[31,x]
F[35,x] = F[25,x]*F[4,x]
F[36,x] = F[37,x]+F[91,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[42,x]
F[40,x] = F[41,x]+F[7,x]
F[41,x] = F[14,x]
F[42,x] = F[37,x]+F[43,x]
F[43,x] = 2*F[13,x]+F[44,x]+F[63,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[48,x]
F[46,x] = F[41,x]+F[47,x]
F[47,x] = F[31,x]
F[48,x] = F[49,x]+F[54,x]
F[49,x] = F[50,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[41,x]
F[53,x] = F[49,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[56,x]
F[56,x] = F[57,x]+F[58,x]
F[57,x] = F[47,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[59,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[65,x]+F[90,x]
F[65,x] = F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[69,x]+F[70,x]
F[69,x] = F[18,x]+F[4,x]
F[70,x] = F[66,x]+F[71,x]
F[71,x] = 2*F[13,x]+F[63,x]+F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]+F[75,x]
F[74,x] = F[18,x]+F[34,x]
F[75,x] = F[76,x]+F[81,x]
F[76,x] = F[77,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = F[18,x]
F[80,x] = F[76,x]
F[81,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[34,x]
F[85,x] = F[86,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[88,x]+F[89,x]
F[88,x] = F[34,x]
F[89,x] = F[86,x]
F[90,x] = F[71,x]
F[91,x] = 2*F[13,x]+F[63,x]+F[92,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[94,x]+F[96,x]
F[94,x] = F[25,x]+F[95,x]
F[95,x] = F[31,x]
F[96,x] = F[102,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[101,x]
F[100,x] = F[25,x]
F[101,x] = F[97,x]
F[102,x] = F[103,x]
F[103,x] = F[104,x]*F[4,x]
F[104,x] = F[105,x]+F[106,x]
F[105,x] = F[95,x]
F[106,x] = F[107,x]
F[107,x] = F[108,x]*F[4,x]
F[108,x] = F[109,x]+F[110,x]
F[109,x] = F[95,x]
F[110,x] = F[107,x]
F[111,x] = F[112,x]*F[4,x]
F[112,x] = F[113,x]+F[140,x]
F[113,x] = F[114,x]+F[2,x]
F[114,x] = F[115,x]+F[13,x]+F[139,x]
F[115,x] = F[116,x]*F[4,x]
F[116,x] = F[117,x]+F[118,x]
F[117,x] = F[12,x]+F[4,x]
F[118,x] = F[119,x]+F[66,x]
F[119,x] = 2*F[13,x]+F[120,x]+F[63,x]
F[120,x] = F[121,x]*F[4,x]
F[121,x] = F[122,x]+F[124,x]
F[122,x] = F[12,x]+F[123,x]
F[123,x] = F[31,x]
F[124,x] = F[125,x]+F[130,x]
F[125,x] = F[126,x]
F[126,x] = F[127,x]*F[4,x]
F[127,x] = F[128,x]+F[129,x]
F[128,x] = F[12,x]
F[129,x] = F[125,x]
F[130,x] = F[131,x]
F[131,x] = F[132,x]*F[4,x]
F[132,x] = F[133,x]+F[134,x]
F[133,x] = F[123,x]
F[134,x] = F[135,x]
F[135,x] = F[136,x]*F[4,x]
F[136,x] = F[137,x]+F[138,x]
F[137,x] = F[123,x]
F[138,x] = F[135,x]
F[139,x] = F[2,x]*F[4,x]
F[140,x] = F[141,x]+F[21,x]
F[141,x] = F[13,x]+F[142,x]+F[155,x]+F[63,x]
F[142,x] = F[143,x]*F[4,x]
F[143,x] = F[144,x]+F[145,x]
F[144,x] = F[12,x]+F[29,x]
F[145,x] = F[125,x]+F[146,x]
F[146,x] = F[147,x]
F[147,x] = F[148,x]*F[4,x]
F[148,x] = F[149,x]+F[150,x]
F[149,x] = F[29,x]
F[150,x] = F[151,x]
F[151,x] = F[152,x]*F[4,x]
F[152,x] = F[153,x]+F[154,x]
F[153,x] = F[29,x]
F[154,x] = F[151,x]
F[155,x] = F[21,x]*F[4,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_{111}\! \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_{36}\! \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_{25}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{13}\! \left(x \right)+F_{30}\! \left(x \right)+F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{30}\! \left(x \right) = 0
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{17}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{31}\! \left(x \right)
F_{35}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{91}\! \left(x \right)
F_{37}\! \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_{42}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{7}\! \left(x \right)
F_{41}\! \left(x \right) = F_{14}\! \left(x \right)
F_{42}\! \left(x \right) = F_{37}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{44}\! \left(x \right)+F_{63}\! \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_{41}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{31}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{54}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \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_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{41}\! \left(x \right)
F_{53}\! \left(x \right) = F_{49}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{58}\! \left(x \right)
F_{57}\! \left(x \right) = F_{47}\! \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_{59}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{90}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \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_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{18}\! \left(x \right)+F_{4}\! \left(x \right)
F_{70}\! \left(x \right) = F_{66}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{63}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{75}\! \left(x \right)
F_{74}\! \left(x \right) = F_{18}\! \left(x \right)+F_{34}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{81}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{18}\! \left(x \right)
F_{80}\! \left(x \right) = F_{76}\! \left(x \right)
F_{81}\! \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_{34}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{89}\! \left(x \right)
F_{88}\! \left(x \right) = F_{34}\! \left(x \right)
F_{89}\! \left(x \right) = F_{86}\! \left(x \right)
F_{90}\! \left(x \right) = F_{71}\! \left(x \right)
F_{91}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{63}\! \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_{96}\! \left(x \right)
F_{94}\! \left(x \right) = F_{25}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{31}\! \left(x \right)
F_{96}\! \left(x \right) = F_{102}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{4}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)
F_{100}\! \left(x \right) = F_{25}\! \left(x \right)
F_{101}\! \left(x \right) = F_{97}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{106}\! \left(x \right)
F_{105}\! \left(x \right) = F_{95}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{109}\! \left(x \right) = F_{95}\! \left(x \right)
F_{110}\! \left(x \right) = F_{107}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{4}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{140}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{2}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{13}\! \left(x \right)+F_{139}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right) F_{4}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{118}\! \left(x \right)
F_{117}\! \left(x \right) = F_{12}\! \left(x \right)+F_{4}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{66}\! \left(x \right)
F_{119}\! \left(x \right) = 2 F_{13}\! \left(x \right)+F_{120}\! \left(x \right)+F_{63}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right) F_{4}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right)+F_{124}\! \left(x \right)
F_{122}\! \left(x \right) = F_{12}\! \left(x \right)+F_{123}\! \left(x \right)
F_{123}\! \left(x \right) = F_{31}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{130}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{4}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{129}\! \left(x \right)
F_{128}\! \left(x \right) = F_{12}\! \left(x \right)
F_{129}\! \left(x \right) = F_{125}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right) F_{4}\! \left(x \right)
F_{132}\! \left(x \right) = F_{133}\! \left(x \right)+F_{134}\! \left(x \right)
F_{133}\! \left(x \right) = F_{123}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right) F_{4}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{138}\! \left(x \right)
F_{137}\! \left(x \right) = F_{123}\! \left(x \right)
F_{138}\! \left(x \right) = F_{135}\! \left(x \right)
F_{139}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{21}\! \left(x \right)
F_{141}\! \left(x \right) = F_{13}\! \left(x \right)+F_{142}\! \left(x \right)+F_{155}\! \left(x \right)+F_{63}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right) F_{4}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)+F_{145}\! \left(x \right)
F_{144}\! \left(x \right) = F_{12}\! \left(x \right)+F_{29}\! \left(x \right)
F_{145}\! \left(x \right) = F_{125}\! \left(x \right)+F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{4}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{150}\! \left(x \right)
F_{149}\! \left(x \right) = F_{29}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right) F_{4}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{154}\! \left(x \right)
F_{153}\! \left(x \right) = F_{29}\! \left(x \right)
F_{154}\! \left(x \right) = F_{151}\! \left(x \right)
F_{155}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \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_111(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_36(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_25(x) + F_29(x))
Eq(F_29(x), F_13(x) + F_30(x) + F_31(x) + F_35(x))
Eq(F_30(x), 0)
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_17(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_31(x))
Eq(F_35(x), F_25(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_91(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_42(x))
Eq(F_40(x), F_41(x) + F_7(x))
Eq(F_41(x), F_14(x))
Eq(F_42(x), F_37(x) + F_43(x))
Eq(F_43(x), 2*F_13(x) + F_44(x) + F_63(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_41(x) + F_47(x))
Eq(F_47(x), F_31(x))
Eq(F_48(x), F_49(x) + F_54(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_41(x))
Eq(F_53(x), F_49(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_58(x))
Eq(F_57(x), F_47(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_59(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_90(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_70(x))
Eq(F_69(x), F_18(x) + F_4(x))
Eq(F_70(x), F_66(x) + F_71(x))
Eq(F_71(x), 2*F_13(x) + F_63(x) + F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_75(x))
Eq(F_74(x), F_18(x) + F_34(x))
Eq(F_75(x), F_76(x) + F_81(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), F_18(x))
Eq(F_80(x), F_76(x))
Eq(F_81(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_34(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_89(x))
Eq(F_88(x), F_34(x))
Eq(F_89(x), F_86(x))
Eq(F_90(x), F_71(x))
Eq(F_91(x), 2*F_13(x) + F_63(x) + F_92(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_96(x))
Eq(F_94(x), F_25(x) + F_95(x))
Eq(F_95(x), F_31(x))
Eq(F_96(x), F_102(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_4(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_101(x))
Eq(F_100(x), F_25(x))
Eq(F_101(x), F_97(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_104(x)*F_4(x))
Eq(F_104(x), F_105(x) + F_106(x))
Eq(F_105(x), F_95(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x)*F_4(x))
Eq(F_108(x), F_109(x) + F_110(x))
Eq(F_109(x), F_95(x))
Eq(F_110(x), F_107(x))
Eq(F_111(x), F_112(x)*F_4(x))
Eq(F_112(x), F_113(x) + F_140(x))
Eq(F_113(x), F_114(x) + F_2(x))
Eq(F_114(x), F_115(x) + F_13(x) + F_139(x))
Eq(F_115(x), F_116(x)*F_4(x))
Eq(F_116(x), F_117(x) + F_118(x))
Eq(F_117(x), F_12(x) + F_4(x))
Eq(F_118(x), F_119(x) + F_66(x))
Eq(F_119(x), F_120(x) + 2*F_13(x) + F_63(x))
Eq(F_120(x), F_121(x)*F_4(x))
Eq(F_121(x), F_122(x) + F_124(x))
Eq(F_122(x), F_12(x) + F_123(x))
Eq(F_123(x), F_31(x))
Eq(F_124(x), F_125(x) + F_130(x))
Eq(F_125(x), F_126(x))
Eq(F_126(x), F_127(x)*F_4(x))
Eq(F_127(x), F_128(x) + F_129(x))
Eq(F_128(x), F_12(x))
Eq(F_129(x), F_125(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_132(x)*F_4(x))
Eq(F_132(x), F_133(x) + F_134(x))
Eq(F_133(x), F_123(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_136(x)*F_4(x))
Eq(F_136(x), F_137(x) + F_138(x))
Eq(F_137(x), F_123(x))
Eq(F_138(x), F_135(x))
Eq(F_139(x), F_2(x)*F_4(x))
Eq(F_140(x), F_141(x) + F_21(x))
Eq(F_141(x), F_13(x) + F_142(x) + F_155(x) + F_63(x))
Eq(F_142(x), F_143(x)*F_4(x))
Eq(F_143(x), F_144(x) + F_145(x))
Eq(F_144(x), F_12(x) + F_29(x))
Eq(F_145(x), F_125(x) + F_146(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_148(x)*F_4(x))
Eq(F_148(x), F_149(x) + F_150(x))
Eq(F_149(x), F_29(x))
Eq(F_150(x), F_151(x))
Eq(F_151(x), F_152(x)*F_4(x))
Eq(F_152(x), F_153(x) + F_154(x))
Eq(F_153(x), F_29(x))
Eq(F_154(x), F_151(x))
Eq(F_155(x), F_21(x)*F_4(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": [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": [2, 1, 3, 0], "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": [2, 1, 3, 0], "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, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, 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