0213_0321_3120
Counting sequence:
1, 1, 2, 6, 21, 73, 239, 736, 2158, 6102, 16813, 45493, 121567, 322108, 848654, 2227722, 5834253, 15258361, 39874967, 104169568, 272109046, 710846406, 1857283957, 4853664901, 12686932951, 33169384588, 86737334054, 226858067466, 593434214373, 1552572159577, 4062403215263, 10630610953408, 27820839709342, 72813654562518, 190581469271389, 498849148871797, 1305794178650863, 3418172609826556, 8947967736583262, 23424150051956778, 61321183884402141, 160532529653574361, 420262111425158087, 1100224117807948096, 2880348669347528806, 7540694346885814278, 19741470488519245669, 51683171760904543621, 135306918894287540263, 354235262753400211852, 927394084291309011638, 2427937138496341947498, 6356397064999393660917, 16641212398205285855353, 43567154561223543862799, 114060075645079878280672, 298612712086045901336398, 781777322022718936963926, 2046717740772636113065357, 5358372801818645771327413, 14028394323615025863254911, 36726797198659504991405116, 96151970755168883153476142, 251729060879536427947211466, 659035101202975958430844461, 1725376016756776544403310393, 4517092487898751832040291959, 11825900506155531192530428576, 30960607112106458079757621078, 81055916919454099420317487302, 212207135677262400338668537813, 555565473879198316731282699013, 1454489252903767169767663058167, 3807902217538380811679262174988, 9969217262762747262050412264134, 26099749292130238485162907003722, 68330030046943990249080883097733, 178890339696444310441886310141721, 468340986700095165573234021328127, 1226132615643695771545213378430848, 3210056850559585592145372716308606, 8404037916390016436153180681513046, 22002056858715911669031406562919997, 57602132578759688656760884301926261, 150804340713149242833661678582811791, 394810889227024513630586499227597308, 1033628326290925839073905481264514174, 2706074088272413272508911202099721706, 7084593935740948890060722506511613693, 18547707713302331968433708813207857177, 48558529192715101651850636390295050663, 127127879841631597250517320203318707328, 332825110285137968606856873773494342342, 871347450918460925545079019949931745798, 2281217242277126161899860863192037507269, 5972304275521728507740323402758057512197, 15635695583495777736178465969146695516743, 40934782473361234409881221668412764034316, 107168651833339570830380361194756294612822, 280571173020081540592575921895591971916458, 734544867213594719644950995776304237470101
Generating function in Maple syntax:
-(7*x^6-36*x^5+64*x^4-62*x^3+33*x^2-9*x+1)/(x^2-3*x+1)/(2*x-1)^2/(x-1)^3
Generating function in latex syntax:
-\frac{7 x^{6}-36 x^{5}+64 x^{4}-62 x^{3}+33 x^{2}-9 x +1}{\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{3}}
Generating function in sympy syntax:
(-7*x**6 + 36*x**5 - 64*x**4 + 62*x**3 - 33*x**2 + 9*x - 1)/((x - 1)**3*(2*x - 1)**2*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
(x^2-3*x+1)*(2*x-1)^2*(x-1)^3*F(x)+7*x^6-36*x^5+64*x^4-62*x^3+33*x^2-9*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{3} F \! \left(x \right)+7 x^{6}-36 x^{5}+64 x^{4}-62 x^{3}+33 x^{2}-9 x +1 = 0
Explicit closed form in Maple syntax:
1/10*(3*5^(1/2)+5)*(3/2-1/2*5^(1/2))^(-n)+1/10*(-3*5^(1/2)+5)*(3/2+1/2*5^(1/2))^(-n)+n^2+2^(-1+n)*n+2*n-6*2^n+6
Explicit closed form in latex syntax:
\frac{\left(3 \sqrt{5}+5\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{10}+\frac{\left(-3 \sqrt{5}+5\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{10}+n^{2}+2^{-1+n} n +2 n -6 \,2^{n}+6
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 73
a(6) = 239
a(n+4) = -4*a(n)+16*a(n+1)-17*a(n+2)+7*a(n+3)-(-1+n)*(n+1), n >= 7
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 21
a \! \left(5\right) = 73
a \! \left(6\right) = 239
a \! \left(n +4\right) = -4 a \! \left(n \right)+16 a \! \left(n +1\right)-17 a \! \left(n +2\right)+7 a \! \left(n +3\right)-\left(-1+n \right) \left(n +1\right), \quad n \geq 7
Specification 1
Strategy pack name: insertion_row_placements
Tree: http://permpal.com/tree/321/
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[14,x]*F[4,x]
F[4,x] = F[34,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[14,x]*F[8,x]
F[8,x] = F[18,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[14,x]
F[12,x] = F[13,x]+F[9,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = x
F[15,x] = F[16,x]
F[16,x] = F[14,x]*F[17,x]
F[17,x] = F[13,x]
F[18,x] = F[19,x]+F[22,x]
F[19,x] = F[20,x]
F[20,x] = F[14,x]*F[21,x]
F[21,x] = F[1,x]+F[19,x]
F[22,x] = F[23,x]+F[24,x]+F[26,x]
F[23,x] = 0
F[24,x] = F[14,x]*F[25,x]
F[25,x] = F[10,x]+F[22,x]
F[26,x] = F[14,x]*F[27,x]
F[27,x] = F[18,x]+F[28,x]
F[28,x] = F[29,x]+F[31,x]
F[29,x] = F[30,x]
F[30,x] = F[14,x]*F[19,x]
F[31,x] = F[32,x]
F[32,x] = F[14,x]*F[33,x]
F[33,x] = F[28,x]
F[34,x] = F[35,x]+F[60,x]
F[35,x] = F[36,x]
F[36,x] = F[14,x]*F[37,x]
F[37,x] = F[38,x]+F[40,x]
F[38,x] = F[1,x]+F[39,x]
F[39,x] = F[14,x]*F[38,x]
F[40,x] = F[41,x]+F[50,x]
F[41,x] = F[42,x]
F[42,x] = F[14,x]*F[43,x]
F[43,x] = F[38,x]+F[44,x]
F[44,x] = F[19,x]+F[45,x]
F[45,x] = F[23,x]+F[46,x]+F[49,x]
F[46,x] = F[14,x]*F[47,x]
F[47,x] = F[45,x]+F[48,x]
F[48,x] = F[39,x]
F[49,x] = F[14,x]*F[44,x]
F[50,x] = F[23,x]+F[51,x]+F[59,x]
F[51,x] = F[14,x]*F[52,x]
F[52,x] = F[53,x]+F[56,x]
F[53,x] = F[48,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[14,x]*F[53,x]
F[56,x] = F[50,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[48,x]^2*F[41,x]
F[59,x] = F[14,x]*F[40,x]
F[60,x] = F[159,x]+F[23,x]+F[61,x]
F[61,x] = F[14,x]*F[62,x]
F[62,x] = F[111,x]+F[63,x]
F[63,x] = F[6,x]+F[64,x]
F[64,x] = F[23,x]+F[65,x]+F[86,x]
F[65,x] = F[14,x]*F[66,x]
F[66,x] = F[67,x]+F[73,x]
F[67,x] = F[48,x]+F[68,x]
F[68,x] = F[23,x]+F[69,x]+F[70,x]
F[69,x] = F[14,x]*F[67,x]
F[70,x] = F[14,x]*F[71,x]
F[71,x] = F[14,x]+F[72,x]
F[72,x] = F[70,x]
F[73,x] = F[74,x]+F[79,x]
F[74,x] = F[23,x]+F[75,x]+F[77,x]
F[75,x] = F[14,x]*F[76,x]
F[76,x] = F[48,x]+F[74,x]
F[77,x] = F[14,x]*F[78,x]
F[78,x] = F[19,x]+F[74,x]
F[79,x] = F[23,x]+F[80,x]+F[82,x]+F[83,x]
F[80,x] = F[14,x]*F[81,x]
F[81,x] = F[68,x]+F[79,x]
F[82,x] = F[14,x]*F[73,x]
F[83,x] = F[14,x]*F[84,x]
F[84,x] = F[29,x]+F[85,x]
F[85,x] = F[83,x]
F[86,x] = F[14,x]*F[87,x]
F[87,x] = F[88,x]+F[96,x]
F[88,x] = F[19,x]+F[89,x]
F[89,x] = F[23,x]+F[75,x]+F[90,x]
F[90,x] = F[14,x]*F[91,x]
F[91,x] = F[88,x]+F[92,x]
F[92,x] = F[29,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[14,x]*F[95,x]
F[95,x] = F[92,x]
F[96,x] = F[100,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[14,x]*F[99,x]
F[99,x] = F[19,x]+F[97,x]
F[100,x] = 2*F[23,x]+F[101,x]+F[103,x]
F[101,x] = F[102,x]*F[14,x]
F[102,x] = F[100,x]+F[89,x]
F[103,x] = F[104,x]*F[14,x]
F[104,x] = F[105,x]+F[96,x]
F[105,x] = F[106,x]+F[108,x]
F[106,x] = F[107,x]
F[107,x] = F[14,x]*F[97,x]
F[108,x] = F[109,x]
F[109,x] = F[110,x]*F[14,x]
F[110,x] = F[105,x]
F[111,x] = F[112,x]+F[60,x]
F[112,x] = 2*F[23,x]+F[113,x]+F[138,x]
F[113,x] = F[114,x]*F[14,x]
F[114,x] = F[115,x]+F[131,x]
F[115,x] = F[116,x]+F[127,x]
F[116,x] = F[117,x]+F[126,x]+F[23,x]
F[117,x] = F[118,x]*F[14,x]
F[118,x] = F[119,x]+F[76,x]
F[119,x] = F[116,x]+F[120,x]
F[120,x] = 2*F[23,x]+F[121,x]+F[122,x]
F[121,x] = F[119,x]*F[14,x]
F[122,x] = F[123,x]*F[14,x]
F[123,x] = F[120,x]+F[124,x]
F[124,x] = F[125,x]
F[125,x] = F[19,x]*F[41,x]
F[126,x] = F[14,x]*F[40,x]
F[127,x] = 2*F[23,x]+F[128,x]+F[129,x]
F[128,x] = F[115,x]*F[14,x]
F[129,x] = F[130,x]
F[130,x] = F[14,x]^2*F[38,x]*F[41,x]
F[131,x] = F[120,x]+F[132,x]
F[132,x] = 2*F[23,x]+F[133,x]+F[135,x]+F[136,x]
F[133,x] = F[134,x]*F[14,x]
F[134,x] = F[127,x]+F[132,x]
F[135,x] = F[131,x]*F[14,x]
F[136,x] = F[137,x]
F[137,x] = F[14,x]^2*F[19,x]*F[38,x]*F[41,x]
F[138,x] = F[139,x]
F[139,x] = F[14,x]*F[140,x]
F[140,x] = F[141,x]+F[148,x]
F[141,x] = F[124,x]+F[142,x]
F[142,x] = 2*F[23,x]+F[121,x]+F[143,x]
F[143,x] = F[144,x]
F[144,x] = F[14,x]*F[145,x]
F[145,x] = F[141,x]+F[146,x]
F[146,x] = F[147,x]
F[147,x] = F[14,x]*F[19,x]*F[38,x]*F[41,x]
F[148,x] = F[149,x]+F[151,x]
F[149,x] = F[150,x]
F[150,x] = F[19,x]^2*F[41,x]
F[151,x] = 3*F[23,x]+F[152,x]+F[154,x]
F[152,x] = F[14,x]*F[153,x]
F[153,x] = F[142,x]+F[151,x]
F[154,x] = F[155,x]
F[155,x] = F[14,x]*F[156,x]
F[156,x] = F[148,x]+F[157,x]
F[157,x] = F[158,x]
F[158,x] = F[19,x]^2*F[14,x]*F[38,x]*F[41,x]
F[159,x] = F[14,x]*F[160,x]
F[160,x] = F[161,x]+F[164,x]
F[161,x] = F[162,x]
F[162,x] = F[163,x]+F[35,x]
F[163,x] = F[41,x]*F[6,x]
F[164,x] = F[165,x]+F[194,x]
F[165,x] = F[166,x]+F[189,x]+F[23,x]
F[166,x] = F[167,x]
F[167,x] = F[14,x]*F[168,x]*F[169,x]
F[168,x] = F[1,x]+F[41,x]
F[169,x] = F[170,x]+F[174,x]
F[170,x] = F[171,x]
F[171,x] = F[14,x]*F[172,x]*F[38,x]
F[172,x] = F[1,x]+F[173,x]
F[173,x] = F[170,x]
F[174,x] = F[175,x]+F[182,x]+F[23,x]
F[175,x] = F[14,x]*F[176,x]
F[176,x] = F[177,x]+F[53,x]
F[177,x] = F[178,x]+F[74,x]
F[178,x] = 2*F[23,x]+F[179,x]+F[181,x]
F[179,x] = F[14,x]*F[180,x]
F[180,x] = F[178,x]+F[54,x]
F[181,x] = F[14,x]*F[177,x]
F[182,x] = F[14,x]*F[183,x]
F[183,x] = F[184,x]+F[78,x]
F[184,x] = F[185,x]+F[97,x]
F[185,x] = 2*F[23,x]+F[186,x]+F[188,x]
F[186,x] = F[14,x]*F[187,x]
F[187,x] = F[185,x]+F[74,x]
F[188,x] = F[14,x]*F[184,x]
F[189,x] = F[190,x]
F[190,x] = F[14,x]*F[191,x]
F[191,x] = F[165,x]+F[192,x]
F[192,x] = F[193,x]+F[35,x]
F[193,x] = F[170,x]*F[41,x]
F[194,x] = F[195,x]
F[195,x] = F[170,x]*F[41,x]*F[48,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_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{34}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{14}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{18}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \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_{9}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{15}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{14}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{13}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{22}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{14}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)+F_{26}\! \left(x \right)
F_{23}\! \left(x \right) = 0
F_{24}\! \left(x \right) = F_{14}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{10}\! \left(x \right)+F_{22}\! \left(x \right)
F_{26}\! \left(x \right) = F_{14}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{18}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{31}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{14}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{28}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{60}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{14}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{40}\! \left(x \right)
F_{38}\! \left(x \right) = F_{1}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{14}\! \left(x \right) F_{38}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{50}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{14}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{38}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{19}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{23}\! \left(x \right)+F_{46}\! \left(x \right)+F_{49}\! \left(x \right)
F_{46}\! \left(x \right) = F_{14}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{45}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{39}\! \left(x \right)
F_{49}\! \left(x \right) = F_{14}\! \left(x \right) F_{44}\! \left(x \right)
F_{50}\! \left(x \right) = F_{23}\! \left(x \right)+F_{51}\! \left(x \right)+F_{59}\! \left(x \right)
F_{51}\! \left(x \right) = F_{14}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{56}\! \left(x \right)
F_{53}\! \left(x \right) = F_{48}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{14}\! \left(x \right) F_{53}\! \left(x \right)
F_{56}\! \left(x \right) = F_{50}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{48} \left(x \right)^{2} F_{41}\! \left(x \right)
F_{59}\! \left(x \right) = F_{14}\! \left(x \right) F_{40}\! \left(x \right)
F_{60}\! \left(x \right) = F_{159}\! \left(x \right)+F_{23}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{14}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{111}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{6}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{23}\! \left(x \right)+F_{65}\! \left(x \right)+F_{86}\! \left(x \right)
F_{65}\! \left(x \right) = F_{14}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{73}\! \left(x \right)
F_{67}\! \left(x \right) = F_{48}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{23}\! \left(x \right)+F_{69}\! \left(x \right)+F_{70}\! \left(x \right)
F_{69}\! \left(x \right) = F_{14}\! \left(x \right) F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{14}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{14}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{70}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{79}\! \left(x \right)
F_{74}\! \left(x \right) = F_{23}\! \left(x \right)+F_{75}\! \left(x \right)+F_{77}\! \left(x \right)
F_{75}\! \left(x \right) = F_{14}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{48}\! \left(x \right)+F_{74}\! \left(x \right)
F_{77}\! \left(x \right) = F_{14}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{19}\! \left(x \right)+F_{74}\! \left(x \right)
F_{79}\! \left(x \right) = F_{23}\! \left(x \right)+F_{80}\! \left(x \right)+F_{82}\! \left(x \right)+F_{83}\! \left(x \right)
F_{80}\! \left(x \right) = F_{14}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{68}\! \left(x \right)+F_{79}\! \left(x \right)
F_{82}\! \left(x \right) = F_{14}\! \left(x \right) F_{73}\! \left(x \right)
F_{83}\! \left(x \right) = F_{14}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{29}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{83}\! \left(x \right)
F_{86}\! \left(x \right) = F_{14}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{96}\! \left(x \right)
F_{88}\! \left(x \right) = F_{19}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{23}\! \left(x \right)+F_{75}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{14}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{88}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{29}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{14}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{92}\! \left(x \right)
F_{96}\! \left(x \right) = F_{100}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{14}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{19}\! \left(x \right)+F_{97}\! \left(x \right)
F_{100}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{101}\! \left(x \right)+F_{103}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{14}\! \left(x \right)
F_{102}\! \left(x \right) = F_{100}\! \left(x \right)+F_{89}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{14}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{96}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{108}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{14}\! \left(x \right) F_{97}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{14}\! \left(x \right)
F_{110}\! \left(x \right) = F_{105}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)+F_{60}\! \left(x \right)
F_{112}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{113}\! \left(x \right)+F_{138}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{14}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{131}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{127}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)+F_{126}\! \left(x \right)+F_{23}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{14}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{76}\! \left(x \right)
F_{119}\! \left(x \right) = F_{116}\! \left(x \right)+F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{121}\! \left(x \right)+F_{122}\! \left(x \right)
F_{121}\! \left(x \right) = F_{119}\! \left(x \right) F_{14}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right) F_{14}\! \left(x \right)
F_{123}\! \left(x \right) = F_{120}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{19}\! \left(x \right) F_{41}\! \left(x \right)
F_{126}\! \left(x \right) = F_{14}\! \left(x \right) F_{40}\! \left(x \right)
F_{127}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{128}\! \left(x \right)+F_{129}\! \left(x \right)
F_{128}\! \left(x \right) = F_{115}\! \left(x \right) F_{14}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{38}\! \left(x \right) F_{41}\! \left(x \right)
F_{131}\! \left(x \right) = F_{120}\! \left(x \right)+F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{133}\! \left(x \right)+F_{135}\! \left(x \right)+F_{136}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right) F_{14}\! \left(x \right)
F_{134}\! \left(x \right) = F_{127}\! \left(x \right)+F_{132}\! \left(x \right)
F_{135}\! \left(x \right) = F_{131}\! \left(x \right) F_{14}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{14} \left(x \right)^{2} F_{19}\! \left(x \right) F_{38}\! \left(x \right) F_{41}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{14}\! \left(x \right) F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right)+F_{148}\! \left(x \right)
F_{141}\! \left(x \right) = F_{124}\! \left(x \right)+F_{142}\! \left(x \right)
F_{142}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{121}\! \left(x \right)+F_{143}\! \left(x \right)
F_{143}\! \left(x \right) = F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{14}\! \left(x \right) F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{141}\! \left(x \right)+F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{14}\! \left(x \right) F_{19}\! \left(x \right) F_{38}\! \left(x \right) F_{41}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right)+F_{151}\! \left(x \right)
F_{149}\! \left(x \right) = F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{19} \left(x \right)^{2} F_{41}\! \left(x \right)
F_{151}\! \left(x \right) = 3 F_{23}\! \left(x \right)+F_{152}\! \left(x \right)+F_{154}\! \left(x \right)
F_{152}\! \left(x \right) = F_{14}\! \left(x \right) F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{142}\! \left(x \right)+F_{151}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{14}\! \left(x \right) F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{148}\! \left(x \right)+F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = F_{19} \left(x \right)^{2} F_{14}\! \left(x \right) F_{38}\! \left(x \right) F_{41}\! \left(x \right)
F_{159}\! \left(x \right) = F_{14}\! \left(x \right) F_{160}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{164}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)+F_{35}\! \left(x \right)
F_{163}\! \left(x \right) = F_{41}\! \left(x \right) F_{6}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)+F_{194}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right)+F_{189}\! \left(x \right)+F_{23}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)
F_{167}\! \left(x \right) = F_{14}\! \left(x \right) F_{168}\! \left(x \right) F_{169}\! \left(x \right)
F_{168}\! \left(x \right) = F_{1}\! \left(x \right)+F_{41}\! \left(x \right)
F_{169}\! \left(x \right) = F_{170}\! \left(x \right)+F_{174}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)
F_{171}\! \left(x \right) = F_{14}\! \left(x \right) F_{172}\! \left(x \right) F_{38}\! \left(x \right)
F_{172}\! \left(x \right) = F_{1}\! \left(x \right)+F_{173}\! \left(x \right)
F_{173}\! \left(x \right) = F_{170}\! \left(x \right)
F_{174}\! \left(x \right) = F_{175}\! \left(x \right)+F_{182}\! \left(x \right)+F_{23}\! \left(x \right)
F_{175}\! \left(x \right) = F_{14}\! \left(x \right) F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)+F_{53}\! \left(x \right)
F_{177}\! \left(x \right) = F_{178}\! \left(x \right)+F_{74}\! \left(x \right)
F_{178}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{179}\! \left(x \right)+F_{181}\! \left(x \right)
F_{179}\! \left(x \right) = F_{14}\! \left(x \right) F_{180}\! \left(x \right)
F_{180}\! \left(x \right) = F_{178}\! \left(x \right)+F_{54}\! \left(x \right)
F_{181}\! \left(x \right) = F_{14}\! \left(x \right) F_{177}\! \left(x \right)
F_{182}\! \left(x \right) = F_{14}\! \left(x \right) F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right)+F_{78}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{97}\! \left(x \right)
F_{185}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{186}\! \left(x \right)+F_{188}\! \left(x \right)
F_{186}\! \left(x \right) = F_{14}\! \left(x \right) F_{187}\! \left(x \right)
F_{187}\! \left(x \right) = F_{185}\! \left(x \right)+F_{74}\! \left(x \right)
F_{188}\! \left(x \right) = F_{14}\! \left(x \right) F_{184}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)
F_{190}\! \left(x \right) = F_{14}\! \left(x \right) F_{191}\! \left(x \right)
F_{191}\! \left(x \right) = F_{165}\! \left(x \right)+F_{192}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{35}\! \left(x \right)
F_{193}\! \left(x \right) = F_{170}\! \left(x \right) F_{41}\! \left(x \right)
F_{194}\! \left(x \right) = F_{195}\! \left(x \right)
F_{195}\! \left(x \right) = F_{170}\! \left(x \right) F_{41}\! \left(x \right) F_{48}\! \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_14(x)*F_4(x))
Eq(F_4(x), F_34(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_14(x)*F_8(x))
Eq(F_8(x), F_18(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_14(x))
Eq(F_12(x), F_13(x) + F_9(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), x)
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)*F_17(x))
Eq(F_17(x), F_13(x))
Eq(F_18(x), F_19(x) + F_22(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_14(x)*F_21(x))
Eq(F_21(x), F_1(x) + F_19(x))
Eq(F_22(x), F_23(x) + F_24(x) + F_26(x))
Eq(F_23(x), 0)
Eq(F_24(x), F_14(x)*F_25(x))
Eq(F_25(x), F_10(x) + F_22(x))
Eq(F_26(x), F_14(x)*F_27(x))
Eq(F_27(x), F_18(x) + F_28(x))
Eq(F_28(x), F_29(x) + F_31(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_14(x)*F_19(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_14(x)*F_33(x))
Eq(F_33(x), F_28(x))
Eq(F_34(x), F_35(x) + F_60(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_14(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_40(x))
Eq(F_38(x), F_1(x) + F_39(x))
Eq(F_39(x), F_14(x)*F_38(x))
Eq(F_40(x), F_41(x) + F_50(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_14(x)*F_43(x))
Eq(F_43(x), F_38(x) + F_44(x))
Eq(F_44(x), F_19(x) + F_45(x))
Eq(F_45(x), F_23(x) + F_46(x) + F_49(x))
Eq(F_46(x), F_14(x)*F_47(x))
Eq(F_47(x), F_45(x) + F_48(x))
Eq(F_48(x), F_39(x))
Eq(F_49(x), F_14(x)*F_44(x))
Eq(F_50(x), F_23(x) + F_51(x) + F_59(x))
Eq(F_51(x), F_14(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_56(x))
Eq(F_53(x), F_48(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_14(x)*F_53(x))
Eq(F_56(x), F_50(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_41(x)*F_48(x)**2)
Eq(F_59(x), F_14(x)*F_40(x))
Eq(F_60(x), F_159(x) + F_23(x) + F_61(x))
Eq(F_61(x), F_14(x)*F_62(x))
Eq(F_62(x), F_111(x) + F_63(x))
Eq(F_63(x), F_6(x) + F_64(x))
Eq(F_64(x), F_23(x) + F_65(x) + F_86(x))
Eq(F_65(x), F_14(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_73(x))
Eq(F_67(x), F_48(x) + F_68(x))
Eq(F_68(x), F_23(x) + F_69(x) + F_70(x))
Eq(F_69(x), F_14(x)*F_67(x))
Eq(F_70(x), F_14(x)*F_71(x))
Eq(F_71(x), F_14(x) + F_72(x))
Eq(F_72(x), F_70(x))
Eq(F_73(x), F_74(x) + F_79(x))
Eq(F_74(x), F_23(x) + F_75(x) + F_77(x))
Eq(F_75(x), F_14(x)*F_76(x))
Eq(F_76(x), F_48(x) + F_74(x))
Eq(F_77(x), F_14(x)*F_78(x))
Eq(F_78(x), F_19(x) + F_74(x))
Eq(F_79(x), F_23(x) + F_80(x) + F_82(x) + F_83(x))
Eq(F_80(x), F_14(x)*F_81(x))
Eq(F_81(x), F_68(x) + F_79(x))
Eq(F_82(x), F_14(x)*F_73(x))
Eq(F_83(x), F_14(x)*F_84(x))
Eq(F_84(x), F_29(x) + F_85(x))
Eq(F_85(x), F_83(x))
Eq(F_86(x), F_14(x)*F_87(x))
Eq(F_87(x), F_88(x) + F_96(x))
Eq(F_88(x), F_19(x) + F_89(x))
Eq(F_89(x), F_23(x) + F_75(x) + F_90(x))
Eq(F_90(x), F_14(x)*F_91(x))
Eq(F_91(x), F_88(x) + F_92(x))
Eq(F_92(x), F_29(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_14(x)*F_95(x))
Eq(F_95(x), F_92(x))
Eq(F_96(x), F_100(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_14(x)*F_99(x))
Eq(F_99(x), F_19(x) + F_97(x))
Eq(F_100(x), F_101(x) + F_103(x) + 2*F_23(x))
Eq(F_101(x), F_102(x)*F_14(x))
Eq(F_102(x), F_100(x) + F_89(x))
Eq(F_103(x), F_104(x)*F_14(x))
Eq(F_104(x), F_105(x) + F_96(x))
Eq(F_105(x), F_106(x) + F_108(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_14(x)*F_97(x))
Eq(F_108(x), F_109(x))
Eq(F_109(x), F_110(x)*F_14(x))
Eq(F_110(x), F_105(x))
Eq(F_111(x), F_112(x) + F_60(x))
Eq(F_112(x), F_113(x) + F_138(x) + 2*F_23(x))
Eq(F_113(x), F_114(x)*F_14(x))
Eq(F_114(x), F_115(x) + F_131(x))
Eq(F_115(x), F_116(x) + F_127(x))
Eq(F_116(x), F_117(x) + F_126(x) + F_23(x))
Eq(F_117(x), F_118(x)*F_14(x))
Eq(F_118(x), F_119(x) + F_76(x))
Eq(F_119(x), F_116(x) + F_120(x))
Eq(F_120(x), F_121(x) + F_122(x) + 2*F_23(x))
Eq(F_121(x), F_119(x)*F_14(x))
Eq(F_122(x), F_123(x)*F_14(x))
Eq(F_123(x), F_120(x) + F_124(x))
Eq(F_124(x), F_125(x))
Eq(F_125(x), F_19(x)*F_41(x))
Eq(F_126(x), F_14(x)*F_40(x))
Eq(F_127(x), F_128(x) + F_129(x) + 2*F_23(x))
Eq(F_128(x), F_115(x)*F_14(x))
Eq(F_129(x), F_130(x))
Eq(F_130(x), F_14(x)**2*F_38(x)*F_41(x))
Eq(F_131(x), F_120(x) + F_132(x))
Eq(F_132(x), F_133(x) + F_135(x) + F_136(x) + 2*F_23(x))
Eq(F_133(x), F_134(x)*F_14(x))
Eq(F_134(x), F_127(x) + F_132(x))
Eq(F_135(x), F_131(x)*F_14(x))
Eq(F_136(x), F_137(x))
Eq(F_137(x), F_14(x)**2*F_19(x)*F_38(x)*F_41(x))
Eq(F_138(x), F_139(x))
Eq(F_139(x), F_14(x)*F_140(x))
Eq(F_140(x), F_141(x) + F_148(x))
Eq(F_141(x), F_124(x) + F_142(x))
Eq(F_142(x), F_121(x) + F_143(x) + 2*F_23(x))
Eq(F_143(x), F_144(x))
Eq(F_144(x), F_14(x)*F_145(x))
Eq(F_145(x), F_141(x) + F_146(x))
Eq(F_146(x), F_147(x))
Eq(F_147(x), F_14(x)*F_19(x)*F_38(x)*F_41(x))
Eq(F_148(x), F_149(x) + F_151(x))
Eq(F_149(x), F_150(x))
Eq(F_150(x), F_19(x)**2*F_41(x))
Eq(F_151(x), F_152(x) + F_154(x) + 3*F_23(x))
Eq(F_152(x), F_14(x)*F_153(x))
Eq(F_153(x), F_142(x) + F_151(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_14(x)*F_156(x))
Eq(F_156(x), F_148(x) + F_157(x))
Eq(F_157(x), F_158(x))
Eq(F_158(x), F_14(x)*F_19(x)**2*F_38(x)*F_41(x))
Eq(F_159(x), F_14(x)*F_160(x))
Eq(F_160(x), F_161(x) + F_164(x))
Eq(F_161(x), F_162(x))
Eq(F_162(x), F_163(x) + F_35(x))
Eq(F_163(x), F_41(x)*F_6(x))
Eq(F_164(x), F_165(x) + F_194(x))
Eq(F_165(x), F_166(x) + F_189(x) + F_23(x))
Eq(F_166(x), F_167(x))
Eq(F_167(x), F_14(x)*F_168(x)*F_169(x))
Eq(F_168(x), F_1(x) + F_41(x))
Eq(F_169(x), F_170(x) + F_174(x))
Eq(F_170(x), F_171(x))
Eq(F_171(x), F_14(x)*F_172(x)*F_38(x))
Eq(F_172(x), F_1(x) + F_173(x))
Eq(F_173(x), F_170(x))
Eq(F_174(x), F_175(x) + F_182(x) + F_23(x))
Eq(F_175(x), F_14(x)*F_176(x))
Eq(F_176(x), F_177(x) + F_53(x))
Eq(F_177(x), F_178(x) + F_74(x))
Eq(F_178(x), F_179(x) + F_181(x) + 2*F_23(x))
Eq(F_179(x), F_14(x)*F_180(x))
Eq(F_180(x), F_178(x) + F_54(x))
Eq(F_181(x), F_14(x)*F_177(x))
Eq(F_182(x), F_14(x)*F_183(x))
Eq(F_183(x), F_184(x) + F_78(x))
Eq(F_184(x), F_185(x) + F_97(x))
Eq(F_185(x), F_186(x) + F_188(x) + 2*F_23(x))
Eq(F_186(x), F_14(x)*F_187(x))
Eq(F_187(x), F_185(x) + F_74(x))
Eq(F_188(x), F_14(x)*F_184(x))
Eq(F_189(x), F_190(x))
Eq(F_190(x), F_14(x)*F_191(x))
Eq(F_191(x), F_165(x) + F_192(x))
Eq(F_192(x), F_193(x) + F_35(x))
Eq(F_193(x), F_170(x)*F_41(x))
Eq(F_194(x), F_195(x))
Eq(F_195(x), F_170(x)*F_41(x)*F_48(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "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}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_row_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 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"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": []}, {"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]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", 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[[2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [3, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}], [{"patt": [0], "pos": [[3, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": 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