0123_1230_2301
Counting sequence:
1, 1, 2, 6, 21, 75, 259, 849, 2638, 7817, 22275, 61539, 166007, 439844, 1150070, 2978785, 7665397, 19643706, 50221841, 128276092, 327669142, 837705012, 2144568913, 5499555762, 14129732967, 36373781931, 93817255940, 242427246020, 627525422189, 1626928665693, 4224001221231, 10980650622515, 28576753756918, 74441446935715, 194077572377951, 506339571517821, 1321805816360383, 3452326189336102, 9020672942476322, 23578631435092563, 61648838348831133, 161226321489962148, 421728859935771949, 1103320342550814918, 2886875370368934238, 7554433844185295462, 19770356858002821021, 51743829618384172116, 135434145583759061615, 354501819556343314469, 927951967695147432512, 2429103570799828577566, 6358833512397798522229, 16646296962184584298911, 43577756034746370872507, 114082161297652499740357, 298658684831042095567294, 781872942450007263176973, 2046916475616992713761403, 5358785547717295017570759, 14029250944292948745130599, 36728573850698104136681784, 96155653186454597416284110, 251736688608210906839815349, 659050891615903053799444709, 1725408685940531084011005918, 4517160039875549756409418377, 11826040111114681026407448512, 30960895471609818307458108166, 81056512232778846174956052520, 212208364082843756805117701993, 555568007428816376295926883942, 1454494475841097223595255473815, 3807912979811595271600689229807, 9969239429551017852165029308988, 26099794929079928937414234969768, 68330123965368601560584874679005, 178890532897901857604811273187569, 468341383983342636430746538109959, 1226133432273086921227220869994055, 3210058528548623217250667184522790, 8404041363037528157460957743284295, 22002063935767659693070595265677271, 57602147105212337146145047542394305, 150804370520424251251958610107510255, 394810950369656766460071639134451674, 1033628451671040442946326448356715258, 2706074345299713929135990777993544583, 7084594462484435605990029476049904717, 18547708792476561215463963456478005096, 48558531403057041795897117222637520549, 127127884367540380877867605234470487018, 332825119549881222618642851118490982926, 871347469878750567239963310304866518778, 2281217281069215232946537157430939433269, 5972304354868733265776057502692265971304, 15635695745755054565391829360724644823391, 40934782805089550857106003172581219792265, 107168652511374185627454562320305353829240, 280571174405623646642030657731488504025826, 734544870044258509954587249318442419948581
Generating function in Maple syntax:
-(18*x^10-134*x^9+446*x^8-918*x^7+1253*x^6-1161*x^5+736*x^4-315*x^3+87*x^2-14*x+1)/(x^2-3*x+1)/(2*x-1)^3/(-1+x)^6
Generating function in latex syntax:
-\frac{18 x^{10}-134 x^{9}+446 x^{8}-918 x^{7}+1253 x^{6}-1161 x^{5}+736 x^{4}-315 x^{3}+87 x^{2}-14 x +1}{\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{3} \left(-1+x \right)^{6}}
Generating function in sympy syntax:
(-18*x**10 + 134*x**9 - 446*x**8 + 918*x**7 - 1253*x**6 + 1161*x**5 - 736*x**4 + 315*x**3 - 87*x**2 + 14*x - 1)/((x - 1)**6*(2*x - 1)**3*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
(x^2-3*x+1)*(2*x-1)^3*(-1+x)^6*F(x)+18*x^10-134*x^9+446*x^8-918*x^7+1253*x^6-1161*x^5+736*x^4-315*x^3+87*x^2-14*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{3} \left(-1+x \right)^{6} F \! \left(x \right)+18 x^{10}-134 x^{9}+446 x^{8}-918 x^{7}+1253 x^{6}-1161 x^{5}+736 x^{4}-315 x^{3}+87 x^{2}-14 x +1 = 0
Explicit closed form in Maple syntax:
1/120*(36*5^(1/2)+60)*(3/2-1/2*5^(1/2))^(-n)+1/120*(-36*5^(1/2)+60)*(3/2+1/2*5^(1/2))^(-n)+2^(n+1)+1/120*(30*n^2-270*n)*2^n-1/120*n^5+1/12*n^4-1/8*n^3+11/12*n^2-13/15*n-2
Explicit closed form in latex syntax:
\frac{\left(36 \sqrt{5}+60\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{120}+\frac{\left(-36 \sqrt{5}+60\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{120}+2^{n +1}+\frac{\left(30 n^{2}-270 n \right) 2^{n}}{120}-\frac{n^{5}}{120}+\frac{n^{4}}{12}-\frac{n^{3}}{8}+\frac{11 n^{2}}{12}-\frac{13 n}{15}-2
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 75
a(6) = 259
a(7) = 849
a(8) = 2638
a(9) = 7817
a(10) = 22275
a(n+5) = 8*a(n)-36*a(n+1)+50*a(n+2)-31*a(n+3)+9*a(n+4)-1/120*n*(n^4-20*n^3+55*n^2+260*n-176), n >= 11
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) = 75
a \! \left(6\right) = 259
a \! \left(7\right) = 849
a \! \left(8\right) = 2638
a \! \left(9\right) = 7817
a \! \left(10\right) = 22275
a \! \left(n +5\right) = 8 a \! \left(n \right)-36 a \! \left(n +1\right)+50 a \! \left(n +2\right)-31 a \! \left(n +3\right)+9 a \! \left(n +4\right)-\frac{n \left(n^{4}-20 n^{3}+55 n^{2}+260 n -176\right)}{120}, \quad n \geq 11
Specification 1
Strategy pack name: insertion_point_placements
Tree: http://permpal.com/tree/246/
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[29,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[4,x]*F[8,x]
F[8,x] = F[6,x]+F[9,x]
F[9,x] = F[10,x]*F[4,x]
F[10,x] = F[11,x]+F[14,x]+F[9,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[11,x]*F[4,x]
F[14,x] = F[15,x]
F[15,x] = F[11,x]*F[16,x]*F[4,x]
F[16,x] = F[17,x]+F[24,x]
F[17,x] = F[11,x]+F[18,x]
F[18,x] = F[12,x]+F[19,x]
F[19,x] = F[20,x]+F[21,x]+F[23,x]
F[20,x] = 0
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[12,x]+F[19,x]
F[23,x] = F[18,x]*F[4,x]
F[24,x] = F[12,x]+F[25,x]
F[25,x] = F[20,x]+F[26,x]+F[28,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[12,x]+F[25,x]
F[28,x] = F[24,x]*F[4,x]
F[29,x] = F[2,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[4,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[12,x]*F[17,x]
F[34,x] = F[112,x]+F[35,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[7,x]
F[38,x] = F[12,x]^2
F[39,x] = F[111,x]+F[40,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]+F[50,x]
F[43,x] = F[44,x]+F[46,x]
F[44,x] = F[12,x]+F[45,x]
F[45,x] = F[11,x]*F[12,x]
F[46,x] = F[47,x]+F[48,x]
F[47,x] = F[12,x]^2
F[48,x] = F[40,x]+F[49,x]
F[49,x] = F[12,x]*F[19,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[12,x]*F[44,x]
F[52,x] = F[53,x]+F[54,x]
F[53,x] = F[12,x]*F[25,x]
F[54,x] = F[110,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[78,x]
F[58,x] = F[12,x]*F[59,x]
F[59,x] = F[60,x]+F[62,x]
F[60,x] = F[22,x]+F[61,x]
F[61,x] = F[11,x]*F[12,x]
F[62,x] = F[63,x]+F[65,x]
F[63,x] = F[47,x]+F[64,x]
F[64,x] = F[11,x]*F[19,x]
F[65,x] = F[20,x]+F[66,x]+F[68,x]+F[70,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[19,x]+F[65,x]
F[68,x] = F[4,x]*F[69,x]
F[69,x] = F[19,x]+F[65,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[72,x]+F[75,x]
F[72,x] = F[73,x]
F[73,x] = F[4,x]*F[74,x]
F[74,x] = F[12,x]+F[72,x]
F[75,x] = 2*F[20,x]+F[70,x]+F[76,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[19,x]+F[75,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = F[11,x]*F[12,x]*F[44,x]
F[80,x] = F[52,x]+F[81,x]
F[81,x] = F[12,x]*F[82,x]
F[82,x] = F[109,x]+F[83,x]
F[83,x] = F[105,x]+F[20,x]+F[84,x]
F[84,x] = F[85,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[104,x]+F[87,x]
F[87,x] = F[20,x]+F[88,x]+F[97,x]
F[88,x] = F[4,x]*F[89,x]
F[89,x] = F[20,x]+F[90,x]+F[92,x]
F[90,x] = F[91,x]
F[91,x] = F[11,x]*F[4,x]*F[89,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[11,x]+F[94,x]+F[95,x]
F[94,x] = F[4,x]*F[93,x]
F[95,x] = F[96,x]
F[96,x] = F[11,x]*F[4,x]*F[93,x]
F[97,x] = F[98,x]
F[98,x] = F[4,x]*F[99,x]
F[99,x] = F[100,x]+F[87,x]
F[100,x] = F[101,x]*F[11,x]*F[4,x]
F[101,x] = F[102,x]+F[20,x]+F[94,x]
F[102,x] = F[103,x]
F[103,x] = F[101,x]*F[11,x]*F[4,x]
F[104,x] = F[11,x]*F[4,x]*F[89,x]
F[105,x] = F[106,x]*F[4,x]
F[106,x] = F[102,x]+F[107,x]+F[20,x]
F[107,x] = F[108,x]*F[4,x]
F[108,x] = F[107,x]+F[20,x]+F[95,x]
F[109,x] = F[106,x]*F[12,x]
F[110,x] = F[12,x]*F[83,x]
F[111,x] = F[12,x]*F[19,x]
F[112,x] = F[113,x]+F[181,x]
F[113,x] = F[114,x]+F[164,x]
F[114,x] = F[115,x]
F[115,x] = F[116,x]*F[4,x]
F[116,x] = F[117,x]+F[33,x]
F[117,x] = F[118,x]+F[133,x]
F[118,x] = F[119,x]+F[36,x]
F[119,x] = F[111,x]+F[120,x]
F[120,x] = F[121,x]
F[121,x] = F[122,x]*F[4,x]
F[122,x] = F[123,x]+F[126,x]
F[123,x] = F[124,x]+F[44,x]
F[124,x] = F[120,x]+F[125,x]
F[125,x] = F[12,x]*F[18,x]
F[126,x] = F[127,x]+F[130,x]
F[127,x] = F[128,x]
F[128,x] = F[129,x]*F[4,x]
F[129,x] = F[12,x]+F[127,x]
F[130,x] = F[131,x]
F[131,x] = F[11,x]*F[12,x]*F[132,x]*F[4,x]
F[132,x] = F[12,x]+F[24,x]
F[133,x] = F[113,x]+F[134,x]
F[134,x] = F[135,x]+F[158,x]
F[135,x] = F[136,x]
F[136,x] = F[137,x]*F[4,x]
F[137,x] = F[138,x]+F[155,x]
F[138,x] = F[139,x]+F[142,x]
F[139,x] = F[140,x]+F[47,x]
F[140,x] = F[12,x]*F[141,x]
F[141,x] = F[25,x]+F[45,x]
F[142,x] = F[143,x]+F[146,x]
F[143,x] = F[135,x]+F[144,x]
F[144,x] = F[145,x]
F[145,x] = F[12,x]^2*F[18,x]
F[146,x] = F[12,x]*F[147,x]
F[147,x] = 2*F[20,x]+F[148,x]+F[150,x]
F[148,x] = F[149,x]*F[4,x]
F[149,x] = F[147,x]+F[25,x]
F[150,x] = F[151,x]*F[4,x]
F[151,x] = F[147,x]+F[152,x]
F[152,x] = F[153,x]
F[153,x] = F[154,x]*F[4,x]
F[154,x] = F[12,x]+F[152,x]
F[155,x] = F[156,x]
F[156,x] = F[12,x]^2*F[157,x]
F[157,x] = F[11,x]+F[24,x]
F[158,x] = F[159,x]
F[159,x] = F[160,x]*F[4,x]
F[160,x] = F[161,x]+F[162,x]
F[161,x] = F[11,x]*F[83,x]
F[162,x] = F[163,x]
F[163,x] = F[11,x]*F[18,x]*F[19,x]
F[164,x] = F[165,x]
F[165,x] = F[166,x]*F[4,x]
F[166,x] = F[167,x]+F[170,x]
F[167,x] = F[12,x]*F[168,x]
F[168,x] = F[169,x]+F[61,x]
F[169,x] = F[11,x]*F[22,x]
F[170,x] = F[171,x]+F[175,x]
F[171,x] = F[172,x]+F[79,x]
F[172,x] = F[173,x]+F[81,x]
F[173,x] = F[174,x]+F[53,x]
F[174,x] = F[110,x]+F[164,x]
F[175,x] = F[12,x]*F[176,x]
F[176,x] = F[177,x]+F[25,x]
F[177,x] = F[150,x]+F[178,x]+F[180,x]+F[20,x]
F[178,x] = F[179,x]*F[4,x]
F[179,x] = F[177,x]+F[25,x]
F[180,x] = F[176,x]*F[4,x]
F[181,x] = F[158,x]+F[182,x]
F[182,x] = F[183,x]
F[183,x] = F[184,x]*F[4,x]
F[184,x] = F[185,x]+F[192,x]
F[185,x] = F[186,x]+F[189,x]
F[186,x] = F[187,x]+F[188,x]
F[187,x] = F[12,x]*F[44,x]
F[188,x] = F[12,x]^2*F[11,x]
F[189,x] = F[190,x]+F[191,x]
F[190,x] = F[12,x]*F[46,x]
F[191,x] = F[11,x]*F[12,x]*F[25,x]
F[192,x] = F[193,x]+F[195,x]
F[193,x] = F[194,x]
F[194,x] = F[12,x]*F[186,x]
F[195,x] = F[196,x]+F[197,x]
F[196,x] = F[12,x]*F[52,x]
F[197,x] = F[11,x]*F[12,x]*F[147,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_{29}\! \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_{4}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{6}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{24}\! \left(x \right)
F_{17}\! \left(x \right) = F_{11}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right)+F_{19}\! \left(x \right)
F_{23}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{20}\! \left(x \right)+F_{26}\! \left(x \right)+F_{28}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right)+F_{25}\! \left(x \right)
F_{28}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{2}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{34}\! \left(x \right) = F_{112}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{7}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12} \left(x \right)^{2}
F_{39}\! \left(x \right) = F_{111}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{50}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{46}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{11}\! \left(x \right) F_{12}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{48}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12} \left(x \right)^{2}
F_{48}\! \left(x \right) = F_{40}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{54}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{54}\! \left(x \right) = F_{110}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{78}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{62}\! \left(x \right)
F_{60}\! \left(x \right) = F_{22}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{11}\! \left(x \right) F_{12}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{65}\! \left(x \right)
F_{63}\! \left(x \right) = F_{47}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right)
F_{65}\! \left(x \right) = F_{20}\! \left(x \right)+F_{66}\! \left(x \right)+F_{68}\! \left(x \right)+F_{70}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{19}\! \left(x \right)+F_{65}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{19}\! \left(x \right)+F_{65}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{75}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right)+F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{70}\! \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_{19}\! \left(x \right)+F_{75}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{11}\! \left(x \right) F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{80}\! \left(x \right) = F_{52}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{109}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{105}\! \left(x \right)+F_{20}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{104}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{20}\! \left(x \right)+F_{88}\! \left(x \right)+F_{97}\! \left(x \right)
F_{88}\! \left(x \right) = F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{20}\! \left(x \right)+F_{90}\! \left(x \right)+F_{92}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{11}\! \left(x \right)+F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{93}\! \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_{87}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{20}\! \left(x \right)+F_{94}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{101}\! \left(x \right) F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right) F_{89}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{4}\! \left(x \right)
F_{106}\! \left(x \right) = F_{102}\! \left(x \right)+F_{107}\! \left(x \right)+F_{20}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{4}\! \left(x \right)
F_{108}\! \left(x \right) = F_{107}\! \left(x \right)+F_{20}\! \left(x \right)+F_{95}\! \left(x \right)
F_{109}\! \left(x \right) = F_{106}\! \left(x \right) F_{12}\! \left(x \right)
F_{110}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \left(x \right)
F_{111}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{181}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{164}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \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_{33}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)+F_{133}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{36}\! \left(x \right)
F_{119}\! \left(x \right) = F_{111}\! \left(x \right)+F_{120}\! \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_{126}\! \left(x \right)
F_{123}\! \left(x \right) = F_{124}\! \left(x \right)+F_{44}\! \left(x \right)
F_{124}\! \left(x \right) = F_{120}\! \left(x \right)+F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{12}\! \left(x \right) F_{18}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{130}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right) F_{4}\! \left(x \right)
F_{129}\! \left(x \right) = F_{12}\! \left(x \right)+F_{127}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{11}\! \left(x \right) F_{12}\! \left(x \right) F_{132}\! \left(x \right) F_{4}\! \left(x \right)
F_{132}\! \left(x \right) = F_{12}\! \left(x \right)+F_{24}\! \left(x \right)
F_{133}\! \left(x \right) = F_{113}\! \left(x \right)+F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)+F_{158}\! \left(x \right)
F_{135}\! \left(x \right) = F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right) F_{4}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)+F_{155}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{142}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)+F_{47}\! \left(x \right)
F_{140}\! \left(x \right) = F_{12}\! \left(x \right) F_{141}\! \left(x \right)
F_{141}\! \left(x \right) = F_{25}\! \left(x \right)+F_{45}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right)+F_{146}\! \left(x \right)
F_{143}\! \left(x \right) = F_{135}\! \left(x \right)+F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{18}\! \left(x \right)
F_{146}\! \left(x \right) = F_{12}\! \left(x \right) F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{148}\! \left(x \right)+F_{150}\! \left(x \right)
F_{148}\! \left(x \right) = F_{149}\! \left(x \right) F_{4}\! \left(x \right)
F_{149}\! \left(x \right) = F_{147}\! \left(x \right)+F_{25}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right) F_{4}\! \left(x \right)
F_{151}\! \left(x \right) = F_{147}\! \left(x \right)+F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{154}\! \left(x \right) F_{4}\! \left(x \right)
F_{154}\! \left(x \right) = F_{12}\! \left(x \right)+F_{152}\! \left(x \right)
F_{155}\! \left(x \right) = F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{11}\! \left(x \right)+F_{24}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right) F_{4}\! \left(x \right)
F_{160}\! \left(x \right) = F_{161}\! \left(x \right)+F_{162}\! \left(x \right)
F_{161}\! \left(x \right) = F_{11}\! \left(x \right) F_{83}\! \left(x \right)
F_{162}\! \left(x \right) = F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right) F_{19}\! \left(x \right)
F_{164}\! \left(x \right) = F_{165}\! \left(x \right)
F_{165}\! \left(x \right) = F_{166}\! \left(x \right) F_{4}\! \left(x \right)
F_{166}\! \left(x \right) = F_{167}\! \left(x \right)+F_{170}\! \left(x \right)
F_{167}\! \left(x \right) = F_{12}\! \left(x \right) F_{168}\! \left(x \right)
F_{168}\! \left(x \right) = F_{169}\! \left(x \right)+F_{61}\! \left(x \right)
F_{169}\! \left(x \right) = F_{11}\! \left(x \right) F_{22}\! \left(x \right)
F_{170}\! \left(x \right) = F_{171}\! \left(x \right)+F_{175}\! \left(x \right)
F_{171}\! \left(x \right) = F_{172}\! \left(x \right)+F_{79}\! \left(x \right)
F_{172}\! \left(x \right) = F_{173}\! \left(x \right)+F_{81}\! \left(x \right)
F_{173}\! \left(x \right) = F_{174}\! \left(x \right)+F_{53}\! \left(x \right)
F_{174}\! \left(x \right) = F_{110}\! \left(x \right)+F_{164}\! \left(x \right)
F_{175}\! \left(x \right) = F_{12}\! \left(x \right) F_{176}\! \left(x \right)
F_{176}\! \left(x \right) = F_{177}\! \left(x \right)+F_{25}\! \left(x \right)
F_{177}\! \left(x \right) = F_{150}\! \left(x \right)+F_{178}\! \left(x \right)+F_{180}\! \left(x \right)+F_{20}\! \left(x \right)
F_{178}\! \left(x \right) = F_{179}\! \left(x \right) F_{4}\! \left(x \right)
F_{179}\! \left(x \right) = F_{177}\! \left(x \right)+F_{25}\! \left(x \right)
F_{180}\! \left(x \right) = F_{176}\! \left(x \right) F_{4}\! \left(x \right)
F_{181}\! \left(x \right) = F_{158}\! \left(x \right)+F_{182}\! \left(x \right)
F_{182}\! \left(x \right) = F_{183}\! \left(x \right)
F_{183}\! \left(x \right) = F_{184}\! \left(x \right) F_{4}\! \left(x \right)
F_{184}\! \left(x \right) = F_{185}\! \left(x \right)+F_{192}\! \left(x \right)
F_{185}\! \left(x \right) = F_{186}\! \left(x \right)+F_{189}\! \left(x \right)
F_{186}\! \left(x \right) = F_{187}\! \left(x \right)+F_{188}\! \left(x \right)
F_{187}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{188}\! \left(x \right) = F_{12} \left(x \right)^{2} F_{11}\! \left(x \right)
F_{189}\! \left(x \right) = F_{190}\! \left(x \right)+F_{191}\! \left(x \right)
F_{190}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{191}\! \left(x \right) = F_{11}\! \left(x \right) F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{192}\! \left(x \right) = F_{193}\! \left(x \right)+F_{195}\! \left(x \right)
F_{193}\! \left(x \right) = F_{194}\! \left(x \right)
F_{194}\! \left(x \right) = F_{12}\! \left(x \right) F_{186}\! \left(x \right)
F_{195}\! \left(x \right) = F_{196}\! \left(x \right)+F_{197}\! \left(x \right)
F_{196}\! \left(x \right) = F_{12}\! \left(x \right) F_{52}\! \left(x \right)
F_{197}\! \left(x \right) = F_{11}\! \left(x \right) F_{12}\! \left(x \right) F_{147}\! \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_29(x) + F_6(x))
Eq(F_6(x), F_1(x) + F_7(x))
Eq(F_7(x), F_4(x)*F_8(x))
Eq(F_8(x), F_6(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_4(x))
Eq(F_10(x), F_11(x) + F_14(x) + F_9(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_11(x)*F_4(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_11(x)*F_16(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_24(x))
Eq(F_17(x), F_11(x) + F_18(x))
Eq(F_18(x), F_12(x) + F_19(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_23(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_12(x) + F_19(x))
Eq(F_23(x), F_18(x)*F_4(x))
Eq(F_24(x), F_12(x) + F_25(x))
Eq(F_25(x), F_20(x) + F_26(x) + F_28(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_12(x) + F_25(x))
Eq(F_28(x), F_24(x)*F_4(x))
Eq(F_29(x), F_2(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_4(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_12(x)*F_17(x))
Eq(F_34(x), F_112(x) + F_35(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_7(x))
Eq(F_38(x), F_12(x)**2)
Eq(F_39(x), F_111(x) + F_40(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_50(x))
Eq(F_43(x), F_44(x) + F_46(x))
Eq(F_44(x), F_12(x) + F_45(x))
Eq(F_45(x), F_11(x)*F_12(x))
Eq(F_46(x), F_47(x) + F_48(x))
Eq(F_47(x), F_12(x)**2)
Eq(F_48(x), F_40(x) + F_49(x))
Eq(F_49(x), F_12(x)*F_19(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_12(x)*F_44(x))
Eq(F_52(x), F_53(x) + F_54(x))
Eq(F_53(x), F_12(x)*F_25(x))
Eq(F_54(x), F_110(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_78(x))
Eq(F_58(x), F_12(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_62(x))
Eq(F_60(x), F_22(x) + F_61(x))
Eq(F_61(x), F_11(x)*F_12(x))
Eq(F_62(x), F_63(x) + F_65(x))
Eq(F_63(x), F_47(x) + F_64(x))
Eq(F_64(x), F_11(x)*F_19(x))
Eq(F_65(x), F_20(x) + F_66(x) + F_68(x) + F_70(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_19(x) + F_65(x))
Eq(F_68(x), F_4(x)*F_69(x))
Eq(F_69(x), F_19(x) + F_65(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_75(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_4(x)*F_74(x))
Eq(F_74(x), F_12(x) + F_72(x))
Eq(F_75(x), 2*F_20(x) + F_70(x) + F_76(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_19(x) + F_75(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), F_11(x)*F_12(x)*F_44(x))
Eq(F_80(x), F_52(x) + F_81(x))
Eq(F_81(x), F_12(x)*F_82(x))
Eq(F_82(x), F_109(x) + F_83(x))
Eq(F_83(x), F_105(x) + F_20(x) + F_84(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_104(x) + F_87(x))
Eq(F_87(x), F_20(x) + F_88(x) + F_97(x))
Eq(F_88(x), F_4(x)*F_89(x))
Eq(F_89(x), F_20(x) + F_90(x) + F_92(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_11(x)*F_4(x)*F_89(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_11(x) + F_94(x) + F_95(x))
Eq(F_94(x), F_4(x)*F_93(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_11(x)*F_4(x)*F_93(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_87(x))
Eq(F_100(x), F_101(x)*F_11(x)*F_4(x))
Eq(F_101(x), F_102(x) + F_20(x) + F_94(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_101(x)*F_11(x)*F_4(x))
Eq(F_104(x), F_11(x)*F_4(x)*F_89(x))
Eq(F_105(x), F_106(x)*F_4(x))
Eq(F_106(x), F_102(x) + F_107(x) + F_20(x))
Eq(F_107(x), F_108(x)*F_4(x))
Eq(F_108(x), F_107(x) + F_20(x) + F_95(x))
Eq(F_109(x), F_106(x)*F_12(x))
Eq(F_110(x), F_12(x)*F_83(x))
Eq(F_111(x), F_12(x)*F_19(x))
Eq(F_112(x), F_113(x) + F_181(x))
Eq(F_113(x), F_114(x) + F_164(x))
Eq(F_114(x), F_115(x))
Eq(F_115(x), F_116(x)*F_4(x))
Eq(F_116(x), F_117(x) + F_33(x))
Eq(F_117(x), F_118(x) + F_133(x))
Eq(F_118(x), F_119(x) + F_36(x))
Eq(F_119(x), F_111(x) + F_120(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_126(x))
Eq(F_123(x), F_124(x) + F_44(x))
Eq(F_124(x), F_120(x) + F_125(x))
Eq(F_125(x), F_12(x)*F_18(x))
Eq(F_126(x), F_127(x) + F_130(x))
Eq(F_127(x), F_128(x))
Eq(F_128(x), F_129(x)*F_4(x))
Eq(F_129(x), F_12(x) + F_127(x))
Eq(F_130(x), F_131(x))
Eq(F_131(x), F_11(x)*F_12(x)*F_132(x)*F_4(x))
Eq(F_132(x), F_12(x) + F_24(x))
Eq(F_133(x), F_113(x) + F_134(x))
Eq(F_134(x), F_135(x) + F_158(x))
Eq(F_135(x), F_136(x))
Eq(F_136(x), F_137(x)*F_4(x))
Eq(F_137(x), F_138(x) + F_155(x))
Eq(F_138(x), F_139(x) + F_142(x))
Eq(F_139(x), F_140(x) + F_47(x))
Eq(F_140(x), F_12(x)*F_141(x))
Eq(F_141(x), F_25(x) + F_45(x))
Eq(F_142(x), F_143(x) + F_146(x))
Eq(F_143(x), F_135(x) + F_144(x))
Eq(F_144(x), F_145(x))
Eq(F_145(x), F_12(x)**2*F_18(x))
Eq(F_146(x), F_12(x)*F_147(x))
Eq(F_147(x), F_148(x) + F_150(x) + 2*F_20(x))
Eq(F_148(x), F_149(x)*F_4(x))
Eq(F_149(x), F_147(x) + F_25(x))
Eq(F_150(x), F_151(x)*F_4(x))
Eq(F_151(x), F_147(x) + F_152(x))
Eq(F_152(x), F_153(x))
Eq(F_153(x), F_154(x)*F_4(x))
Eq(F_154(x), F_12(x) + F_152(x))
Eq(F_155(x), F_156(x))
Eq(F_156(x), F_12(x)**2*F_157(x))
Eq(F_157(x), F_11(x) + F_24(x))
Eq(F_158(x), F_159(x))
Eq(F_159(x), F_160(x)*F_4(x))
Eq(F_160(x), F_161(x) + F_162(x))
Eq(F_161(x), F_11(x)*F_83(x))
Eq(F_162(x), F_163(x))
Eq(F_163(x), F_11(x)*F_18(x)*F_19(x))
Eq(F_164(x), F_165(x))
Eq(F_165(x), F_166(x)*F_4(x))
Eq(F_166(x), F_167(x) + F_170(x))
Eq(F_167(x), F_12(x)*F_168(x))
Eq(F_168(x), F_169(x) + F_61(x))
Eq(F_169(x), F_11(x)*F_22(x))
Eq(F_170(x), F_171(x) + F_175(x))
Eq(F_171(x), F_172(x) + F_79(x))
Eq(F_172(x), F_173(x) + F_81(x))
Eq(F_173(x), F_174(x) + F_53(x))
Eq(F_174(x), F_110(x) + F_164(x))
Eq(F_175(x), F_12(x)*F_176(x))
Eq(F_176(x), F_177(x) + F_25(x))
Eq(F_177(x), F_150(x) + F_178(x) + F_180(x) + F_20(x))
Eq(F_178(x), F_179(x)*F_4(x))
Eq(F_179(x), F_177(x) + F_25(x))
Eq(F_180(x), F_176(x)*F_4(x))
Eq(F_181(x), F_158(x) + F_182(x))
Eq(F_182(x), F_183(x))
Eq(F_183(x), F_184(x)*F_4(x))
Eq(F_184(x), F_185(x) + F_192(x))
Eq(F_185(x), F_186(x) + F_189(x))
Eq(F_186(x), F_187(x) + F_188(x))
Eq(F_187(x), F_12(x)*F_44(x))
Eq(F_188(x), F_11(x)*F_12(x)**2)
Eq(F_189(x), F_190(x) + F_191(x))
Eq(F_190(x), F_12(x)*F_46(x))
Eq(F_191(x), F_11(x)*F_12(x)*F_25(x))
Eq(F_192(x), F_193(x) + F_195(x))
Eq(F_193(x), F_194(x))
Eq(F_194(x), F_12(x)*F_186(x))
Eq(F_195(x), F_196(x) + F_197(x))
Eq(F_196(x), F_12(x)*F_52(x))
Eq(F_197(x), F_11(x)*F_12(x)*F_147(x))
Pack JSON:
{"expansion_strats": [[{"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}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_point_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, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [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": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[0, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], 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