0132_0213_1023
Counting sequence:
1, 1, 2, 6, 21, 78, 298, 1157, 4539, 17936, 71251, 284188, 1137076, 4561093, 18333337, 73816489, 297635750, 1201551286, 4855672249, 19640147061, 79501958895, 322037615290, 1305256267511, 5293166568270, 21475362822956, 87166344495561, 353933533606927, 1437615706473895, 5841143389365176, 23739654103621223, 96507564715368946, 392418108335073646, 1595984950415421365, 6492215247412954278, 26414020478861111378, 107484890224656918033, 437447640413103368167, 1780596376150842978819, 7248716410940597885968, 29512693386188099140367, 120172463800541940435382, 489379836497167927701020, 1993099893627583483795119, 8118038667358149750472877, 33068129168865678300925689, 134710737589318290634871356, 548815909818893893028038861, 2236047610051984732828380850, 9110944819862133209274573842, 37125480795164429961200955181, 151288344408183432336256869487, 616541191434941957907700491981, 2512699798679384329501052162682, 10240937786394822931825484898817, 41740561761745746673080773917826, 170135599590373043533352428310664, 693504728973249100434816921271409, 2826962393649890255842763187156243, 11524076195018983047510351020541931, 46979335176611828462711274054443428, 191523245036343978075324231058393579, 780817015675163982587555766651369002, 3183387582442459709056506410298675226, 12979010966589401737357146135099077365, 52918181781109288206321549342405781611, 215763956771072521811447733196984893696, 879757588527639041309830605707686872451, 3587209878761863487840811155198656703732, 14627150314885273483041187170653671777452, 59644635922884595987689163285567361994833, 243215569309644789208395693259757078459589, 991788967669060619598706216533714557471365, 4044405774921188254877147530737921605968702, 16492913003314697479639889540620511812701289, 67258453994168085598426634798116332556077302, 274285560243137748950609555121205187866665556, 1118575401364019996517843589662662311787692621, 4561771824187286693573377601904599177897087163, 18604052666793127926834794819785156965740306367, 75872958295853702971823095919690962883707625764, 309436607392671757386889987769364138404234654915, 1262005806365561838074538066141812506684818685656, 5147019200975028527525021842674292275234194820444, 20992047096755578722231383695276069354652434359771, 85616637901227724562296634031307074523373814968455, 349193165878958556255374769166070718826350547017535, 1424220767435598066631890050937112196826489238293186, 5808884457860461558864274775394541706891694714959725, 23692552305365317559314673746562159558520438417329096, 96635009147985674200951090537208980275718534874704826, 394149087715741799411990535837704658669939933883906471, 1607643730133827617018939037345470690158259420966015547, 6557257174353356206865754734663207254522893443079205877, 26745924726713628360979590206199094821141595433735849868, 109092751308466052705046742802724337434542648886200605779, 444976353933293765872429645359907685493777786410231397300, 1815016695813800169897771930018216695828853651112602183652, 7403325840846314410496335205583722135006862528050051030789, 30197817331705259184377454082664272330552966315512699122337, 123176142061598708874362684643158032775804522161524993917081, 502435023463949220687017754390108753835483587341999467515846
Generating function in Maple syntax:
(-x*(-4*x+1)^(1/2)-4*x^2+9*x-2)/(2*x^3-8*x^2+10*x-2)
Generating function in latex syntax:
\frac{-x \sqrt{-4 x +1}-4 x^{2}+9 x -2}{2 x^{3}-8 x^{2}+10 x -2}
Generating function in sympy syntax:
(-4*x**2 - x*sqrt(1 - 4*x) + 9*x - 2)/(2*x**3 - 8*x**2 + 10*x - 2)
Implicit equation for the generating function in Maple syntax:
(x^3-4*x^2+5*x-1)*F(x)^2+(4*x-1)*(x-2)*F(x)+4*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{3}-4 x^{2}+5 x -1\right) F \! \left(x \right)^{2}+\left(4 x -1\right) \left(x -2\right) F \! \left(x \right)+4 x -1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+4) = -2*(3+2*n)/(3+n)*a(n)+3*(7+3*n)/(3+n)*a(3+n)+(27+17*n)/(3+n)*a(n+1)-6*(7+4*n)/(3+n)*a(n+2), n >= 4
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(n +4\right) = -\frac{2 \left(3+2 n \right) a \! \left(n \right)}{3+n}+\frac{3 \left(7+3 n \right) a \! \left(3+n \right)}{3+n}+\frac{\left(27+17 n \right) a \! \left(n +1\right)}{3+n}-\frac{6 \left(7+4 n \right) a \! \left(n +2\right)}{3+n}, \quad n \geq 4
Specification 1
Strategy pack name: insertion_point_placements_tracked_fusion
Tree: http://permpal.com/tree/253/
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[16,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[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[7,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[4,x]
F[16,x] = F[17,x]+F[2,x]
F[17,x] = F[18,x]
F[18,x] = F[10,x]*F[19,x]*F[4,x]
F[19,x] = F[16,x]+F[20,x]
F[20,x] = F[21,x,1]
F[21,x,k[0]] = F[22,x,k[0]]+F[31,x,k[0]]
F[22,x,k[0]] = F[23,x,k[0]]+F[7,x]
F[23,x,k[0]] = F[24,x]*F[27,x,k[0]]
F[24,x] = F[25,x]
F[25,x] = F[26,x]*F[4,x]
F[26,x] = F[1,x]+F[25,x]
F[27,x,k[0]] = F[28,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]*F[30,x,k[0]]
F[29,x,k[0]] = k[0]*x
F[30,x,k[0]] = F[1,x]+F[27,x,k[0]]
F[31,x,k[0]] = F[32,x]+F[39,x,k[0]]
F[32,x] = F[33,x]
F[33,x] = F[10,x]*F[34,x]*F[4,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[16,x]+F[7,x]
F[36,x] = F[37,x]+F[38,x]
F[37,x] = F[24,x]^2
F[38,x] = F[31,x,1]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[4,x]*F[41,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]+F[72,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]+F[57,x,k[0]]
F[43,x,k[0]] = F[44,x]+F[45,x,k[0]]+F[55,x,k[0]]
F[44,x] = 0
F[45,x,k[0]] = F[4,x]*F[46,x,k[0]]
F[46,x,k[0]] = F[47,x,k[0]]+F[50,x,k[0]]
F[47,x,k[0]] = F[29,x,k[0]]+F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[4,x]*F[47,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]+F[53,x,k[0]]
F[51,x,k[0]] = F[52,x,k[0]]
F[52,x,k[0]] = F[29,x,k[0]]*F[7,x]
F[53,x,k[0]] = F[54,x,k[0]]
F[54,x,k[0]] = F[4,x]*F[50,x,k[0]]
F[55,x,k[0]] = F[29,x,k[0]]*F[56,x,k[0]]
F[56,x,k[0]] = F[43,x,k[0]]+F[7,x]
F[57,x,k[0]] = F[58,x,k[0]]+F[62,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]
F[59,x,k[0]] = F[29,x,k[0]]*F[60,x,k[0]]
F[60,x,k[0]] = F[21,x,k[0]]+F[61,x,k[0]]
F[61,x,k[0]] = F[2,x]+F[58,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[29,x,k[0]]*F[64,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]+F[71,x]
F[65,x,k[0]] = F[66,x,k[0]]+F[67,x,k[0]]
F[66,x,k[0]] = F[17,x]+F[62,x,k[0]]
F[67,x,k[0]] = F[68,x,k[0]]+F[70,x,k[0]]
F[68,x,k[0]] = F[69,x,k[0]]
F[69,x,k[0]] = F[24,x]^2*F[30,x,k[0]]
F[70,x,k[0]] = (F[39,x,k[0]]-F[39,x,1])/(-1+k[0])
F[71,x] = F[11,x]*F[19,x]
F[72,x,k[0]] = F[73,x,k[0]]+F[75,x,k[0]]
F[73,x,k[0]] = F[74,x,k[0]]
F[74,x,k[0]] = F[24,x]^2*F[27,x,k[0]]
F[75,x,k[0]] = -k[0]*(-F[39,x,k[0]]+F[39,x,1])/(-1+k[0])
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_{16}\! \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_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{2}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{10}\! \left(x \right) F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{16}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x , 1\right)
F_{21}\! \left(x , y\right) = F_{22}\! \left(x , y\right)+F_{31}\! \left(x , y\right)
F_{22}\! \left(x , y\right) = F_{23}\! \left(x , y\right)+F_{7}\! \left(x \right)
F_{23}\! \left(x , y\right) = F_{24}\! \left(x \right) F_{27}\! \left(x , y\right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{30}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = y x
F_{30}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{27}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x \right)+F_{39}\! \left(x , y\right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{10}\! \left(x \right) F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{16}\! \left(x \right)+F_{7}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{38}\! \left(x \right)
F_{37}\! \left(x \right) = F_{24} \left(x \right)^{2}
F_{38}\! \left(x \right) = F_{31}\! \left(x , 1\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{44}\! \left(x \right)+F_{45}\! \left(x , y\right)+F_{55}\! \left(x , y\right)
F_{44}\! \left(x \right) = 0
F_{45}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{46}\! \left(x , y\right)
F_{46}\! \left(x , y\right) = F_{47}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{47}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right)+F_{53}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{7}\! \left(x \right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{4}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{56}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{43}\! \left(x , y\right)+F_{7}\! \left(x \right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{21}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{2}\! \left(x \right)+F_{58}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{29}\! \left(x , y\right) F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)+F_{71}\! \left(x \right)
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{24} \left(x \right)^{2} F_{30}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = \frac{F_{39}\! \left(x , y\right)-F_{39}\! \left(x , 1\right)}{-1+y}
F_{71}\! \left(x \right) = F_{11}\! \left(x \right) F_{19}\! \left(x \right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{24} \left(x \right)^{2} F_{27}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = -\frac{y \left(-F_{39}\! \left(x , y\right)+F_{39}\! \left(x , 1\right)\right)}{-1+y}
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_16(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_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_7(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_4(x))
Eq(F_16(x), F_17(x) + F_2(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_10(x)*F_19(x)*F_4(x))
Eq(F_19(x), F_16(x) + F_20(x))
Eq(F_20(x), F_21(x, 1))
Eq(F_21(x, k_0), F_22(x, k_0) + F_31(x, k_0))
Eq(F_22(x, k_0), F_23(x, k_0) + F_7(x))
Eq(F_23(x, k_0), F_24(x)*F_27(x, k_0))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_26(x)*F_4(x))
Eq(F_26(x), F_1(x) + F_25(x))
Eq(F_27(x, k_0), F_28(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0)*F_30(x, k_0))
Eq(F_29(x, k_0), k_0*x)
Eq(F_30(x, k_0), F_1(x) + F_27(x, k_0))
Eq(F_31(x, k_0), F_32(x) + F_39(x, k_0))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_10(x)*F_34(x)*F_4(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_16(x) + F_7(x))
Eq(F_36(x), F_37(x) + F_38(x))
Eq(F_37(x), F_24(x)**2)
Eq(F_38(x), F_31(x, 1))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_4(x)*F_41(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0) + F_72(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0) + F_57(x, k_0))
Eq(F_43(x, k_0), F_44(x) + F_45(x, k_0) + F_55(x, k_0))
Eq(F_44(x), 0)
Eq(F_45(x, k_0), F_4(x)*F_46(x, k_0))
Eq(F_46(x, k_0), F_47(x, k_0) + F_50(x, k_0))
Eq(F_47(x, k_0), F_29(x, k_0) + F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_4(x)*F_47(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0) + F_53(x, k_0))
Eq(F_51(x, k_0), F_52(x, k_0))
Eq(F_52(x, k_0), F_29(x, k_0)*F_7(x))
Eq(F_53(x, k_0), F_54(x, k_0))
Eq(F_54(x, k_0), F_4(x)*F_50(x, k_0))
Eq(F_55(x, k_0), F_29(x, k_0)*F_56(x, k_0))
Eq(F_56(x, k_0), F_43(x, k_0) + F_7(x))
Eq(F_57(x, k_0), F_58(x, k_0) + F_62(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0))
Eq(F_59(x, k_0), F_29(x, k_0)*F_60(x, k_0))
Eq(F_60(x, k_0), F_21(x, k_0) + F_61(x, k_0))
Eq(F_61(x, k_0), F_2(x) + F_58(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_29(x, k_0)*F_64(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0) + F_71(x))
Eq(F_65(x, k_0), F_66(x, k_0) + F_67(x, k_0))
Eq(F_66(x, k_0), F_17(x) + F_62(x, k_0))
Eq(F_67(x, k_0), F_68(x, k_0) + F_70(x, k_0))
Eq(F_68(x, k_0), F_69(x, k_0))
Eq(F_69(x, k_0), F_24(x)**2*F_30(x, k_0))
Eq(F_70(x, k_0), -F_39(x, k_0) + (k_0*F_39(x, k_0) - F_39(x, 1))/(k_0 - 1))
Eq(F_71(x), F_11(x)*F_19(x))
Eq(F_72(x, k_0), F_73(x, k_0) + F_75(x, k_0))
Eq(F_73(x, k_0), F_74(x, k_0))
Eq(F_74(x, k_0), F_24(x)**2*F_27(x, k_0))
Eq(F_75(x, k_0), -F_39(x, 1) + (k_0*F_39(x, k_0) - F_39(x, 1))/(k_0 - 1))
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.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}, {"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_tracked_fusion", "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:
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[{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "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, 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, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [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, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [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}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 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2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [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, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "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, 0], [0, 1], [0, 1]]}, {"patt": [0, 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[[0, 1]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[3, 3]]}, {"patt": [0, 1], "pos": [[2, 3], [2, 3]]}, {"patt": [1, 0], "pos": [[0, 2], [0, 2]]}, {"patt": [1, 0], "pos": [[2, 3], [2, 3]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[3, 0], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [3, 0], [3, 1], [3, 0]]}, {"patt": 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