0123_0132_0213_0231_1230_3012
Counting sequence:
1, 1, 2, 6, 18, 53, 157, 480, 1528, 5045, 17135, 59417, 209200, 745167, 2678821, 9703400, 35374508, 129678117, 477704915, 1767395077, 6564383532, 24466792447, 91483613545, 343061712341, 1289908343398, 4861954792083, 18367369851667, 69533584473035, 263748018862148, 1002242350872371, 3814986770531413, 14544636576101880, 55534065950794516, 212336132559731717, 812944046444703515, 3116285503497241837, 11959798403040329220, 45950804358981487871, 176733862855726185905, 680425371867414762297, 2622127042551370024902, 10113918592187653957787, 39044429913003955597675, 150853479207284374927731, 583300119597394739611484, 2257117854086044166289171, 8740328711550765576104925, 33868773757226231258533501, 131327898242239734222185778, 509552245179757875542981195, 1978261657756442128600503535, 7684785670514879335184257067, 29869166945773751850049280960, 116157871455784686050367553227, 451959718027957975047236903345, 1759414616608827878191734641767, 6852456927844891511948167972530, 26700952856774887933042239904351, 104088460289122376091092356769275, 405944995127577129845831519253839, 1583850964596120330917148930783148, 6182127958584856226947833150674043, 24139737743045627978632963153156277, 94295850558771982093778394160111896, 368479169875816664090695061140974564, 1440418573150919678095861931098682821, 5632681584560312753440659779558740395, 22033725021956517500252040761476098941, 86218923998960285799972616958539362868, 337485502510215975704357746044735087743, 1321422108420282270785090082369582422849, 5175569924646105560009236004353771422801, 20276890389709399864109590188972052386278, 79463489365077377843569420873784091550987, 311496878311103321142258658001678779303131, 1221395654430378811838205454973701421283235, 4790408930363303911347275674326343041946828, 18793142726809884575249140210950502355029907, 73745243611532458459765709718373243562827885, 289450081175264899454434961756942595911306577, 1136359577947336271931935108459571113961369562, 4462290049988320482463845760415940498087089987, 17526585015616776834736349443735270265571025775, 68854441132780194707890469886307876401334707011, 270557451039395118028647298992447024937370197024, 1063353702922273835973046329450033375756501149211, 4180080073556524734514715170984021292495546711905, 16435314834665426797069183646389113811501181094911, 64633260585762914370496714857398636798948716562258, 254224158304000796523953595521346557759081734526863, 1000134600800354781929399560021551685707529814845419, 3935312233584004685417854191733369152464169129703391, 15487357822491889407128328201718382517394206027081308, 60960876535340415751462566056709727462730278705812027, 239993345518077005168915781575236880147801927084856261, 944973797977428207852605880358459911120272957428031885, 3721443204405954385563870561186287288275591095764820298, 14657929356129575437016877886271114018845123747671873147, 57743358069601357782187700687271018848285069218300708775, 227508830794229349661819540554145178984570357788629100107, 896519947090131496687170070391013282477894871912921867512
Generating function in Maple syntax:
1/2*(-2*(x-1/2)*(x-1)^4*(1-4*x)^(1/2)+2*x^7-2*x^6+6*x^5-11*x^4+16*x^3-14*x^2+6*x-1)/x/(2*x-1)/(x-1)^4
Generating function in latex syntax:
\frac{-2 \left(x -\frac{1}{2}\right) \left(x -1\right)^{4} \sqrt{1-4 x}+2 x^{7}-2 x^{6}+6 x^{5}-11 x^{4}+16 x^{3}-14 x^{2}+6 x -1}{2 x \left(2 x -1\right) \left(x -1\right)^{4}}
Generating function in sympy syntax:
(x**7 - x**6 + 3*x**5 - 11*x**4/2 + 8*x**3 - 7*x**2 + 3*x + sqrt(1 - 4*x)*(1 - 2*x)*(x - 1)**4/2 - 1/2)/(x*(x - 1)**4*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*(x-1)^8*F(x)^2-(2*x-1)*(2*x^7-2*x^6+6*x^5-11*x^4+16*x^3-14*x^2+6*x-1)*(x-1)^4*F(x)+x^13-2*x^12+7*x^11-13*x^10-x^9+91*x^8-282*x^7+481*x^6-533*x^5+398*x^4-199*x^3+64*x^2-12*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} \left(x -1\right)^{8} F \! \left(x \right)^{2}-\left(2 x -1\right) \left(2 x^{7}-2 x^{6}+6 x^{5}-11 x^{4}+16 x^{3}-14 x^{2}+6 x -1\right) \left(x -1\right)^{4} F \! \left(x \right)+x^{13}-2 x^{12}+7 x^{11}-13 x^{10}-x^{9}+91 x^{8}-282 x^{7}+481 x^{6}-533 x^{5}+398 x^{4}-199 x^{3}+64 x^{2}-12 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 18
a(5) = 53
a(6) = 157
a(7) = 480
a(8) = 1528
a(9) = 5045
a(n+3) = 8*(2*n+1)/(n+4)*a(n)-4*(5*n+8)/(n+4)*a(1+n)+2*(4*n+11)/(n+4)*a(n+2)-1/2*(n^4-15*n^3+54*n^2-40*n-4)/(n+4), n >= 10
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) = 18
a \! \left(5\right) = 53
a \! \left(6\right) = 157
a \! \left(7\right) = 480
a \! \left(8\right) = 1528
a \! \left(9\right) = 5045
a \! \left(n +3\right) = \frac{8 \left(2 n +1\right) a \! \left(n \right)}{n +4}-\frac{4 \left(5 n +8\right) a \! \left(1+n \right)}{n +4}+\frac{2 \left(4 n +11\right) a \! \left(n +2\right)}{n +4}-\frac{n^{4}-15 n^{3}+54 n^{2}-40 n -4}{2 \left(n +4\right)}, \quad n \geq 10
Specification 1
Strategy pack name: requirement_placements_tracked_fusion
Tree: http://www.permpal.com/tree/22056/
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[9,x]
F[4,x] = F[46,x]+F[5,x]
F[5,x] = F[10,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[6,x]*F[9,x]
F[9,x] = x
F[10,x] = F[11,x]+F[23,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[9,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[1,x]+F[9,x]
F[15,x] = F[11,x]+F[16,x]
F[16,x] = F[17,x]+F[18,x]+F[22,x]
F[17,x] = 0
F[18,x] = F[19,x]*F[9,x]
F[19,x] = F[20,x]+F[21,x]
F[20,x] = F[9,x]
F[21,x] = F[16,x]
F[22,x] = F[11,x]*F[9,x]
F[23,x] = F[17,x]+F[24,x]+F[41,x]
F[24,x] = F[25,x]*F[9,x]
F[25,x] = F[26,x]+F[30,x]
F[26,x] = F[27,x]+F[7,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[9,x]
F[29,x] = F[27,x]+F[9,x]
F[30,x] = F[23,x]+F[31,x]
F[31,x] = 2*F[17,x]+F[32,x]+F[36,x]
F[32,x] = F[33,x]*F[9,x]
F[33,x] = F[34,x]+F[35,x]
F[34,x] = F[27,x]
F[35,x] = F[31,x]
F[36,x] = F[37,x]*F[9,x]
F[37,x] = F[38,x]+F[40,x]
F[38,x] = F[39,x]
F[39,x] = F[7,x]*F[9,x]
F[40,x] = F[36,x]
F[41,x] = F[42,x]*F[9,x]
F[42,x] = F[43,x]+F[7,x]
F[43,x] = F[17,x]+F[41,x]+F[44,x]
F[44,x] = F[45,x]*F[9,x]
F[45,x] = F[43,x]+F[7,x]
F[46,x] = F[47,x]
F[47,x] = F[48,x,1]
F[48,x,k[0]] = F[49,x,k[0]]
F[49,x,k[0]] = F[50,x,k[0]]
F[50,x,k[0]] = F[51,x,k[0]]*F[60,x,k[0]]*F[9,x]
F[51,x,k[0]] = F[52,x,k[0]]+F[70,x,k[0]]
F[52,x,k[0]] = F[42,x]+F[53,x,k[0]]
F[53,x,k[0]] = F[54,x,k[0]]+F[61,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]*F[9,x]
F[56,x,k[0]] = F[54,x,k[0]]+F[57,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]*F[60,x,k[0]]
F[59,x,k[0]] = k[0]*x
F[60,x,k[0]] = F[1,x]+F[57,x,k[0]]
F[61,x,k[0]] = 2*F[17,x]+F[62,x,k[0]]+F[69,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]*F[9,x]
F[63,x,k[0]] = F[61,x,k[0]]+F[64,x,k[0]]
F[64,x,k[0]] = F[17,x]+F[65,x,k[0]]+F[67,x,k[0]]
F[65,x,k[0]] = F[59,x,k[0]]*F[66,x,k[0]]
F[66,x,k[0]] = F[64,x,k[0]]+F[7,x]
F[67,x,k[0]] = F[68,x,k[0]]*F[9,x]
F[68,x,k[0]] = F[57,x,k[0]]+F[64,x,k[0]]
F[69,x,k[0]] = F[53,x,k[0]]*F[9,x]
F[70,x,k[0]] = (F[49,x,k[0]]*k[0]-F[49,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_{9}\! \left(x \right)
F_{4}\! \left(x \right) = F_{46}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{10}\! \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_{6}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = x
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{23}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \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) = F_{1}\! \left(x \right)+F_{9}\! \left(x \right)
F_{15}\! \left(x \right) = F_{11}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{18}\! \left(x \right)+F_{22}\! \left(x \right)
F_{17}\! \left(x \right) = 0
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{9}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)
F_{20}\! \left(x \right) = F_{9}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right) F_{9}\! \left(x \right)
F_{23}\! \left(x \right) = F_{17}\! \left(x \right)+F_{24}\! \left(x \right)+F_{41}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{9}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{30}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{7}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{9}\! \left(x \right)
F_{29}\! \left(x \right) = F_{27}\! \left(x \right)+F_{9}\! \left(x \right)
F_{30}\! \left(x \right) = F_{23}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = 2 F_{17}\! \left(x \right)+F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{9}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)
F_{34}\! \left(x \right) = F_{27}\! \left(x \right)
F_{35}\! \left(x \right) = F_{31}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{9}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{40}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{7}\! \left(x \right) F_{9}\! \left(x \right)
F_{40}\! \left(x \right) = F_{36}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right) F_{9}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{7}\! \left(x \right)
F_{43}\! \left(x \right) = F_{17}\! \left(x \right)+F_{41}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right) F_{9}\! \left(x \right)
F_{45}\! \left(x \right) = F_{43}\! \left(x \right)+F_{7}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x , 1\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{51}\! \left(x , y\right) F_{60}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{51}\! \left(x , y\right) = F_{52}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{42}\! \left(x \right)+F_{53}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{61}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{56}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right) F_{60}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = y x
F_{60}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{57}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = 2 F_{17}\! \left(x \right)+F_{62}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{63}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{65}\! \left(x , y\right)+F_{67}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{59}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{7}\! \left(x \right)
F_{67}\! \left(x , y\right) = F_{68}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{68}\! \left(x , y\right) = F_{57}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{53}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{70}\! \left(x , y\right) = \frac{y F_{49}\! \left(x , y\right)-F_{49}\! \left(x , 1\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_9(x))
Eq(F_4(x), F_46(x) + F_5(x))
Eq(F_5(x), F_10(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_6(x)*F_9(x))
Eq(F_9(x), x)
Eq(F_10(x), F_11(x) + F_23(x))
Eq(F_11(x), F_12(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), F_1(x) + F_9(x))
Eq(F_15(x), F_11(x) + F_16(x))
Eq(F_16(x), F_17(x) + F_18(x) + F_22(x))
Eq(F_17(x), 0)
Eq(F_18(x), F_19(x)*F_9(x))
Eq(F_19(x), F_20(x) + F_21(x))
Eq(F_20(x), F_9(x))
Eq(F_21(x), F_16(x))
Eq(F_22(x), F_11(x)*F_9(x))
Eq(F_23(x), F_17(x) + F_24(x) + F_41(x))
Eq(F_24(x), F_25(x)*F_9(x))
Eq(F_25(x), F_26(x) + F_30(x))
Eq(F_26(x), F_27(x) + F_7(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_9(x))
Eq(F_29(x), F_27(x) + F_9(x))
Eq(F_30(x), F_23(x) + F_31(x))
Eq(F_31(x), 2*F_17(x) + F_32(x) + F_36(x))
Eq(F_32(x), F_33(x)*F_9(x))
Eq(F_33(x), F_34(x) + F_35(x))
Eq(F_34(x), F_27(x))
Eq(F_35(x), F_31(x))
Eq(F_36(x), F_37(x)*F_9(x))
Eq(F_37(x), F_38(x) + F_40(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_7(x)*F_9(x))
Eq(F_40(x), F_36(x))
Eq(F_41(x), F_42(x)*F_9(x))
Eq(F_42(x), F_43(x) + F_7(x))
Eq(F_43(x), F_17(x) + F_41(x) + F_44(x))
Eq(F_44(x), F_45(x)*F_9(x))
Eq(F_45(x), F_43(x) + F_7(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_48(x, 1))
Eq(F_48(x, k_0), F_49(x, k_0))
Eq(F_49(x, k_0), F_50(x, k_0))
Eq(F_50(x, k_0), F_51(x, k_0)*F_60(x, k_0)*F_9(x))
Eq(F_51(x, k_0), F_52(x, k_0) + F_70(x, k_0))
Eq(F_52(x, k_0), F_42(x) + F_53(x, k_0))
Eq(F_53(x, k_0), F_54(x, k_0) + F_61(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0)*F_9(x))
Eq(F_56(x, k_0), F_54(x, k_0) + F_57(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0)*F_60(x, k_0))
Eq(F_59(x, k_0), k_0*x)
Eq(F_60(x, k_0), F_1(x) + F_57(x, k_0))
Eq(F_61(x, k_0), 2*F_17(x) + F_62(x, k_0) + F_69(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0)*F_9(x))
Eq(F_63(x, k_0), F_61(x, k_0) + F_64(x, k_0))
Eq(F_64(x, k_0), F_17(x) + F_65(x, k_0) + F_67(x, k_0))
Eq(F_65(x, k_0), F_59(x, k_0)*F_66(x, k_0))
Eq(F_66(x, k_0), F_64(x, k_0) + F_7(x))
Eq(F_67(x, k_0), F_68(x, k_0)*F_9(x))
Eq(F_68(x, k_0), F_57(x, k_0) + F_64(x, k_0))
Eq(F_69(x, k_0), F_53(x, k_0)*F_9(x))
Eq(F_70(x, k_0), (-k_0*F_49(x, k_0) + F_49(x, 1))/(1 - k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "limited_insertion": true, "maxreqlen": 2, "strategy_class": "RequirementInsertionFactory"}, {"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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "requirement_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:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "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": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 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": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]], "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, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}]]}], "class_module": 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{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 2]]}, {"patt": [0, 1], "pos": [[0, 2], [0, 2]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 4], [0, 4]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 4], [0, 4]]}, {"patt": [0, 1, 2], "pos": [[0, 4], [0, 4], [0, 4]]}], "requirements": [[{"patt": [0], "pos": [[0, 2]]}, {"patt": [0, 1], "pos": [[0, 4], [0, 4]]}], [{"patt": [0], "pos": [[1, 3]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [0, 2], [0, 4]], [[1, 3]], [[2, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": 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