0132_0213_1203_1230_2013
Counting sequence:
1, 1, 2, 6, 19, 60, 192, 625, 2073, 6999, 24009, 83502, 293865, 1044685, 3746192, 13534810, 49221332, 180031647, 661839164, 2444131541, 9062807635, 33728304306, 125942291971, 471699822487, 1771597431122, 6670701477771, 25176688220071, 95229090065070, 360924430561897, 1370494833290179, 5213124263278016, 19862264967393376, 75792225388975918, 289630998227293191, 1108288564849724766, 4246334862695027911, 16289141640843232295, 62557051291102970544, 240503971838185149485, 925575792148781724563, 3565522139151830539104, 13747857288421527895897, 53055256925471334485031, 204920547785063823798788, 792117575799989509278599, 3064258068545311610711167, 11862550757080392465287346, 45955164609146506196086243, 178148167042785842676065449, 691046474362825266650284454, 2682259627162411350585702969, 10417211628617766498934203107, 40480824298617026007983940560, 157392860054746749718617398935, 612279449765030304838837615251, 2383059888027040865349238626766, 9279678676153208762039571351025, 36152317086318329189193941505059, 140908584507140149616189693327880, 549452486936415739134232198823075, 2143422622893778775499451131465107, 8364969612998350875356622415325326, 32658334019214059448150115870657737, 127553175267803414418268269606107956, 498368813461203650869228888796822995, 1947904973578109127546340209154142864, 7616180351165036874142540376140183884, 29788912603672927136695934262393864398, 116550916796087017333157709702142146332, 456158925303459089828284969099688540380, 1785879301498911574461840662714302172862, 6993903724939299962426096391690296696392, 27397765805217113153770209652013951725654, 107358166862167403127495661304868222045596, 420800350664132331996454223713441601056440, 1649813792201891769248573370825668043982856, 6470062705553147313594669273782815703152076, 25380126691823441525088306910169257675566712, 99583628424115364575215981108196576026238848, 390830284634030517068048386560374191311923230, 1534235104667139810539995731539503349573190378, 6024160114502693452157311417721872627881040518, 23659170575664008926046530944142873389918459006, 92939122195011240331697020222022592520617436944, 365166868744465269969187632639912243511311287370, 1435078667713353374731298118352826991975650688454, 5640913717842168066478651063839809480352056803604, 22177396066259279284277415021622877590551523202038, 87208136593385563150764971085394484616433260547802, 342994296055423687427411986096925215691735814067180, 1349268458028735691340010425271952497064581038909842, 5308717568778400353290825905867239393981119625713222, 20890985090194669873305810603602151611610623330481264, 82225132359929126510711947266999148523424979093657886, 323686792912124907460387353957536330399528467104509350, 1274437488891649936665114281134867083636200544397797686, 5018613264156311808768993836267343701846985152485333736, 19766012965682031969429464316980827227352629062059752872, 77861567297056318966969682349456841006673608383688099258, 306757038496432170775637938674090242768645458399010450070, 1208737265457889053210573112642947827100422901745788092548
Generating function in Maple syntax:
1/2*(-(1-4*x)^(1/2)*x^3-(1-4*x)^(1/2)*x^2+3*x^3+3*x^2+(1-4*x)^(1/2)-1)/(x^2+x-1)/x
Generating function in latex syntax:
\frac{-\sqrt{1-4 x}\, x^{3}-\sqrt{1-4 x}\, x^{2}+3 x^{3}+3 x^{2}+\sqrt{1-4 x}-1}{2 \left(x^{2}+x -1\right) x}
Generating function in sympy syntax:
(-x**3*sqrt(1 - 4*x)/2 + 3*x**3/2 - x**2*sqrt(1 - 4*x)/2 + 3*x**2/2 + sqrt(1 - 4*x)/2 - 1/2)/(x*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
x*(x^2+x-1)^2*F(x)^2-(x^2+x-1)*(3*x^3+3*x^2-1)*F(x)+x^6+4*x^5+5*x^4-3*x^2-x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(x^{2}+x -1\right)^{2} F \! \left(x \right)^{2}-\left(x^{2}+x -1\right) \left(3 x^{3}+3 x^{2}-1\right) F \! \left(x \right)+x^{6}+4 x^{5}+5 x^{4}-3 x^{2}-x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 60
a(6) = 192
a(n+6) = 2*(-1+2*n)/(n+7)*a(n)+(3+7*n)/(n+7)*a(1+n)-2*(n-2)/(n+7)*a(n+2)-2*(15+4*n)/(n+7)*a(n+3)-2*(n+6)/(n+7)*a(n+4)+(29+5*n)/(n+7)*a(n+5), 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) = 19
a \! \left(5\right) = 60
a \! \left(6\right) = 192
a \! \left(n +6\right) = \frac{2 \left(-1+2 n \right) a \! \left(n \right)}{n +7}+\frac{\left(3+7 n \right) a \! \left(1+n \right)}{n +7}-\frac{2 \left(n -2\right) a \! \left(n +2\right)}{n +7}-\frac{2 \left(15+4 n \right) a \! \left(n +3\right)}{n +7}-\frac{2 \left(n +6\right) a \! \left(n +4\right)}{n +7}+\frac{\left(29+5 n \right) a \! \left(n +5\right)}{n +7}, \quad n \geq 7
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21620/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[16,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[64,x]
F[4,x] = F[5,x]
F[5,x] = F[16,x]*F[6,x]
F[6,x] = F[7,x,1]
F[7,x,k[0]] = F[61,x,k[0]]+F[8,x,k[0]]
F[8,x,k[0]] = F[27,x,k[0]]+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[16,x]
F[12,x] = F[13,x]+F[17,x]
F[13,x] = F[1,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[16,x]
F[16,x] = x
F[17,x] = F[18,x]+F[25,x]
F[18,x] = F[19,x]
F[19,x] = F[16,x]*F[20,x]
F[20,x] = F[21,x]+F[22,x]
F[21,x] = F[1,x]+F[16,x]
F[22,x] = F[18,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[16,x]*F[18,x]
F[25,x] = F[26,x]
F[26,x] = F[16,x]*F[17,x]
F[27,x,k[0]] = F[28,x,k[0]]+F[32,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]
F[29,x,k[0]] = F[30,x,k[0]]*F[31,x,k[0]]
F[30,x,k[0]] = F[1,x]+F[28,x,k[0]]
F[31,x,k[0]] = k[0]*x
F[32,x,k[0]] = F[33,x]+F[34,x,k[0]]+F[36,x,k[0]]
F[33,x] = 0
F[34,x,k[0]] = F[31,x,k[0]]*F[35,x,k[0]]
F[35,x,k[0]] = F[10,x]+F[32,x,k[0]]
F[36,x,k[0]] = F[16,x]*F[37,x,k[0]]
F[37,x,k[0]] = F[38,x,k[0]]+F[41,x,k[0]]
F[38,x,k[0]] = F[28,x,k[0]]+F[39,x,k[0]]
F[39,x,k[0]] = F[40,x,k[0]]
F[40,x,k[0]] = F[16,x]*F[38,x,k[0]]
F[41,x,k[0]] = F[42,x,k[0]]+F[59,x,k[0]]
F[42,x,k[0]] = F[33,x]+F[43,x,k[0]]+F[51,x,k[0]]
F[43,x,k[0]] = F[31,x,k[0]]*F[44,x,k[0]]
F[44,x,k[0]] = F[45,x]+F[48,x,k[0]]
F[45,x] = F[46,x]
F[46,x] = F[16,x]*F[47,x]
F[47,x] = F[1,x]+F[45,x]
F[48,x,k[0]] = F[33,x]+F[43,x,k[0]]+F[49,x,k[0]]
F[49,x,k[0]] = F[16,x]*F[50,x,k[0]]
F[50,x,k[0]] = F[28,x,k[0]]+F[48,x,k[0]]
F[51,x,k[0]] = F[16,x]*F[52,x,k[0]]
F[52,x,k[0]] = F[53,x,k[0]]+F[56,x,k[0]]
F[53,x,k[0]] = F[28,x,k[0]]+F[54,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]
F[55,x,k[0]] = F[16,x]*F[28,x,k[0]]
F[56,x,k[0]] = F[42,x,k[0]]+F[57,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]
F[58,x,k[0]] = F[16,x]*F[42,x,k[0]]
F[59,x,k[0]] = F[60,x,k[0]]
F[60,x,k[0]] = F[16,x]*F[41,x,k[0]]
F[61,x,k[0]] = F[62,x,k[0]]
F[62,x,k[0]] = F[16,x]*F[30,x,k[0]]*F[63,x]
F[63,x] = F[14,x]+F[9,x]
F[64,x] = F[16,x]*F[65,x]
F[65,x] = F[66,x,1]
F[66,x,k[0]] = F[1,x]+F[67,x,k[0]]+F[68,x,k[0]]+F[70,x,k[0]]
F[67,x,k[0]] = F[31,x,k[0]]*F[66,x,k[0]]
F[68,x,k[0]] = F[16,x]*F[69,x,k[0]]
F[69,x,k[0]] = (F[66,x,k[0]]*k[0]-F[66,x,1])/(-1+k[0])
F[70,x,k[0]] = F[71,x,k[0]]
F[71,x,k[0]] = F[16,x]*F[72,x,k[0]]
F[72,x,k[0]] = (F[7,x,k[0]]*k[0]-F[7,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_{16}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{64}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{16}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x , 1\right)
F_{7}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{27}\! \left(x , y\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_{16}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{17}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{25}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \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 \right)+F_{22}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{16}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{16}\! \left(x \right) F_{18}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{16}\! \left(x \right) F_{17}\! \left(x \right)
F_{27}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{32}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{30}\! \left(x , y\right) F_{31}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{28}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = y x
F_{32}\! \left(x , y\right) = F_{33}\! \left(x \right)+F_{34}\! \left(x , y\right)+F_{36}\! \left(x , y\right)
F_{33}\! \left(x \right) = 0
F_{34}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{10}\! \left(x \right)+F_{32}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{38}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{39}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x , y\right)
F_{40}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{38}\! \left(x , y\right)
F_{41}\! \left(x , y\right) = F_{42}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{33}\! \left(x \right)+F_{43}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{43}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{44}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{45}\! \left(x \right)+F_{48}\! \left(x , y\right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{16}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{1}\! \left(x \right)+F_{45}\! \left(x \right)
F_{48}\! \left(x , y\right) = F_{33}\! \left(x \right)+F_{43}\! \left(x , y\right)+F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{50}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{52}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x , y\right)+F_{56}\! \left(x , y\right)
F_{53}\! \left(x , y\right) = F_{28}\! \left(x , y\right)+F_{54}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{28}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{42}\! \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_{16}\! \left(x \right) F_{42}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{41}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{30}\! \left(x , y\right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{64}\! \left(x \right) = F_{16}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x , 1\right)
F_{66}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{67}\! \left(x , y\right)+F_{68}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{31}\! \left(x , y\right) F_{66}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = \frac{F_{66}\! \left(x , y\right) y -F_{66}\! \left(x , 1\right)}{-1+y}
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{16}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = \frac{F_{7}\! \left(x , y\right) y -F_{7}\! \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_16(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_64(x))
Eq(F_4(x), F_5(x))
Eq(F_5(x), F_16(x)*F_6(x))
Eq(F_6(x), F_7(x, 1))
Eq(F_7(x, k_0), F_61(x, k_0) + F_8(x, k_0))
Eq(F_8(x, k_0), F_27(x, k_0) + 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_16(x))
Eq(F_12(x), F_13(x) + F_17(x))
Eq(F_13(x), F_1(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_16(x))
Eq(F_16(x), x)
Eq(F_17(x), F_18(x) + F_25(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_16(x)*F_20(x))
Eq(F_20(x), F_21(x) + F_22(x))
Eq(F_21(x), F_1(x) + F_16(x))
Eq(F_22(x), F_18(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_16(x)*F_18(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_16(x)*F_17(x))
Eq(F_27(x, k_0), F_28(x, k_0) + F_32(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0))
Eq(F_29(x, k_0), F_30(x, k_0)*F_31(x, k_0))
Eq(F_30(x, k_0), F_1(x) + F_28(x, k_0))
Eq(F_31(x, k_0), k_0*x)
Eq(F_32(x, k_0), F_33(x) + F_34(x, k_0) + F_36(x, k_0))
Eq(F_33(x), 0)
Eq(F_34(x, k_0), F_31(x, k_0)*F_35(x, k_0))
Eq(F_35(x, k_0), F_10(x) + F_32(x, k_0))
Eq(F_36(x, k_0), F_16(x)*F_37(x, k_0))
Eq(F_37(x, k_0), F_38(x, k_0) + F_41(x, k_0))
Eq(F_38(x, k_0), F_28(x, k_0) + F_39(x, k_0))
Eq(F_39(x, k_0), F_40(x, k_0))
Eq(F_40(x, k_0), F_16(x)*F_38(x, k_0))
Eq(F_41(x, k_0), F_42(x, k_0) + F_59(x, k_0))
Eq(F_42(x, k_0), F_33(x) + F_43(x, k_0) + F_51(x, k_0))
Eq(F_43(x, k_0), F_31(x, k_0)*F_44(x, k_0))
Eq(F_44(x, k_0), F_45(x) + F_48(x, k_0))
Eq(F_45(x), F_46(x))
Eq(F_46(x), F_16(x)*F_47(x))
Eq(F_47(x), F_1(x) + F_45(x))
Eq(F_48(x, k_0), F_33(x) + F_43(x, k_0) + F_49(x, k_0))
Eq(F_49(x, k_0), F_16(x)*F_50(x, k_0))
Eq(F_50(x, k_0), F_28(x, k_0) + F_48(x, k_0))
Eq(F_51(x, k_0), F_16(x)*F_52(x, k_0))
Eq(F_52(x, k_0), F_53(x, k_0) + F_56(x, k_0))
Eq(F_53(x, k_0), F_28(x, k_0) + F_54(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0))
Eq(F_55(x, k_0), F_16(x)*F_28(x, k_0))
Eq(F_56(x, k_0), F_42(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_16(x)*F_42(x, k_0))
Eq(F_59(x, k_0), F_60(x, k_0))
Eq(F_60(x, k_0), F_16(x)*F_41(x, k_0))
Eq(F_61(x, k_0), F_62(x, k_0))
Eq(F_62(x, k_0), F_16(x)*F_30(x, k_0)*F_63(x))
Eq(F_63(x), F_14(x) + F_9(x))
Eq(F_64(x), F_16(x)*F_65(x))
Eq(F_65(x), F_66(x, 1))
Eq(F_66(x, k_0), F_1(x) + F_67(x, k_0) + F_68(x, k_0) + F_70(x, k_0))
Eq(F_67(x, k_0), F_31(x, k_0)*F_66(x, k_0))
Eq(F_68(x, k_0), F_16(x)*F_69(x, k_0))
Eq(F_69(x, k_0), (-k_0*F_66(x, k_0) + F_66(x, 1))/(1 - k_0))
Eq(F_70(x, k_0), F_71(x, k_0))
Eq(F_71(x, k_0), F_16(x)*F_72(x, k_0))
Eq(F_72(x, k_0), (-k_0*F_7(x, k_0) + F_7(x, 1))/(1 - k_0))
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.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.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_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, 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, 2, 0, 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, 0, 1, 3], "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], "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, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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, 2, 0, 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, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[1, 0], [1, 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, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 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"pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[1, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": 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"rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0, 0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"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": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 1], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], 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2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 2], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 2], [2, 2], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 1], [3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 2], [3, 1]], [[1, 0]]], "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"}}, 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