0123_0231_1230_3012
Counting sequence:
1, 1, 2, 6, 20, 66, 213, 683, 2211, 7291, 24552, 84305, 294297, 1041213, 3723752, 13434874, 48825190, 178535378, 656304995, 2423830156, 8988474672, 33455790056, 124940450615, 468004258314, 1757916793968, 6619879972334, 24987266598591, 94520884623106, 358268970590814, 1360511455677230, 5175498494640009, 19720135607608275, 75254202632139623, 287590337339349499, 1100534388079014292, 4216819900166184141, 16176618320386375369, 62127422713727593801, 238861285638173247968, 919286657643026954559, 3541413700469274876485, 13655332293206684637459, 52699762207310151851388, 203553241416793550022287, 786853361018586336131587, 3043971215113426595428731, 11784299926681784357562846, 45653073683943199988168917, 176980971926253302954515015, 686533217106151915985833065, 2664794874862875519563027606, 10349580545378317804700685109, 40218747491153195554656786541, 156376618946940133404838001537, 608336336974902612051702250520, 2367750953583739497442691606989, 9220207881428649023789369033727, 35921160738203572985628627872729, 140009621027326021134315022539026, 545954616154903295095334617616169, 2129805580751023914242859700076781, 8311933539335880717651445154138261, 32451671282381509849205912914103632, 126747521841153494248827316287869706, 495226691716970162951208395856190446, 1935645264867889850270442363809605330, 7568326849428202622157846217077851515, 29602051871384720159303375125973005716, 115820975870345006033062968379350524864, 453306478380560981884994667013761973072, 1774728586800843252965232654562697166967, 6950298511446948813564764469275174184254, 27227188901156348678854946278964637814244, 106690678266233726524785550394183551909810, 418187556577337047671766574878731976361739, 1639583211007715859519416762818172688004766, 6429992141371019770885581903075994310736002, 25223134868180904346172501045889453827402250, 98968378479713362806013768627988611713573117, 388418459654978262260599846112383036271638808, 1524778037602314534192837186026857807526602674, 5987068087590635016657287409352605620200960348, 23513653103207411851394845778907490514946603657, 92368094235987606559287733516854596174630631056, 362925545275382724587939868212580079628699557416, 1426279248197656560560995869069170372418598257180, 5606359321754181295075730382866305498980940165475, 22041674156419608092144952714881646978615711751936, 86674934742182522462641744943532739113831609399634, 340899093046183318986595495207384207545447706203372, 1341033693846538100915995364713945714598046245712277, 5276345927430542786333850175417334509752352824856204, 20763703749922432193462179615075756312526833750936064, 81724580285262847944924748147665562346017662254866680, 321717925803339853113840534674662599635340688936085699, 1266691723780768060966446424936642825038655845556972866, 4988134928186722446530317005929970741880331339707637772, 19646064284316297883547194931815166017857623884151338550, 77389422353917655665734895698314347380407030695995845467, 304898253148147005327554436410915851393506063671712689298, 1201418200238278502014724507118841783928458285958810196354
Generating function in Maple syntax:
1/2*(2*(x-1)^3*(x-1/2)*(1-4*x)^(1/2)-6*x^5+8*x^4-x^3-7*x^2+5*x-1)/x/(2*x-1)/(x-1)^4
Generating function in latex syntax:
\frac{2 \left(x -1\right)^{3} \left(x -\frac{1}{2}\right) \sqrt{1-4 x}-6 x^{5}+8 x^{4}-x^{3}-7 x^{2}+5 x -1}{2 x \left(2 x -1\right) \left(x -1\right)^{4}}
Generating function in sympy syntax:
(-3*x**5 + 4*x**4 - x**3/2 - 7*x**2/2 + 5*x/2 + sqrt(1 - 4*x)*(x - 1)**3*(x - 1/2) - 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)*(6*x^5-8*x^4+x^3+7*x^2-5*x+1)*(x-1)^4*F(x)+9*x^9-20*x^8-10*x^7+109*x^6-210*x^5+218*x^4-137*x^3+52*x^2-11*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(6 x^{5}-8 x^{4}+x^{3}+7 x^{2}-5 x +1\right) \left(x -1\right)^{4} F \! \left(x \right)+9 x^{9}-20 x^{8}-10 x^{7}+109 x^{6}-210 x^{5}+218 x^{4}-137 x^{3}+52 x^{2}-11 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 66
a(6) = 213
a(7) = 683
a(n+4) = -8*(2*n+3)/(5+n)*a(n)+4*(9*n+19)/(5+n)*a(1+n)-2*(14*n+41)/(5+n)*a(n+2)+(9*n+35)/(5+n)*a(n+3)+1/2*(3*n^3-14*n^2-9*n+4)/(5+n), n >= 8
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) = 20
a \! \left(5\right) = 66
a \! \left(6\right) = 213
a \! \left(7\right) = 683
a \! \left(n +4\right) = -\frac{8 \left(2 n +3\right) a \! \left(n \right)}{5+n}+\frac{4 \left(9 n +19\right) a \! \left(1+n \right)}{5+n}-\frac{2 \left(14 n +41\right) a \! \left(n +2\right)}{5+n}+\frac{\left(9 n +35\right) a \! \left(n +3\right)}{5+n}+\frac{3 n^{3}-14 n^{2}-9 n +4}{2 n +10}, \quad n \geq 8
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21157/
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[9,x]
F[3,x] = F[1,x]+F[4,x]+F[71,x]
F[4,x] = F[5,x]*F[9,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[10,x,k[0]]+F[50,x]+F[7,x,k[0]]
F[7,x,k[0]] = F[8,x,k[0]]*F[9,x]
F[8,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[9,x] = x
F[10,x,k[0]] = F[11,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]*F[21,x,k[0]]*F[25,x]
F[12,x,k[0]] = F[1,x]+F[13,x,k[0]]+F[48,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]*F[9,x]
F[14,x,k[0]] = F[1,x]+F[15,x,k[0]]+F[45,x,k[0]]+F[47,x,k[0]]
F[15,x,k[0]] = F[16,x,k[0]]*F[9,x]
F[16,x,k[0]] = F[17,x,k[0]]+F[28,x,k[0]]
F[17,x,k[0]] = F[18,x,k[0]]+F[22,x,k[0]]
F[18,x,k[0]] = F[1,x]+F[19,x,k[0]]
F[19,x,k[0]] = F[20,x,k[0]]
F[20,x,k[0]] = F[18,x,k[0]]*F[21,x,k[0]]
F[21,x,k[0]] = k[0]*x
F[22,x,k[0]] = F[23,x]+F[26,x,k[0]]
F[23,x] = F[24,x]
F[24,x] = F[25,x]*F[9,x]
F[25,x] = F[1,x]+F[23,x]
F[26,x,k[0]] = F[27,x,k[0]]
F[27,x,k[0]] = F[21,x,k[0]]*F[22,x,k[0]]
F[28,x,k[0]] = F[29,x,k[0]]+F[35,x,k[0]]
F[29,x,k[0]] = F[23,x]+F[30,x,k[0]]
F[30,x,k[0]] = F[31,x]+F[32,x,k[0]]+F[34,x,k[0]]
F[31,x] = 0
F[32,x,k[0]] = F[33,x,k[0]]*F[9,x]
F[33,x,k[0]] = F[19,x,k[0]]+F[30,x,k[0]]
F[34,x,k[0]] = F[21,x,k[0]]*F[29,x,k[0]]
F[35,x,k[0]] = F[36,x]+F[41,x,k[0]]
F[36,x] = F[31,x]+F[37,x]+F[39,x]
F[37,x] = F[38,x]*F[9,x]
F[38,x] = F[23,x]+F[36,x]
F[39,x] = F[40,x]*F[9,x]
F[40,x] = F[23,x]+F[36,x]
F[41,x,k[0]] = 2*F[31,x]+F[42,x,k[0]]+F[44,x,k[0]]
F[42,x,k[0]] = F[43,x,k[0]]*F[9,x]
F[43,x,k[0]] = F[26,x,k[0]]+F[41,x,k[0]]
F[44,x,k[0]] = F[21,x,k[0]]*F[35,x,k[0]]
F[45,x,k[0]] = F[46,x,k[0]]*F[9,x]
F[46,x,k[0]] = 1/(-1+k[0])*(F[14,x,k[0]]*k[0]-F[14,x,1])
F[47,x,k[0]] = F[14,x,k[0]]*F[21,x,k[0]]
F[48,x,k[0]] = F[21,x,k[0]]*F[49,x,k[0]]
F[49,x,k[0]] = F[18,x,k[0]]+F[29,x,k[0]]
F[50,x] = F[51,x]*F[9,x]
F[51,x] = F[52,x]+F[60,x]
F[52,x] = F[25,x]+F[53,x]
F[53,x] = F[23,x]+F[54,x]
F[54,x] = F[31,x]+F[55,x]+F[57,x]
F[55,x] = F[56,x]*F[9,x]
F[56,x] = F[23,x]+F[54,x]
F[57,x] = F[58,x]*F[9,x]
F[58,x] = F[23,x]+F[59,x]
F[59,x] = F[57,x]
F[60,x] = F[61,x]+F[65,x]
F[61,x] = F[23,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[64,x]*F[9,x]
F[64,x] = F[23,x]+F[62,x]
F[65,x] = F[36,x]+F[66,x]
F[66,x] = 2*F[31,x]+F[67,x]+F[69,x]
F[67,x] = F[68,x]*F[9,x]
F[68,x] = F[54,x]+F[66,x]
F[69,x] = F[70,x]*F[9,x]
F[70,x] = F[62,x]+F[66,x]
F[71,x] = F[72,x]*F[9,x]
F[72,x] = F[1,x]+F[144,x]+F[73,x]+F[95,x]
F[73,x] = F[74,x,1]
F[74,x,k[0]] = F[21,x,k[0]]*F[75,x,k[0]]
F[75,x,k[0]] = F[1,x]+F[74,x,k[0]]+F[76,x,k[0]]+F[78,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]*F[9,x]
F[77,x,k[0]] = 1/(-1+k[0])*(F[75,x,k[0]]*k[0]-F[75,x,1])
F[78,x,k[0]] = F[79,x,k[0]]*F[9,x]
F[79,x,k[0]] = F[80,x]+F[81,x,k[0]]
F[80,x] = F[25,x]+F[40,x]
F[81,x,k[0]] = F[82,x,k[0]]+F[87,x,k[0]]
F[82,x,k[0]] = F[19,x,k[0]]+F[83,x,k[0]]
F[83,x,k[0]] = F[31,x]+F[84,x,k[0]]+F[86,x,k[0]]
F[84,x,k[0]] = F[21,x,k[0]]*F[85,x,k[0]]
F[85,x,k[0]] = F[23,x]+F[83,x,k[0]]
F[86,x,k[0]] = F[82,x,k[0]]*F[9,x]
F[87,x,k[0]] = F[88,x,k[0]]+F[91,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]
F[89,x,k[0]] = F[9,x]*F[90,x,k[0]]
F[90,x,k[0]] = F[19,x,k[0]]+F[88,x,k[0]]
F[91,x,k[0]] = 2*F[31,x]+F[92,x,k[0]]+F[94,x,k[0]]
F[92,x,k[0]] = F[9,x]*F[93,x,k[0]]
F[93,x,k[0]] = F[83,x,k[0]]+F[91,x,k[0]]
F[94,x,k[0]] = F[87,x,k[0]]*F[9,x]
F[95,x] = F[9,x]*F[96,x]
F[96,x] = F[97,x,1]
F[97,x,k[0]] = F[1,x]+F[100,x,k[0]]+F[102,x,k[0]]+F[74,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[9,x]*F[99,x,k[0]]
F[99,x,k[0]] = 1/(-1+k[0])*(F[75,x,k[0]]*k[0]-F[75,x,1])
F[100,x,k[0]] = F[101,x,k[0]]*F[9,x]
F[101,x,k[0]] = (F[97,x,k[0]]*k[0]-F[97,x,1])/(-1+k[0])
F[102,x,k[0]] = F[103,x,k[0]]*F[9,x]
F[103,x,k[0]] = F[104,x,k[0]]+F[79,x,k[0]]
F[104,x,k[0]] = F[105,x]+F[123,x,k[0]]
F[105,x] = F[106,x]+F[40,x]
F[106,x] = F[107,x]+F[36,x]
F[107,x] = F[108,x]+F[116,x]+F[118,x]+F[31,x]
F[108,x] = F[109,x]*F[9,x]
F[109,x] = F[110,x]+F[62,x]
F[110,x] = 2*F[31,x]+F[108,x]+F[111,x]
F[111,x] = F[112,x]*F[9,x]
F[112,x] = F[113,x]+F[62,x]
F[113,x] = 2*F[31,x]+F[111,x]+F[114,x]
F[114,x] = F[115,x]*F[9,x]
F[115,x] = F[113,x]+F[62,x]
F[116,x] = F[117,x]*F[9,x]
F[117,x] = F[107,x]+F[36,x]
F[118,x] = F[119,x]*F[9,x]
F[119,x] = F[120,x]+F[59,x]
F[120,x] = 2*F[31,x]+F[118,x]+F[121,x]
F[121,x] = F[122,x]*F[9,x]
F[122,x] = F[120,x]+F[36,x]
F[123,x,k[0]] = F[124,x,k[0]]+F[129,x,k[0]]
F[124,x,k[0]] = F[125,x,k[0]]+F[26,x,k[0]]
F[125,x,k[0]] = 2*F[31,x]+F[126,x,k[0]]+F[128,x,k[0]]
F[126,x,k[0]] = F[127,x,k[0]]*F[21,x,k[0]]
F[127,x,k[0]] = F[125,x,k[0]]+F[36,x]
F[128,x,k[0]] = F[124,x,k[0]]*F[9,x]
F[129,x,k[0]] = F[130,x,k[0]]+F[133,x,k[0]]
F[130,x,k[0]] = F[131,x,k[0]]
F[131,x,k[0]] = F[132,x,k[0]]*F[9,x]
F[132,x,k[0]] = F[130,x,k[0]]+F[26,x,k[0]]
F[133,x,k[0]] = 3*F[31,x]+F[134,x,k[0]]+F[136,x,k[0]]
F[134,x,k[0]] = F[135,x,k[0]]*F[9,x]
F[135,x,k[0]] = F[125,x,k[0]]+F[133,x,k[0]]
F[136,x,k[0]] = F[137,x,k[0]]*F[9,x]
F[137,x,k[0]] = F[138,x,k[0]]+F[141,x,k[0]]
F[138,x,k[0]] = F[139,x,k[0]]
F[139,x,k[0]] = F[140,x,k[0]]*F[9,x]
F[140,x,k[0]] = F[138,x,k[0]]+F[26,x,k[0]]
F[141,x,k[0]] = 3*F[31,x]+F[136,x,k[0]]+F[142,x,k[0]]
F[142,x,k[0]] = F[143,x,k[0]]*F[9,x]
F[143,x,k[0]] = F[125,x,k[0]]+F[141,x,k[0]]
F[144,x] = F[145,x]*F[9,x]
F[145,x] = F[105,x]+F[80,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_{9}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{71}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right) F_{9}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{10}\! \left(x , y\right)+F_{50}\! \left(x \right)+F_{7}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{8}\! \left(x , y\right) = -\frac{-y F_{6}\! \left(x , y\right)+F_{6}\! \left(x , 1\right)}{-1+y}
F_{9}\! \left(x \right) = x
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{21}\! \left(x , y\right) F_{25}\! \left(x \right)
F_{12}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)+F_{48}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{14}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{15}\! \left(x , y\right)+F_{45}\! \left(x , y\right)+F_{47}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = F_{16}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{16}\! \left(x , y\right) = F_{17}\! \left(x , y\right)+F_{28}\! \left(x , y\right)
F_{17}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{22}\! \left(x , y\right)
F_{18}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{19}\! \left(x , y\right)
F_{19}\! \left(x , y\right) = F_{20}\! \left(x , y\right)
F_{20}\! \left(x , y\right) = F_{18}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{21}\! \left(x , y\right) = y x
F_{22}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{26}\! \left(x , y\right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{9}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{26}\! \left(x , y\right) = F_{27}\! \left(x , y\right)
F_{27}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{22}\! \left(x , y\right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{29}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{30}\! \left(x , y\right)
F_{30}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{32}\! \left(x , y\right)+F_{34}\! \left(x , y\right)
F_{31}\! \left(x \right) = 0
F_{32}\! \left(x , y\right) = F_{33}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{33}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{30}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{29}\! \left(x , y\right)
F_{35}\! \left(x , y\right) = F_{36}\! \left(x \right)+F_{41}\! \left(x , y\right)
F_{36}\! \left(x \right) = F_{31}\! \left(x \right)+F_{37}\! \left(x \right)+F_{39}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{9}\! \left(x \right)
F_{38}\! \left(x \right) = F_{23}\! \left(x \right)+F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right) F_{9}\! \left(x \right)
F_{40}\! \left(x \right) = F_{23}\! \left(x \right)+F_{36}\! \left(x \right)
F_{41}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{42}\! \left(x , y\right)+F_{44}\! \left(x , y\right)
F_{42}\! \left(x , y\right) = F_{43}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{43}\! \left(x , y\right) = F_{26}\! \left(x , y\right)+F_{41}\! \left(x , y\right)
F_{44}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{35}\! \left(x , y\right)
F_{45}\! \left(x , y\right) = F_{46}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{46}\! \left(x , y\right) = -\frac{-y F_{14}\! \left(x , y\right)+F_{14}\! \left(x , 1\right)}{-1+y}
F_{47}\! \left(x , y\right) = F_{14}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{49}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{18}\! \left(x , y\right)+F_{29}\! \left(x , y\right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right) F_{9}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{60}\! \left(x \right)
F_{52}\! \left(x \right) = F_{25}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{23}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{31}\! \left(x \right)+F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right) F_{9}\! \left(x \right)
F_{56}\! \left(x \right) = F_{23}\! \left(x \right)+F_{54}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right) F_{9}\! \left(x \right)
F_{58}\! \left(x \right) = F_{23}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{57}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{65}\! \left(x \right)
F_{61}\! \left(x \right) = F_{23}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right) F_{9}\! \left(x \right)
F_{64}\! \left(x \right) = F_{23}\! \left(x \right)+F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = F_{36}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{67}\! \left(x \right)+F_{69}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right) F_{9}\! \left(x \right)
F_{68}\! \left(x \right) = F_{54}\! \left(x \right)+F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right) F_{9}\! \left(x \right)
F_{70}\! \left(x \right) = F_{62}\! \left(x \right)+F_{66}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right) F_{9}\! \left(x \right)
F_{72}\! \left(x \right) = F_{1}\! \left(x \right)+F_{144}\! \left(x \right)+F_{73}\! \left(x \right)+F_{95}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x , 1\right)
F_{74}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{74}\! \left(x , y\right)+F_{76}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{77}\! \left(x , y\right) = -\frac{-y F_{75}\! \left(x , y\right)+F_{75}\! \left(x , 1\right)}{-1+y}
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x \right)+F_{81}\! \left(x , y\right)
F_{80}\! \left(x \right) = F_{25}\! \left(x \right)+F_{40}\! \left(x \right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{31}\! \left(x \right)+F_{84}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{21}\! \left(x , y\right) F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{83}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{82}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{9}\! \left(x \right) F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{19}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{92}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{9}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{83}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{87}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{95}\! \left(x \right) = F_{9}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x , 1\right)
F_{97}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{102}\! \left(x , y\right)+F_{74}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{9}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = -\frac{-y F_{75}\! \left(x , y\right)+F_{75}\! \left(x , 1\right)}{-1+y}
F_{100}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{101}\! \left(x , y\right) = -\frac{-y F_{97}\! \left(x , y\right)+F_{97}\! \left(x , 1\right)}{-1+y}
F_{102}\! \left(x , y\right) = F_{103}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{104}\! \left(x , y\right) = F_{105}\! \left(x \right)+F_{123}\! \left(x , y\right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{40}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{36}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{116}\! \left(x \right)+F_{118}\! \left(x \right)+F_{31}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{9}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{62}\! \left(x \right)
F_{110}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{108}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{9}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{62}\! \left(x \right)
F_{113}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{111}\! \left(x \right)+F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{9}\! \left(x \right)
F_{115}\! \left(x \right) = F_{113}\! \left(x \right)+F_{62}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right) F_{9}\! \left(x \right)
F_{117}\! \left(x \right) = F_{107}\! \left(x \right)+F_{36}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right) F_{9}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{59}\! \left(x \right)
F_{120}\! \left(x \right) = 2 F_{31}\! \left(x \right)+F_{118}\! \left(x \right)+F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{122}\! \left(x \right) F_{9}\! \left(x \right)
F_{122}\! \left(x \right) = F_{120}\! \left(x \right)+F_{36}\! \left(x \right)
F_{123}\! \left(x , y\right) = F_{124}\! \left(x , y\right)+F_{129}\! \left(x , y\right)
F_{124}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{125}\! \left(x , y\right) = 2 F_{31}\! \left(x \right)+F_{126}\! \left(x , y\right)+F_{128}\! \left(x , y\right)
F_{126}\! \left(x , y\right) = F_{127}\! \left(x , y\right) F_{21}\! \left(x , y\right)
F_{127}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{36}\! \left(x \right)
F_{128}\! \left(x , y\right) = F_{124}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{129}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{130}\! \left(x , y\right) = F_{131}\! \left(x , y\right)
F_{131}\! \left(x , y\right) = F_{132}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{132}\! \left(x , y\right) = F_{130}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{133}\! \left(x , y\right) = 3 F_{31}\! \left(x \right)+F_{134}\! \left(x , y\right)+F_{136}\! \left(x , y\right)
F_{134}\! \left(x , y\right) = F_{135}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{135}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{133}\! \left(x , y\right)
F_{136}\! \left(x , y\right) = F_{137}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{137}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{138}\! \left(x , y\right) = F_{139}\! \left(x , y\right)
F_{139}\! \left(x , y\right) = F_{140}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{140}\! \left(x , y\right) = F_{138}\! \left(x , y\right)+F_{26}\! \left(x , y\right)
F_{141}\! \left(x , y\right) = 3 F_{31}\! \left(x \right)+F_{136}\! \left(x , y\right)+F_{142}\! \left(x , y\right)
F_{142}\! \left(x , y\right) = F_{143}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{143}\! \left(x , y\right) = F_{125}\! \left(x , y\right)+F_{141}\! \left(x , y\right)
F_{144}\! \left(x \right) = F_{145}\! \left(x \right) F_{9}\! \left(x \right)
F_{145}\! \left(x \right) = F_{105}\! \left(x \right)+F_{80}\! \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)*F_9(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_71(x))
Eq(F_4(x), F_5(x)*F_9(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_10(x, k_0) + F_50(x) + F_7(x, k_0))
Eq(F_7(x, k_0), F_8(x, k_0)*F_9(x))
Eq(F_8(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_9(x), x)
Eq(F_10(x, k_0), F_11(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0)*F_21(x, k_0)*F_25(x))
Eq(F_12(x, k_0), F_1(x) + F_13(x, k_0) + F_48(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0)*F_9(x))
Eq(F_14(x, k_0), F_1(x) + F_15(x, k_0) + F_45(x, k_0) + F_47(x, k_0))
Eq(F_15(x, k_0), F_16(x, k_0)*F_9(x))
Eq(F_16(x, k_0), F_17(x, k_0) + F_28(x, k_0))
Eq(F_17(x, k_0), F_18(x, k_0) + F_22(x, k_0))
Eq(F_18(x, k_0), F_1(x) + F_19(x, k_0))
Eq(F_19(x, k_0), F_20(x, k_0))
Eq(F_20(x, k_0), F_18(x, k_0)*F_21(x, k_0))
Eq(F_21(x, k_0), k_0*x)
Eq(F_22(x, k_0), F_23(x) + F_26(x, k_0))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_25(x)*F_9(x))
Eq(F_25(x), F_1(x) + F_23(x))
Eq(F_26(x, k_0), F_27(x, k_0))
Eq(F_27(x, k_0), F_21(x, k_0)*F_22(x, k_0))
Eq(F_28(x, k_0), F_29(x, k_0) + F_35(x, k_0))
Eq(F_29(x, k_0), F_23(x) + F_30(x, k_0))
Eq(F_30(x, k_0), F_31(x) + F_32(x, k_0) + F_34(x, k_0))
Eq(F_31(x), 0)
Eq(F_32(x, k_0), F_33(x, k_0)*F_9(x))
Eq(F_33(x, k_0), F_19(x, k_0) + F_30(x, k_0))
Eq(F_34(x, k_0), F_21(x, k_0)*F_29(x, k_0))
Eq(F_35(x, k_0), F_36(x) + F_41(x, k_0))
Eq(F_36(x), F_31(x) + F_37(x) + F_39(x))
Eq(F_37(x), F_38(x)*F_9(x))
Eq(F_38(x), F_23(x) + F_36(x))
Eq(F_39(x), F_40(x)*F_9(x))
Eq(F_40(x), F_23(x) + F_36(x))
Eq(F_41(x, k_0), 2*F_31(x) + F_42(x, k_0) + F_44(x, k_0))
Eq(F_42(x, k_0), F_43(x, k_0)*F_9(x))
Eq(F_43(x, k_0), F_26(x, k_0) + F_41(x, k_0))
Eq(F_44(x, k_0), F_21(x, k_0)*F_35(x, k_0))
Eq(F_45(x, k_0), F_46(x, k_0)*F_9(x))
Eq(F_46(x, k_0), (k_0*F_14(x, k_0) - F_14(x, 1))/(k_0 - 1))
Eq(F_47(x, k_0), F_14(x, k_0)*F_21(x, k_0))
Eq(F_48(x, k_0), F_21(x, k_0)*F_49(x, k_0))
Eq(F_49(x, k_0), F_18(x, k_0) + F_29(x, k_0))
Eq(F_50(x), F_51(x)*F_9(x))
Eq(F_51(x), F_52(x) + F_60(x))
Eq(F_52(x), F_25(x) + F_53(x))
Eq(F_53(x), F_23(x) + F_54(x))
Eq(F_54(x), F_31(x) + F_55(x) + F_57(x))
Eq(F_55(x), F_56(x)*F_9(x))
Eq(F_56(x), F_23(x) + F_54(x))
Eq(F_57(x), F_58(x)*F_9(x))
Eq(F_58(x), F_23(x) + F_59(x))
Eq(F_59(x), F_57(x))
Eq(F_60(x), F_61(x) + F_65(x))
Eq(F_61(x), F_23(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_64(x)*F_9(x))
Eq(F_64(x), F_23(x) + F_62(x))
Eq(F_65(x), F_36(x) + F_66(x))
Eq(F_66(x), 2*F_31(x) + F_67(x) + F_69(x))
Eq(F_67(x), F_68(x)*F_9(x))
Eq(F_68(x), F_54(x) + F_66(x))
Eq(F_69(x), F_70(x)*F_9(x))
Eq(F_70(x), F_62(x) + F_66(x))
Eq(F_71(x), F_72(x)*F_9(x))
Eq(F_72(x), F_1(x) + F_144(x) + F_73(x) + F_95(x))
Eq(F_73(x), F_74(x, 1))
Eq(F_74(x, k_0), F_21(x, k_0)*F_75(x, k_0))
Eq(F_75(x, k_0), F_1(x) + F_74(x, k_0) + F_76(x, k_0) + F_78(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0)*F_9(x))
Eq(F_77(x, k_0), (-k_0*F_75(x, k_0) + F_75(x, 1))/(1 - k_0))
Eq(F_78(x, k_0), F_79(x, k_0)*F_9(x))
Eq(F_79(x, k_0), F_80(x) + F_81(x, k_0))
Eq(F_80(x), F_25(x) + F_40(x))
Eq(F_81(x, k_0), F_82(x, k_0) + F_87(x, k_0))
Eq(F_82(x, k_0), F_19(x, k_0) + F_83(x, k_0))
Eq(F_83(x, k_0), F_31(x) + F_84(x, k_0) + F_86(x, k_0))
Eq(F_84(x, k_0), F_21(x, k_0)*F_85(x, k_0))
Eq(F_85(x, k_0), F_23(x) + F_83(x, k_0))
Eq(F_86(x, k_0), F_82(x, k_0)*F_9(x))
Eq(F_87(x, k_0), F_88(x, k_0) + F_91(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0))
Eq(F_89(x, k_0), F_9(x)*F_90(x, k_0))
Eq(F_90(x, k_0), F_19(x, k_0) + F_88(x, k_0))
Eq(F_91(x, k_0), 2*F_31(x) + F_92(x, k_0) + F_94(x, k_0))
Eq(F_92(x, k_0), F_9(x)*F_93(x, k_0))
Eq(F_93(x, k_0), F_83(x, k_0) + F_91(x, k_0))
Eq(F_94(x, k_0), F_87(x, k_0)*F_9(x))
Eq(F_95(x), F_9(x)*F_96(x))
Eq(F_96(x), F_97(x, 1))
Eq(F_97(x, k_0), F_1(x) + F_100(x, k_0) + F_102(x, k_0) + F_74(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_9(x)*F_99(x, k_0))
Eq(F_99(x, k_0), (k_0*F_75(x, k_0) - F_75(x, 1))/(k_0 - 1))
Eq(F_100(x, k_0), F_101(x, k_0)*F_9(x))
Eq(F_101(x, k_0), (-k_0*F_97(x, k_0) + F_97(x, 1))/(1 - k_0))
Eq(F_102(x, k_0), F_103(x, k_0)*F_9(x))
Eq(F_103(x, k_0), F_104(x, k_0) + F_79(x, k_0))
Eq(F_104(x, k_0), F_105(x) + F_123(x, k_0))
Eq(F_105(x), F_106(x) + F_40(x))
Eq(F_106(x), F_107(x) + F_36(x))
Eq(F_107(x), F_108(x) + F_116(x) + F_118(x) + F_31(x))
Eq(F_108(x), F_109(x)*F_9(x))
Eq(F_109(x), F_110(x) + F_62(x))
Eq(F_110(x), F_108(x) + F_111(x) + 2*F_31(x))
Eq(F_111(x), F_112(x)*F_9(x))
Eq(F_112(x), F_113(x) + F_62(x))
Eq(F_113(x), F_111(x) + F_114(x) + 2*F_31(x))
Eq(F_114(x), F_115(x)*F_9(x))
Eq(F_115(x), F_113(x) + F_62(x))
Eq(F_116(x), F_117(x)*F_9(x))
Eq(F_117(x), F_107(x) + F_36(x))
Eq(F_118(x), F_119(x)*F_9(x))
Eq(F_119(x), F_120(x) + F_59(x))
Eq(F_120(x), F_118(x) + F_121(x) + 2*F_31(x))
Eq(F_121(x), F_122(x)*F_9(x))
Eq(F_122(x), F_120(x) + F_36(x))
Eq(F_123(x, k_0), F_124(x, k_0) + F_129(x, k_0))
Eq(F_124(x, k_0), F_125(x, k_0) + F_26(x, k_0))
Eq(F_125(x, k_0), F_126(x, k_0) + F_128(x, k_0) + 2*F_31(x))
Eq(F_126(x, k_0), F_127(x, k_0)*F_21(x, k_0))
Eq(F_127(x, k_0), F_125(x, k_0) + F_36(x))
Eq(F_128(x, k_0), F_124(x, k_0)*F_9(x))
Eq(F_129(x, k_0), F_130(x, k_0) + F_133(x, k_0))
Eq(F_130(x, k_0), F_131(x, k_0))
Eq(F_131(x, k_0), F_132(x, k_0)*F_9(x))
Eq(F_132(x, k_0), F_130(x, k_0) + F_26(x, k_0))
Eq(F_133(x, k_0), F_134(x, k_0) + F_136(x, k_0) + 3*F_31(x))
Eq(F_134(x, k_0), F_135(x, k_0)*F_9(x))
Eq(F_135(x, k_0), F_125(x, k_0) + F_133(x, k_0))
Eq(F_136(x, k_0), F_137(x, k_0)*F_9(x))
Eq(F_137(x, k_0), F_138(x, k_0) + F_141(x, k_0))
Eq(F_138(x, k_0), F_139(x, k_0))
Eq(F_139(x, k_0), F_140(x, k_0)*F_9(x))
Eq(F_140(x, k_0), F_138(x, k_0) + F_26(x, k_0))
Eq(F_141(x, k_0), F_136(x, k_0) + F_142(x, k_0) + 3*F_31(x))
Eq(F_142(x, k_0), F_143(x, k_0)*F_9(x))
Eq(F_143(x, k_0), F_125(x, k_0) + F_141(x, k_0))
Eq(F_144(x), F_145(x)*F_9(x))
Eq(F_145(x), F_105(x) + F_80(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.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:
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{"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 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, 2, 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_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"}}, {"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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 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{"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, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [2, 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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": 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