0231_1032_2103_3102
Counting sequence:
1, 1, 2, 6, 20, 62, 176, 473, 1239, 3218, 8353, 21726, 56637, 147901, 386660, 1011522, 2647166, 6929018, 18138674, 47485493, 124315953, 325460126, 852061747, 2230721946, 5840100375, 15289574857, 40028619206, 104796277038, 274360205384, 718284331718, 1880492781428, 4923194003201, 12889089217707, 33744073638266, 88343131684165, 231285321399942, 605512832499921, 1585253176082533, 4150246695728744, 10865486911083018, 28446214037497778, 74473155201385826, 194973251566633142, 510446599498484861, 1336366546928790405, 3498653041287852902, 9159592576934732311, 23980124689516305378, 62780781491614142379, 164362219785326077393, 430305877864364042378, 1126555413807765999126, 2949360363558933901052, 7721525676869035646606, 20215216667048172977720, 52924124324275483221737, 138557156305778276618751, 362747344593059346561698, 949684877473399762989289, 2486307287827139942324718, 6509236986008020063898853, 17041403670196920249281101, 44614974024582740683848812, 116803518403551301802164626, 305795581186071164722539110, 800583225154662192365341322, 2095954094277915412373367866, 5487279057679084044754639493, 14365883078759336721890421849, 37610370178598926120916491118, 98465227457037441640858910203, 257785312192513398801660091626, 674890709120502754764121210047, 1766886815168994865490703376921, 4625769736386481841707988751950, 12110422393990450659633262702782, 31705497445584870137191799172656, 83006069942764159751942134623638, 217312712382707609118634604498684, 568932067205358667603961678664593, 1489483489233368393693250431278803, 3899518400494746513475789614946826, 10209071712250871146734118413327757, 26727696736257866926726565624793366, 69974018496522729633445578460799865, 183194358753310321973610169757344117, 479609057763408236287384930810960496, 1255632814536914386888544622675255258, 3287289385847334924378248937214512794, 8606235343005090386246202188967980018, 22531416643167936234360357629689113278, 58988014586498718316834870700099034701, 154432627116328218716144254470607654317, 404309866762485937831597892711723580086, 1058496973171129594778649423664562725855, 2771181052750902846504350378281964225202, 7255046185081578944734401711181329565011, 18993957502493833987698854755262024072353, 49726826322399923018362162554604742241554, 130186521464705935067387632908552202228518, 340832738071717882183800736171051864006628
Generating function in Maple syntax:
-(2*x^6+4*x^5-9*x^4+15*x^3-14*x^2+6*x-1)/(x^2-3*x+1)/(x-1)^4
Generating function in latex syntax:
-\frac{2 x^{6}+4 x^{5}-9 x^{4}+15 x^{3}-14 x^{2}+6 x -1}{\left(x^{2}-3 x +1\right) \left(x -1\right)^{4}}
Generating function in sympy syntax:
(-2*x**6 - 4*x**5 + 9*x**4 - 15*x**3 + 14*x**2 - 6*x + 1)/((x - 1)**4*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
(x^2-3*x+1)*(x-1)^4*F(x)+2*x^6+4*x^5-9*x^4+15*x^3-14*x^2+6*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}-3 x +1\right) \left(x -1\right)^{4} F \! \left(x \right)+2 x^{6}+4 x^{5}-9 x^{4}+15 x^{3}-14 x^{2}+6 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/10*(-49*5^(1/2)+115)*(3/2-1/2*5^(1/2))^(-n)+1/10*(49*5^(1/2)+115)*(3/2+1/2*5^(1/2))^(-n)+1/2*n^3-5*n^2+31/2*n-20)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(-49 \sqrt{5}+115\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{10}+\frac{\left(49 \sqrt{5}+115\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{10}+\frac{n^{3}}{2}-5 n^{2}\\+\frac{31 n}{2}-20 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 62
a(6) = 176
a(n+2) = -1/2*n^3+7/2*n^2-a(n)+3*a(n+1)-4*n+2, 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) = 20
a \! \left(5\right) = 62
a \! \left(6\right) = 176
a \! \left(n +2\right) = -\frac{n^{3}}{2}+\frac{7 n^{2}}{2}-a \! \left(n \right)+3 a \! \left(n +1\right)-4 n +2, \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15883/
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[24,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[6,x]
F[10,x] = F[11,x]+F[16,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[4,x]
F[13,x] = F[14,x]+F[15,x]
F[14,x] = F[1,x]+F[11,x]
F[15,x] = F[11,x]
F[16,x] = F[17,x]
F[17,x] = F[18,x]*F[4,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]+F[23,x]
F[20,x] = F[21,x]
F[21,x] = F[22,x]*F[4,x]
F[22,x] = F[1,x]+F[20,x]
F[23,x] = F[17,x]
F[24,x] = F[25,x]+F[33,x]
F[25,x] = F[26,x]
F[26,x] = F[27,x]*F[4,x]
F[27,x] = F[14,x]+F[28,x]
F[28,x] = F[25,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[28,x]+F[32,x]
F[32,x] = F[29,x]
F[33,x] = F[34,x]+F[35,x]+F[56,x]
F[34,x] = 0
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[37,x]+F[43,x]
F[37,x] = F[20,x]+F[38,x]
F[38,x] = F[34,x]+F[39,x]+F[41,x]
F[39,x] = F[4,x]*F[40,x]
F[40,x] = F[37,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[11,x]+F[23,x]
F[43,x] = F[44,x]+F[47,x]
F[44,x] = F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[25,x]+F[44,x]
F[47,x] = 2*F[34,x]+F[48,x]+F[50,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[43,x]
F[50,x] = F[4,x]*F[51,x]
F[51,x] = F[29,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[44,x]+F[52,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[24,x]+F[58,x]
F[58,x] = F[59,x]+F[77,x]
F[59,x] = F[34,x]+F[60,x]+F[74,x]
F[60,x] = F[4,x]*F[61,x]
F[61,x] = F[62,x]+F[68,x]
F[62,x] = F[20,x]+F[63,x]
F[63,x] = F[34,x]+F[64,x]+F[66,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[62,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[11,x]
F[68,x] = F[44,x]+F[69,x]
F[69,x] = 2*F[34,x]+F[70,x]+F[72,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[68,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[29,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[28,x]+F[76,x]
F[76,x] = F[59,x]
F[77,x] = 2*F[34,x]+F[78,x]+F[94,x]
F[78,x] = F[4,x]*F[79,x]
F[79,x] = F[80,x]+F[87,x]
F[80,x] = F[81,x]+F[84,x]
F[81,x] = F[82,x]
F[82,x] = F[4,x]*F[83,x]
F[83,x] = F[20,x]+F[81,x]
F[84,x] = F[85,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[80,x]
F[87,x] = F[88,x]+F[91,x]
F[88,x] = F[89,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[44,x]+F[88,x]
F[91,x] = F[92,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[87,x]
F[94,x] = F[4,x]*F[95,x]
F[95,x] = F[55,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{5}\! \left(x \right)
F_{4}\! \left(x \right) = x
F_{5}\! \left(x \right) = F_{24}\! \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_{6}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{16}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \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_{11}\! \left(x \right)
F_{15}\! \left(x \right) = F_{11}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{20}\! \left(x \right)
F_{23}\! \left(x \right) = F_{17}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{33}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{14}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{25}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{28}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{29}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{35}\! \left(x \right)+F_{56}\! \left(x \right)
F_{34}\! \left(x \right) = 0
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{43}\! \left(x \right)
F_{37}\! \left(x \right) = F_{20}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{34}\! \left(x \right)+F_{39}\! \left(x \right)+F_{41}\! \left(x \right)
F_{39}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{37}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{11}\! \left(x \right)+F_{23}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{47}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{25}\! \left(x \right)+F_{44}\! \left(x \right)
F_{47}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{48}\! \left(x \right)+F_{50}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{43}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{29}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{44}\! \left(x \right)+F_{52}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{24}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{77}\! \left(x \right)
F_{59}\! \left(x \right) = F_{34}\! \left(x \right)+F_{60}\! \left(x \right)+F_{74}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{68}\! \left(x \right)
F_{62}\! \left(x \right) = F_{20}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{34}\! \left(x \right)+F_{64}\! \left(x \right)+F_{66}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{62}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{11}\! \left(x \right)
F_{68}\! \left(x \right) = F_{44}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{70}\! \left(x \right)+F_{72}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{68}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{29}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{28}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{59}\! \left(x \right)
F_{77}\! \left(x \right) = 2 F_{34}\! \left(x \right)+F_{78}\! \left(x \right)+F_{94}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{87}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{84}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{4}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{20}\! \left(x \right)+F_{81}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{80}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{91}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{44}\! \left(x \right)+F_{88}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{87}\! \left(x \right)
F_{94}\! \left(x \right) = F_{4}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{55}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_24(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_6(x))
Eq(F_10(x), F_11(x) + F_16(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_15(x))
Eq(F_14(x), F_1(x) + F_11(x))
Eq(F_15(x), F_11(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_18(x)*F_4(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x) + F_23(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_22(x)*F_4(x))
Eq(F_22(x), F_1(x) + F_20(x))
Eq(F_23(x), F_17(x))
Eq(F_24(x), F_25(x) + F_33(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_27(x)*F_4(x))
Eq(F_27(x), F_14(x) + F_28(x))
Eq(F_28(x), F_25(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_28(x) + F_32(x))
Eq(F_32(x), F_29(x))
Eq(F_33(x), F_34(x) + F_35(x) + F_56(x))
Eq(F_34(x), 0)
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_37(x) + F_43(x))
Eq(F_37(x), F_20(x) + F_38(x))
Eq(F_38(x), F_34(x) + F_39(x) + F_41(x))
Eq(F_39(x), F_4(x)*F_40(x))
Eq(F_40(x), F_37(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_11(x) + F_23(x))
Eq(F_43(x), F_44(x) + F_47(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_25(x) + F_44(x))
Eq(F_47(x), 2*F_34(x) + F_48(x) + F_50(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_43(x))
Eq(F_50(x), F_4(x)*F_51(x))
Eq(F_51(x), F_29(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_44(x) + F_52(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_24(x) + F_58(x))
Eq(F_58(x), F_59(x) + F_77(x))
Eq(F_59(x), F_34(x) + F_60(x) + F_74(x))
Eq(F_60(x), F_4(x)*F_61(x))
Eq(F_61(x), F_62(x) + F_68(x))
Eq(F_62(x), F_20(x) + F_63(x))
Eq(F_63(x), F_34(x) + F_64(x) + F_66(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_62(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_11(x))
Eq(F_68(x), F_44(x) + F_69(x))
Eq(F_69(x), 2*F_34(x) + F_70(x) + F_72(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_68(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_29(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_28(x) + F_76(x))
Eq(F_76(x), F_59(x))
Eq(F_77(x), 2*F_34(x) + F_78(x) + F_94(x))
Eq(F_78(x), F_4(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_87(x))
Eq(F_80(x), F_81(x) + F_84(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_4(x)*F_83(x))
Eq(F_83(x), F_20(x) + F_81(x))
Eq(F_84(x), F_85(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_80(x))
Eq(F_87(x), F_88(x) + F_91(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_44(x) + F_88(x))
Eq(F_91(x), F_92(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_87(x))
Eq(F_94(x), F_4(x)*F_95(x))
Eq(F_95(x), F_55(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
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"ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": 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