0132_0213_1302_2310
Counting sequence:
1, 1, 2, 6, 20, 61, 165, 406, 936, 2070, 4467, 9515, 20148, 42575, 89929, 189948, 401104, 846396, 1784007, 3754761, 7889324, 16547181, 34643741, 72402850, 151058424, 314650930, 654406779, 1359069975, 2818711140, 5838637019, 12079792401, 24964729784, 51539880352, 106300759224, 219043702543, 450971994837, 927713430108, 1906966046745, 3917010822821, 8040179517630, 16492675256648, 33809983505230, 69269233623555, 141837001191619, 290271071089428, 593736280517799, 1213860838760793, 2480498234152244, 5066549582892144, 10344205396446068, 21110623255877335, 43065671439577953, 87820192736863756, 179018085191431173, 364791569820803757, 743093938520291226, 1513209474801039512, 3080462145126394794, 6269010681305159435, 12754194144719159599, 25940733853660491972, 52746158835770240179, 107221699928444353569, 217902164370702296688, 442721857769038132032, 899278773593350253168, 1826227663297255986207, 3707795558815631063213, 7526271582073509109948, 15273904093031521703217, 30990530043832060649269, 62866503803202166868022, 127503895037480436816360, 258549564937113092644422, 524182679598530637127571, 1062532458645670192769115, 2153399116188558238483316, 4363466630171552199916543, 8840270055931975863999849, 17907213703041694675874668, 36267774588438875268385296, 73442243541588722392346028, 148697875812599388519639783, 301022529084042664534544057, 609298613085773104086640236, 1233104336006921758237147037, 2495222891684594616632617021, 5048474222710691433614388882, 10213005324104387267961610552, 20658124405574783337425522466, 41780476325881584277894498203, 84489407681227203761917073991, 170835725421382477936133904164, 345385270960621096696913464971, 698198182156954475043167047985, 1411251644785333513385065918504, 2852213850513516153367649975520, 5763848822912730559930393757992, 11646539889596857626251035830063, 23530764266736508265282632296837, 47536897508558602556126453326620
Generating function in Maple syntax:
(x^9-3*x^8-6*x^7+40*x^6-80*x^5+97*x^4-75*x^3+35*x^2-9*x+1)/(2*x-1)^2/(x-1)^6
Generating function in latex syntax:
\frac{x^{9}-3 x^{8}-6 x^{7}+40 x^{6}-80 x^{5}+97 x^{4}-75 x^{3}+35 x^{2}-9 x +1}{\left(2 x -1\right)^{2} \left(x -1\right)^{6}}
Generating function in sympy syntax:
(x**9 - 3*x**8 - 6*x**7 + 40*x**6 - 80*x**5 + 97*x**4 - 75*x**3 + 35*x**2 - 9*x + 1)/((x - 1)**6*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
-(2*x-1)^2*(x-1)^6*F(x)+x^9-3*x^8-6*x^7+40*x^6-80*x^5+97*x^4-75*x^3+35*x^2-9*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right)^{2} \left(x -1\right)^{6} F \! \left(x \right)+x^{9}-3 x^{8}-6 x^{7}+40 x^{6}-80 x^{5}+97 x^{4}-75 x^{3}+35 x^{2}-9 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/120*n*(n^4-25*n^2+45*2^n+24))
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{n \left(n^{4}-25 n^{2}+45 \,2^{n}+24\right)}{120} & \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) = 61
a(6) = 165
a(7) = 406
a(8) = 936
a(9) = 2070
a(n+2) = -4*a(n)+4*a(n+1)+1/120*(n+1)*(n^4-11*n^3-14*n^2+204*n-120), 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) = 20
a \! \left(5\right) = 61
a \! \left(6\right) = 165
a \! \left(7\right) = 406
a \! \left(8\right) = 936
a \! \left(9\right) = 2070
a \! \left(n +2\right) = -4 a \! \left(n \right)+4 a \! \left(n +1\right)+\frac{\left(n +1\right) \left(n^{4}-11 n^{3}-14 n^{2}+204 n -120\right)}{120}, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15287/
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[12,x]*F[4,x]
F[4,x] = F[25,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+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[9,x]
F[12,x] = x
F[13,x] = F[14,x]+F[23,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[9,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[19,x]
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[1,x]+F[18,x]
F[21,x] = F[22,x]
F[22,x] = F[12,x]*F[17,x]
F[23,x] = F[24,x]
F[24,x] = F[12,x]*F[13,x]
F[25,x] = F[26,x]+F[48,x]
F[26,x] = F[27,x]
F[27,x] = F[12,x]*F[28,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = F[1,x]+F[14,x]
F[30,x] = F[18,x]+F[31,x]
F[31,x] = F[32,x]+F[33,x]+F[35,x]
F[32,x] = 0
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[14,x]+F[31,x]
F[35,x] = F[12,x]*F[36,x]
F[36,x] = F[37,x]+F[42,x]
F[37,x] = F[18,x]+F[38,x]
F[38,x] = F[32,x]+F[39,x]+F[41,x]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[10,x]+F[38,x]
F[41,x] = F[12,x]*F[37,x]
F[42,x] = F[43,x]+F[46,x]
F[43,x] = F[44,x]
F[44,x] = F[12,x]*F[45,x]
F[45,x] = F[18,x]+F[43,x]
F[46,x] = F[47,x]
F[47,x] = F[12,x]*F[42,x]
F[48,x] = F[32,x]+F[49,x]+F[77,x]
F[49,x] = F[12,x]*F[50,x]
F[50,x] = F[51,x]+F[58,x]
F[51,x] = F[52,x]+F[6,x]
F[52,x] = F[53,x]
F[53,x] = F[12,x]*F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[10,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[12,x]*F[55,x]
F[58,x] = F[59,x]+F[67,x]
F[59,x] = F[32,x]+F[60,x]+F[62,x]
F[60,x] = F[12,x]*F[61,x]
F[61,x] = F[59,x]+F[6,x]
F[62,x] = F[12,x]*F[63,x]
F[63,x] = F[37,x]+F[64,x]
F[64,x] = F[31,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[12,x]*F[64,x]
F[67,x] = 2*F[32,x]+F[68,x]+F[70,x]
F[68,x] = F[12,x]*F[69,x]
F[69,x] = F[52,x]+F[67,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[38,x]+F[73,x]
F[73,x] = 2*F[32,x]+F[74,x]+F[76,x]
F[74,x] = F[12,x]*F[75,x]
F[75,x] = F[56,x]+F[73,x]
F[76,x] = F[12,x]*F[72,x]
F[77,x] = F[12,x]*F[78,x]
F[78,x] = F[79,x]+F[90,x]
F[79,x] = F[26,x]+F[80,x]
F[80,x] = F[32,x]+F[81,x]+F[89,x]
F[81,x] = F[12,x]*F[82,x]
F[82,x] = F[83,x]+F[85,x]
F[83,x] = F[10,x]+F[84,x]
F[84,x] = F[53,x]
F[85,x] = F[38,x]+F[86,x]
F[86,x] = 2*F[32,x]+F[70,x]+F[87,x]
F[87,x] = F[12,x]*F[88,x]
F[88,x] = F[84,x]+F[86,x]
F[89,x] = F[12,x]*F[79,x]
F[90,x] = F[100,x]+F[91,x]
F[91,x] = F[32,x]+F[35,x]+F[92,x]
F[92,x] = F[12,x]*F[93,x]
F[93,x] = F[94,x]+F[96,x]
F[94,x] = F[14,x]+F[95,x]
F[95,x] = F[53,x]
F[96,x] = F[31,x]+F[97,x]
F[97,x] = 2*F[32,x]+F[70,x]+F[98,x]
F[98,x] = F[12,x]*F[99,x]
F[99,x] = F[95,x]+F[97,x]
F[100,x] = F[101,x]
F[101,x] = F[12,x]*F[90,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{25}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \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_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{23}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{9}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{48}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{30}\! \left(x \right) = F_{18}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = 0
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{14}\! \left(x \right)+F_{31}\! \left(x \right)
F_{35}\! \left(x \right) = F_{12}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{42}\! \left(x \right)
F_{37}\! \left(x \right) = F_{18}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{32}\! \left(x \right)+F_{39}\! \left(x \right)+F_{41}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{10}\! \left(x \right)+F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{18}\! \left(x \right)+F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{48}\! \left(x \right) = F_{32}\! \left(x \right)+F_{49}\! \left(x \right)+F_{77}\! \left(x \right)
F_{49}\! \left(x \right) = F_{12}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{58}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{6}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{10}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{67}\! \left(x \right)
F_{59}\! \left(x \right) = F_{32}\! \left(x \right)+F_{60}\! \left(x \right)+F_{62}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{59}\! \left(x \right)+F_{6}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{37}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{31}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{67}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{68}\! \left(x \right)+F_{70}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{52}\! \left(x \right)+F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{38}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{74}\! \left(x \right)+F_{76}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{56}\! \left(x \right)+F_{73}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{90}\! \left(x \right)
F_{79}\! \left(x \right) = F_{26}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{32}\! \left(x \right)+F_{81}\! \left(x \right)+F_{89}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{85}\! \left(x \right)
F_{83}\! \left(x \right) = F_{10}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{53}\! \left(x \right)
F_{85}\! \left(x \right) = F_{38}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{70}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{84}\! \left(x \right)+F_{86}\! \left(x \right)
F_{89}\! \left(x \right) = F_{12}\! \left(x \right) F_{79}\! \left(x \right)
F_{90}\! \left(x \right) = F_{100}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{96}\! \left(x \right)
F_{94}\! \left(x \right) = F_{14}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{53}\! \left(x \right)
F_{96}\! \left(x \right) = F_{31}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{70}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{95}\! \left(x \right)+F_{97}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{12}\! \left(x \right) F_{90}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_25(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + 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_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_23(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_9(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_1(x) + F_18(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_12(x)*F_17(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_12(x)*F_13(x))
Eq(F_25(x), F_26(x) + F_48(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_12(x)*F_28(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), F_1(x) + F_14(x))
Eq(F_30(x), F_18(x) + F_31(x))
Eq(F_31(x), F_32(x) + F_33(x) + F_35(x))
Eq(F_32(x), 0)
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_14(x) + F_31(x))
Eq(F_35(x), F_12(x)*F_36(x))
Eq(F_36(x), F_37(x) + F_42(x))
Eq(F_37(x), F_18(x) + F_38(x))
Eq(F_38(x), F_32(x) + F_39(x) + F_41(x))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_10(x) + F_38(x))
Eq(F_41(x), F_12(x)*F_37(x))
Eq(F_42(x), F_43(x) + F_46(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_12(x)*F_45(x))
Eq(F_45(x), F_18(x) + F_43(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_12(x)*F_42(x))
Eq(F_48(x), F_32(x) + F_49(x) + F_77(x))
Eq(F_49(x), F_12(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_58(x))
Eq(F_51(x), F_52(x) + F_6(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_12(x)*F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_10(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_12(x)*F_55(x))
Eq(F_58(x), F_59(x) + F_67(x))
Eq(F_59(x), F_32(x) + F_60(x) + F_62(x))
Eq(F_60(x), F_12(x)*F_61(x))
Eq(F_61(x), F_59(x) + F_6(x))
Eq(F_62(x), F_12(x)*F_63(x))
Eq(F_63(x), F_37(x) + F_64(x))
Eq(F_64(x), F_31(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_12(x)*F_64(x))
Eq(F_67(x), 2*F_32(x) + F_68(x) + F_70(x))
Eq(F_68(x), F_12(x)*F_69(x))
Eq(F_69(x), F_52(x) + F_67(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_38(x) + F_73(x))
Eq(F_73(x), 2*F_32(x) + F_74(x) + F_76(x))
Eq(F_74(x), F_12(x)*F_75(x))
Eq(F_75(x), F_56(x) + F_73(x))
Eq(F_76(x), F_12(x)*F_72(x))
Eq(F_77(x), F_12(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_90(x))
Eq(F_79(x), F_26(x) + F_80(x))
Eq(F_80(x), F_32(x) + F_81(x) + F_89(x))
Eq(F_81(x), F_12(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_85(x))
Eq(F_83(x), F_10(x) + F_84(x))
Eq(F_84(x), F_53(x))
Eq(F_85(x), F_38(x) + F_86(x))
Eq(F_86(x), 2*F_32(x) + F_70(x) + F_87(x))
Eq(F_87(x), F_12(x)*F_88(x))
Eq(F_88(x), F_84(x) + F_86(x))
Eq(F_89(x), F_12(x)*F_79(x))
Eq(F_90(x), F_100(x) + F_91(x))
Eq(F_91(x), F_32(x) + F_35(x) + F_92(x))
Eq(F_92(x), F_12(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_96(x))
Eq(F_94(x), F_14(x) + F_95(x))
Eq(F_95(x), F_53(x))
Eq(F_96(x), F_31(x) + F_97(x))
Eq(F_97(x), 2*F_32(x) + F_70(x) + F_98(x))
Eq(F_98(x), F_12(x)*F_99(x))
Eq(F_99(x), F_95(x) + F_97(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_12(x)*F_90(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:
{"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, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "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, 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, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "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, 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, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 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0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 1, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 0], "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": 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