0213_1320_2130_2301
Counting sequence:
1, 1, 2, 6, 20, 63, 182, 492, 1264, 3121, 7470, 17446, 39960, 90115, 200678, 442304, 966544, 2096981, 4521742, 9699002, 20708952, 44039655, 93322598, 197131476, 415235120, 872414073, 1828715182, 3825203662, 7985952984, 16642996171, 34628171430, 71940699496, 149250110480, 309237641885, 639950123278, 1322849922914, 2731599195544, 5634997087151, 11613591562662, 23914377897852, 49203145336112, 101155069747905, 207807697641518, 426610511568246, 875211255700120, 1794402976520083, 3676766883271782, 7529455626998032, 15410754974895504, 31525197391579621, 64457769666725390, 131730289100571146, 269090077735370200, 549439154539182455, 1121396307215234278, 2287828610704191524, 4665729213955812144, 9511602413006464521, 19383492796202590382, 39487561532784483102, 80416274946327549272, 163714853654172241755, 333194314831378745638, 677917844708825989816, 1378894119509788949520, 2803905099203851810093, 5700043918776251411982, 11584555278289598375602, 23538045438053387820824, 47813960639055157745471, 97103660804007079661350, 197158800659807687624396, 400220559423202431811120, 812247035053578976703825, 1648105902521506179525678, 3343435469871708811240134, 6781318269400810526808344, 13751531198116406862221091, 27880851714862385341596902, 56517282066983913917446752, 114545721408486114303340432, 232113757366008801543513205, 470272143830090748960626958, 952633545856327789668388186, 1929445608104948162830975320, 3907248248994481492650276103, 7911210563558133319277127782, 16015849258254607306507328372, 32418554778785895948920720944, 65610822082125154569653485721, 132769069213357034482930971310, 268632988524927519653109851246, 543455677246281940680715425240, 1099290754885417684110422197995, 2223340310556542973718826989478, 4496198222684501158433619060744, 9091431648511832738859168176144, 18380933703309326321702196348861, 37158008219189974331372112574222, 75108298063522592038679664780802, 151801159377330470829230208701592
Generating function in Maple syntax:
-(4*x^8-4*x^7+8*x^5-21*x^4+28*x^3-20*x^2+7*x-1)/(2*x-1)^2/(x-1)^4
Generating function in latex syntax:
-\frac{4 x^{8}-4 x^{7}+8 x^{5}-21 x^{4}+28 x^{3}-20 x^{2}+7 x -1}{\left(2 x -1\right)^{2} \left(x -1\right)^{4}}
Generating function in sympy syntax:
(-4*x**8 + 4*x**7 - 8*x**5 + 21*x**4 - 28*x**3 + 20*x**2 - 7*x + 1)/((x - 1)**4*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^2*(x-1)^4*F(x)+4*x^8-4*x^7+8*x^5-21*x^4+28*x^3-20*x^2+7*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{2} \left(x -1\right)^{4} F \! \left(x \right)+4 x^{8}-4 x^{7}+8 x^{5}-21 x^{4}+28 x^{3}-20 x^{2}+7 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,16+5/4*2^n*n-21/4*2^n-16/3*n+5/2*n^2-1/6*n^3)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ 16+\frac{5 \,2^{n} n}{4}-\frac{21 \,2^{n}}{4}-\frac{16 n}{3}+\frac{5 n^{2}}{2}-\frac{n^{3}}{6} & \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) = 63
a(6) = 182
a(7) = 492
a(8) = 1264
a(n+2) = -1/6*n^3+7/2*n^2-4*a(n)+4*a(n+1)-46/3*n+26, n >= 9
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) = 63
a \! \left(6\right) = 182
a \! \left(7\right) = 492
a \! \left(8\right) = 1264
a \! \left(n +2\right) = -\frac{n^{3}}{6}+\frac{7 n^{2}}{2}-4 a \! \left(n \right)+4 a \! \left(n +1\right)-\frac{46 n}{3}+26, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/21398/
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[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[12,x]*F[7,x]
F[7,x] = F[8,x]+F[90,x]
F[8,x] = F[74,x]+F[9,x]
F[9,x] = F[10,x]+F[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[10,x]*F[12,x]
F[12,x] = x
F[13,x] = F[14,x]+F[24,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[19,x]
F[17,x] = F[1,x]+F[18,x]
F[18,x] = F[12,x]*F[17,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]*F[17,x]*F[21,x]
F[21,x] = F[16,x]+F[22,x]
F[22,x] = F[10,x]*F[23,x]
F[23,x] = F[18,x]
F[24,x] = F[25,x]+F[26,x]+F[32,x]
F[25,x] = 0
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[28,x]+F[35,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = F[11,x]
F[30,x] = F[25,x]+F[31,x]+F[32,x]
F[31,x] = F[12,x]*F[28,x]
F[32,x] = F[12,x]*F[33,x]
F[33,x] = F[23,x]+F[34,x]
F[34,x] = F[32,x]
F[35,x] = F[36,x]+F[53,x]
F[36,x] = F[25,x]+F[37,x]+F[42,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[39,x]+F[45,x]
F[39,x] = F[29,x]+F[40,x]
F[40,x] = F[25,x]+F[41,x]+F[42,x]
F[41,x] = F[12,x]*F[39,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[12,x]+F[44,x]
F[44,x] = F[42,x]
F[45,x] = F[36,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[49,x]+F[52,x]
F[49,x] = F[25,x]+F[42,x]+F[50,x]
F[50,x] = F[12,x]*F[51,x]
F[51,x] = F[29,x]+F[49,x]
F[52,x] = F[47,x]
F[53,x] = F[25,x]+F[54,x]+F[59,x]+F[71,x]
F[54,x] = F[12,x]*F[55,x]
F[55,x] = F[56,x]+F[64,x]
F[56,x] = F[30,x]+F[57,x]
F[57,x] = 2*F[25,x]+F[58,x]+F[59,x]
F[58,x] = F[12,x]*F[56,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = F[61,x]+F[63,x]
F[61,x] = F[62,x]
F[62,x] = F[12,x]*F[23,x]
F[63,x] = F[59,x]
F[64,x] = F[53,x]+F[65,x]
F[65,x] = F[66,x]
F[66,x] = F[12,x]*F[67,x]
F[67,x] = F[68,x]+F[73,x]
F[68,x] = F[25,x]+F[59,x]+F[69,x]+F[71,x]
F[69,x] = F[12,x]*F[70,x]
F[70,x] = F[30,x]+F[68,x]
F[71,x] = F[12,x]*F[72,x]
F[72,x] = F[49,x]+F[68,x]
F[73,x] = F[66,x]
F[74,x] = F[75,x]
F[75,x] = F[76,x]*F[82,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[10,x]*F[17,x]
F[78,x] = F[79,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[81,x]
F[81,x] = F[12,x]*F[17,x]*F[21,x]
F[82,x] = F[83,x]
F[83,x] = F[84,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[86,x]+F[87,x]
F[86,x] = F[1,x]+F[83,x]
F[87,x] = F[88,x]
F[88,x] = F[12,x]*F[89,x]
F[89,x] = F[22,x]+F[85,x]
F[90,x] = F[91,x]
F[91,x] = F[92,x]+F[98,x]
F[92,x] = F[14,x]*F[93,x]
F[93,x] = F[94,x]+F[96,x]
F[94,x] = F[86,x]*F[95,x]
F[95,x] = F[1,x]+F[12,x]
F[96,x] = F[97,x]
F[97,x] = F[12,x]*F[29,x]
F[98,x] = F[23,x]*F[29,x]*F[99,x]
F[99,x] = F[10,x]+F[82,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_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{12}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{8}\! \left(x \right)+F_{90}\! \left(x \right)
F_{8}\! \left(x \right) = F_{74}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{24}\! \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_{19}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{16}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{10}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{18}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)+F_{32}\! \left(x \right)
F_{25}\! \left(x \right) = 0
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{35}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right)
F_{30}\! \left(x \right) = F_{25}\! \left(x \right)+F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{23}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{32}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{53}\! \left(x \right)
F_{36}\! \left(x \right) = F_{25}\! \left(x \right)+F_{37}\! \left(x \right)+F_{42}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{45}\! \left(x \right)
F_{39}\! \left(x \right) = F_{29}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{25}\! \left(x \right)+F_{41}\! \left(x \right)+F_{42}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{36}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{52}\! \left(x \right)
F_{49}\! \left(x \right) = F_{25}\! \left(x \right)+F_{42}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{29}\! \left(x \right)+F_{49}\! \left(x \right)
F_{52}\! \left(x \right) = F_{47}\! \left(x \right)
F_{53}\! \left(x \right) = F_{25}\! \left(x \right)+F_{54}\! \left(x \right)+F_{59}\! \left(x \right)+F_{71}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{64}\! \left(x \right)
F_{56}\! \left(x \right) = F_{30}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = 2 F_{25}\! \left(x \right)+F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{63}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{63}\! \left(x \right) = F_{59}\! \left(x \right)
F_{64}\! \left(x \right) = F_{53}\! \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_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{73}\! \left(x \right)
F_{68}\! \left(x \right) = F_{25}\! \left(x \right)+F_{59}\! \left(x \right)+F_{69}\! \left(x \right)+F_{71}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{30}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{49}\! \left(x \right)+F_{68}\! \left(x \right)
F_{73}\! \left(x \right) = F_{66}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right) F_{82}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{10}\! \left(x \right) F_{17}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right) F_{21}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{1}\! \left(x \right)+F_{83}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{22}\! \left(x \right)+F_{85}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{98}\! \left(x \right)
F_{92}\! \left(x \right) = F_{14}\! \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_{86}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{98}\! \left(x \right) = F_{23}\! \left(x \right) F_{29}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{10}\! \left(x \right)+F_{82}\! \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_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_12(x)*F_7(x))
Eq(F_7(x), F_8(x) + F_90(x))
Eq(F_8(x), F_74(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_10(x)*F_12(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_24(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_19(x))
Eq(F_17(x), F_1(x) + F_18(x))
Eq(F_18(x), F_12(x)*F_17(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)*F_17(x)*F_21(x))
Eq(F_21(x), F_16(x) + F_22(x))
Eq(F_22(x), F_10(x)*F_23(x))
Eq(F_23(x), F_18(x))
Eq(F_24(x), F_25(x) + F_26(x) + F_32(x))
Eq(F_25(x), 0)
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_35(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), F_11(x))
Eq(F_30(x), F_25(x) + F_31(x) + F_32(x))
Eq(F_31(x), F_12(x)*F_28(x))
Eq(F_32(x), F_12(x)*F_33(x))
Eq(F_33(x), F_23(x) + F_34(x))
Eq(F_34(x), F_32(x))
Eq(F_35(x), F_36(x) + F_53(x))
Eq(F_36(x), F_25(x) + F_37(x) + F_42(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_45(x))
Eq(F_39(x), F_29(x) + F_40(x))
Eq(F_40(x), F_25(x) + F_41(x) + F_42(x))
Eq(F_41(x), F_12(x)*F_39(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_12(x) + F_44(x))
Eq(F_44(x), F_42(x))
Eq(F_45(x), F_36(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_49(x) + F_52(x))
Eq(F_49(x), F_25(x) + F_42(x) + F_50(x))
Eq(F_50(x), F_12(x)*F_51(x))
Eq(F_51(x), F_29(x) + F_49(x))
Eq(F_52(x), F_47(x))
Eq(F_53(x), F_25(x) + F_54(x) + F_59(x) + F_71(x))
Eq(F_54(x), F_12(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_64(x))
Eq(F_56(x), F_30(x) + F_57(x))
Eq(F_57(x), 2*F_25(x) + F_58(x) + F_59(x))
Eq(F_58(x), F_12(x)*F_56(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_63(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_12(x)*F_23(x))
Eq(F_63(x), F_59(x))
Eq(F_64(x), F_53(x) + F_65(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_12(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_73(x))
Eq(F_68(x), F_25(x) + F_59(x) + F_69(x) + F_71(x))
Eq(F_69(x), F_12(x)*F_70(x))
Eq(F_70(x), F_30(x) + F_68(x))
Eq(F_71(x), F_12(x)*F_72(x))
Eq(F_72(x), F_49(x) + F_68(x))
Eq(F_73(x), F_66(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_76(x)*F_82(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_10(x)*F_17(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_12(x)*F_17(x)*F_21(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_87(x))
Eq(F_86(x), F_1(x) + F_83(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_12(x)*F_89(x))
Eq(F_89(x), F_22(x) + F_85(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_92(x) + F_98(x))
Eq(F_92(x), F_14(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_96(x))
Eq(F_94(x), F_86(x)*F_95(x))
Eq(F_95(x), F_1(x) + F_12(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_12(x)*F_29(x))
Eq(F_98(x), F_23(x)*F_29(x)*F_99(x))
Eq(F_99(x), F_10(x) + F_82(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": 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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 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, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": 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{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 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, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": 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"strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 1], [3, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[3, 2], [3, 2], [3, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [1, 0], [2, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [1, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [2, 1], [2, 1], [3, 2]]}, {"patt": [1, 3, 2, 0], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[3, 2], [3, 2], [3, 2], [3, 2]]}], "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", 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[[0, 1], [2, 0], [3, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [3, 1], [3, 1], [4, 3]]}, {"patt": [1, 3, 2, 0], "pos": [[4, 3], [4, 3], [4, 3], [4, 3]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [3, 1]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[4, 3], [4, 3], [4, 3], [4, 3]]}], "requirements": [[{"patt": [0], "pos": [[1, 2]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 0], [3, 1], [4, 3]], [[1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": 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