0132_0231_1032_1302_3120
Counting sequence:
1, 1, 2, 6, 19, 56, 156, 415, 1064, 2649, 6442, 15371, 36108, 83725, 192014, 436239, 983056, 2199569, 4890642, 10813459, 23789588, 52101141, 113639446, 246939671, 534773784, 1154482201, 2485125146, 5335154715, 11425284124, 24410849309, 52042924062, 110729625631, 235149459488, 498484641825, 1054951342114, 2229088026659, 4702989189156, 9908489551909, 20847771254822, 43808666419239, 91946659872808, 192758132244521, 403658206347306, 844424930132011, 1764716162580524, 3684463464677421, 7685586278154286, 16017685393440815, 33354784740212784, 69401173945221169, 144291109936300082, 299770850196848691, 622341173507260468, 1291125718171779125, 2676827028518338614, 5546182941106765879, 11484179049794764856, 23765495233634107449, 49152286333121593402, 101601207593478389819, 209903771432484077628, 433426428138136535101, 894522972386837397566, 1845250868123258585151, 3804640965202595020864, 7841019152831166283841, 16152430279541926133826, 33259479564898321563715, 68455867257536146047044, 140840891002772426588229, 289650775445387379474502, 595460898699344326164551, 1223683214873596815999048, 2513774708412548017815625, 5162136861586880924221514, 10596990387559483859533899, 21746497653614716209070156, 44612196163669538333786189, 91491128239116506370146382, 187572396699582307888005199, 384438410637452077556564048, 787690729342656821644492881, 1613462622003174462292230226, 3303994265006781534471979091, 6763939960743850232481054804, 13843409560407118679560421461, 28325131953570761563365703766, 57941396682489947085317603415, 118494073135347493188000546904, 242268734250771686611117670489, 495214701340379778093240287322, 1012015982115798374730034053211, 2067669350616406404150262235228, 4223541929031896152887087071325, 8625347223720887065359648030814, 17610934998873819790714941210719, 35949778740847443183070567465056, 73370230248365918132721294508129, 149711516591016748925200487153762, 305424566492489021423111928545379, 622971041849660486498036081492068
Generating function in Maple syntax:
(3*x^7-3*x^6+2*x^5-11*x^4+23*x^3-19*x^2+7*x-1)/(-1+x)^2/(2*x-1)^3
Generating function in latex syntax:
\frac{3 x^{7}-3 x^{6}+2 x^{5}-11 x^{4}+23 x^{3}-19 x^{2}+7 x -1}{\left(-1+x \right)^{2} \left(2 x -1\right)^{3}}
Generating function in sympy syntax:
(3*x**7 - 3*x**6 + 2*x**5 - 11*x**4 + 23*x**3 - 19*x**2 + 7*x - 1)/((x - 1)**2*(2*x - 1)**3)
Implicit equation for the generating function in Maple syntax:
-(-1+x)^2*(2*x-1)^3*F(x)+3*x^7-3*x^6+2*x^5-11*x^4+23*x^3-19*x^2+7*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(-1+x \right)^{2} \left(2 x -1\right)^{3} F \! \left(x \right)+3 x^{7}-3 x^{6}+2 x^{5}-11 x^{4}+23 x^{3}-19 x^{2}+7 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,1/64*(3*n^2+15*n-48)*2^n+n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ \frac{\left(3 n^{2}+15 n -48\right) 2^{n}}{64}+n & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 56
a(6) = 156
a(7) = 415
a(n+3) = 8*a(n)-12*a(n+1)+6*a(n+2)-n+3, 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) = 19
a \! \left(5\right) = 56
a \! \left(6\right) = 156
a \! \left(7\right) = 415
a \! \left(n +3\right) = 8 a \! \left(n \right)-12 a \! \left(n +1\right)+6 a \! \left(n +2\right)-n +3, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/21700/
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[21,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[21,x]*F[7,x]
F[7,x] = F[8,x]+F[90,x]
F[8,x] = F[47,x]+F[9,x]
F[9,x] = F[10,x]+F[43,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[21,x]
F[13,x] = F[14,x]+F[31,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[21,x]
F[17,x] = F[18,x]+F[22,x]
F[18,x] = F[1,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[18,x]*F[21,x]
F[21,x] = x
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[24,x]
F[24,x] = F[21,x]*F[25,x]
F[25,x] = F[1,x]+F[23,x]
F[26,x] = F[27,x]+F[28,x]+F[30,x]
F[27,x] = 0
F[28,x] = F[21,x]*F[29,x]
F[29,x] = F[19,x]+F[26,x]
F[30,x] = F[21,x]*F[22,x]
F[31,x] = F[23,x]+F[32,x]
F[32,x] = F[27,x]+F[28,x]+F[33,x]
F[33,x] = F[21,x]*F[34,x]
F[34,x] = F[22,x]+F[35,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[37,x]
F[37,x] = F[21,x]*F[38,x]
F[38,x] = F[23,x]+F[36,x]
F[39,x] = 2*F[27,x]+F[40,x]+F[42,x]
F[40,x] = F[21,x]*F[41,x]
F[41,x] = F[26,x]+F[39,x]
F[42,x] = F[21,x]*F[35,x]
F[43,x] = F[11,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[21,x]*F[46,x]
F[46,x] = F[15,x]
F[47,x] = F[48,x]+F[89,x]
F[48,x] = F[21,x]+F[49,x]
F[49,x] = F[27,x]+F[50,x]+F[51,x]
F[50,x] = F[15,x]*F[21,x]
F[51,x] = F[21,x]*F[52,x]
F[52,x] = F[53,x]+F[68,x]
F[53,x] = F[21,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[21,x]*F[56,x]
F[56,x] = F[57,x]+F[60,x]
F[57,x] = F[21,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[21,x]*F[57,x]
F[60,x] = F[61,x]+F[64,x]
F[61,x] = F[62,x]
F[62,x] = F[21,x]*F[63,x]
F[63,x] = F[21,x]+F[61,x]
F[64,x] = 2*F[27,x]+F[65,x]+F[67,x]
F[65,x] = F[21,x]*F[66,x]
F[66,x] = F[58,x]+F[64,x]
F[67,x] = F[21,x]*F[60,x]
F[68,x] = F[69,x]+F[73,x]
F[69,x] = F[27,x]+F[70,x]+F[71,x]
F[70,x] = F[21,x]*F[23,x]
F[71,x] = F[21,x]*F[72,x]
F[72,x] = F[21,x]+F[69,x]
F[73,x] = 2*F[27,x]+F[74,x]+F[79,x]
F[74,x] = F[21,x]*F[75,x]
F[75,x] = F[58,x]+F[76,x]
F[76,x] = 2*F[27,x]+F[74,x]+F[77,x]
F[77,x] = F[21,x]*F[78,x]
F[78,x] = F[69,x]+F[76,x]
F[79,x] = F[21,x]*F[80,x]
F[80,x] = F[78,x]+F[81,x]
F[81,x] = F[82,x]+F[85,x]
F[82,x] = F[83,x]
F[83,x] = F[21,x]*F[84,x]
F[84,x] = F[69,x]+F[82,x]
F[85,x] = 3*F[27,x]+F[86,x]+F[88,x]
F[86,x] = F[21,x]*F[87,x]
F[87,x] = F[76,x]+F[85,x]
F[88,x] = F[21,x]*F[81,x]
F[89,x] = F[50,x]
F[90,x] = F[91,x]
F[91,x] = F[92,x]*F[98,x]
F[92,x] = F[93,x]
F[93,x] = F[21,x]*F[94,x]
F[94,x] = F[25,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[21,x]*F[25,x]*F[97,x]
F[97,x] = F[24,x]+F[94,x]
F[98,x] = F[104,x]+F[99,x]
F[99,x] = F[100,x]+F[102,x]
F[100,x] = F[101,x]*F[14,x]
F[101,x] = F[1,x]+F[21,x]
F[102,x] = F[103,x]
F[103,x] = F[21,x]^2*F[15,x]*F[17,x]
F[104,x] = F[105,x]+F[50,x]
F[105,x] = F[11,x]+F[50,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_{21}\! \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_{21}\! \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_{47}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{43}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{21}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{31}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{21}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{18}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = x
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{21}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = 0
F_{28}\! \left(x \right) = F_{21}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{19}\! \left(x \right)+F_{26}\! \left(x \right)
F_{30}\! \left(x \right) = F_{21}\! \left(x \right) F_{22}\! \left(x \right)
F_{31}\! \left(x \right) = F_{23}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{21}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{22}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{21}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{23}\! \left(x \right)+F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{40}\! \left(x \right)+F_{42}\! \left(x \right)
F_{40}\! \left(x \right) = F_{21}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{26}\! \left(x \right)+F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{21}\! \left(x \right) F_{35}\! \left(x \right)
F_{43}\! \left(x \right) = F_{11}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{21}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{15}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{89}\! \left(x \right)
F_{48}\! \left(x \right) = F_{21}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{27}\! \left(x \right)+F_{50}\! \left(x \right)+F_{51}\! \left(x \right)
F_{50}\! \left(x \right) = F_{15}\! \left(x \right) F_{21}\! \left(x \right)
F_{51}\! \left(x \right) = F_{21}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{68}\! \left(x \right)
F_{53}\! \left(x \right) = F_{21}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{21}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{60}\! \left(x \right)
F_{57}\! \left(x \right) = F_{21}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{21}\! \left(x \right) F_{57}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{64}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{21}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{21}\! \left(x \right)+F_{61}\! \left(x \right)
F_{64}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{65}\! \left(x \right) = F_{21}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{58}\! \left(x \right)+F_{64}\! \left(x \right)
F_{67}\! \left(x \right) = F_{21}\! \left(x \right) F_{60}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{73}\! \left(x \right)
F_{69}\! \left(x \right) = F_{27}\! \left(x \right)+F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{21}\! \left(x \right) F_{23}\! \left(x \right)
F_{71}\! \left(x \right) = F_{21}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{21}\! \left(x \right)+F_{69}\! \left(x \right)
F_{73}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{74}\! \left(x \right)+F_{79}\! \left(x \right)
F_{74}\! \left(x \right) = F_{21}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{58}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{74}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{21}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{69}\! \left(x \right)+F_{76}\! \left(x \right)
F_{79}\! \left(x \right) = F_{21}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{78}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{85}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{21}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{69}\! \left(x \right)+F_{82}\! \left(x \right)
F_{85}\! \left(x \right) = 3 F_{27}\! \left(x \right)+F_{86}\! \left(x \right)+F_{88}\! \left(x \right)
F_{86}\! \left(x \right) = F_{21}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{76}\! \left(x \right)+F_{85}\! \left(x \right)
F_{88}\! \left(x \right) = F_{21}\! \left(x \right) F_{81}\! \left(x \right)
F_{89}\! \left(x \right) = F_{50}\! \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_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{21}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{25}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{21}\! \left(x \right) F_{25}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{24}\! \left(x \right)+F_{94}\! \left(x \right)
F_{98}\! \left(x \right) = F_{104}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{102}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{14}\! \left(x \right)
F_{101}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{21} \left(x \right)^{2} F_{15}\! \left(x \right) F_{17}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{50}\! \left(x \right)
F_{105}\! \left(x \right) = F_{11}\! \left(x \right)+F_{50}\! \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_21(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_21(x)*F_7(x))
Eq(F_7(x), F_8(x) + F_90(x))
Eq(F_8(x), F_47(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_43(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_21(x))
Eq(F_13(x), F_14(x) + F_31(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_21(x))
Eq(F_17(x), F_18(x) + F_22(x))
Eq(F_18(x), F_1(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_18(x)*F_21(x))
Eq(F_21(x), x)
Eq(F_22(x), F_23(x) + F_26(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_21(x)*F_25(x))
Eq(F_25(x), F_1(x) + F_23(x))
Eq(F_26(x), F_27(x) + F_28(x) + F_30(x))
Eq(F_27(x), 0)
Eq(F_28(x), F_21(x)*F_29(x))
Eq(F_29(x), F_19(x) + F_26(x))
Eq(F_30(x), F_21(x)*F_22(x))
Eq(F_31(x), F_23(x) + F_32(x))
Eq(F_32(x), F_27(x) + F_28(x) + F_33(x))
Eq(F_33(x), F_21(x)*F_34(x))
Eq(F_34(x), F_22(x) + F_35(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_21(x)*F_38(x))
Eq(F_38(x), F_23(x) + F_36(x))
Eq(F_39(x), 2*F_27(x) + F_40(x) + F_42(x))
Eq(F_40(x), F_21(x)*F_41(x))
Eq(F_41(x), F_26(x) + F_39(x))
Eq(F_42(x), F_21(x)*F_35(x))
Eq(F_43(x), F_11(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_21(x)*F_46(x))
Eq(F_46(x), F_15(x))
Eq(F_47(x), F_48(x) + F_89(x))
Eq(F_48(x), F_21(x) + F_49(x))
Eq(F_49(x), F_27(x) + F_50(x) + F_51(x))
Eq(F_50(x), F_15(x)*F_21(x))
Eq(F_51(x), F_21(x)*F_52(x))
Eq(F_52(x), F_53(x) + F_68(x))
Eq(F_53(x), F_21(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_21(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_60(x))
Eq(F_57(x), F_21(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_21(x)*F_57(x))
Eq(F_60(x), F_61(x) + F_64(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_21(x)*F_63(x))
Eq(F_63(x), F_21(x) + F_61(x))
Eq(F_64(x), 2*F_27(x) + F_65(x) + F_67(x))
Eq(F_65(x), F_21(x)*F_66(x))
Eq(F_66(x), F_58(x) + F_64(x))
Eq(F_67(x), F_21(x)*F_60(x))
Eq(F_68(x), F_69(x) + F_73(x))
Eq(F_69(x), F_27(x) + F_70(x) + F_71(x))
Eq(F_70(x), F_21(x)*F_23(x))
Eq(F_71(x), F_21(x)*F_72(x))
Eq(F_72(x), F_21(x) + F_69(x))
Eq(F_73(x), 2*F_27(x) + F_74(x) + F_79(x))
Eq(F_74(x), F_21(x)*F_75(x))
Eq(F_75(x), F_58(x) + F_76(x))
Eq(F_76(x), 2*F_27(x) + F_74(x) + F_77(x))
Eq(F_77(x), F_21(x)*F_78(x))
Eq(F_78(x), F_69(x) + F_76(x))
Eq(F_79(x), F_21(x)*F_80(x))
Eq(F_80(x), F_78(x) + F_81(x))
Eq(F_81(x), F_82(x) + F_85(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_21(x)*F_84(x))
Eq(F_84(x), F_69(x) + F_82(x))
Eq(F_85(x), 3*F_27(x) + F_86(x) + F_88(x))
Eq(F_86(x), F_21(x)*F_87(x))
Eq(F_87(x), F_76(x) + F_85(x))
Eq(F_88(x), F_21(x)*F_81(x))
Eq(F_89(x), F_50(x))
Eq(F_90(x), F_91(x))
Eq(F_91(x), F_92(x)*F_98(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_21(x)*F_94(x))
Eq(F_94(x), F_25(x) + F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_21(x)*F_25(x)*F_97(x))
Eq(F_97(x), F_24(x) + F_94(x))
Eq(F_98(x), F_104(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_102(x))
Eq(F_100(x), F_101(x)*F_14(x))
Eq(F_101(x), F_1(x) + F_21(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_15(x)*F_17(x)*F_21(x)**2)
Eq(F_104(x), F_105(x) + F_50(x))
Eq(F_105(x), F_11(x) + F_50(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, 1, 3, 2], "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, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 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": 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, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 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": [[1, 1]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 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