0213_0231_1230_2103_3021
Counting sequence:
1, 1, 2, 6, 19, 51, 115, 234, 449, 831, 1509, 2718, 4887, 8803, 15911, 28866, 52549, 95935, 175529, 321686, 590235, 1083859, 1991419, 3660282, 6729353, 12373759, 22754893, 41848174, 76965535, 141555715, 260354799, 478859538, 880751501, 1619945087, 2979533009, 5480203942, 10079653667, 18539359347, 34099182595, 62718157962, 115356658769, 212173954495, 390248722485, 717779282878, 1320201902631, 2428229846179, 4466210965047, 8214642642146, 15109083376341, 27789936900927, 51113662830969, 94012683013686, 172916282644651, 318042628381715, 584971593925515, 1075930504830106, 1978944727008025, 3639846825626495, 6694722057319325, 12313513609800078, 22648082492583343, 41656318159531075, 76617914261733375, 140922314913656882, 259196547334720285, 476736776509899007, 876855638758053793, 1612788962602439494, 2966381377870147123, 5456025979230383283, 10035196319702700435, 18457603676802948650, 33948825975735737057, 62441625972241077311, 114848055624779440261, 211238507572755917534, 388528189169776083255, 714614752367311074019, 1314381449109842692167, 2417524390646929450754, 4446520592124082801765, 8178426431880854512575, 15042471414651866315593, 27667418438656803162582, 50888316285189523505083, 93598206138498192478803, 172153940862344518622747, 316640463286032234063162, 582392610286874944601001, 1071187014435251696702463, 1970220088008158874760941, 3623799712730285515436974, 6665206815173696086250687, 12259226615912140475776131, 22548233143816122076768015, 41472666574901958638075218, 76280126334630221189875373, 140301026053348301903949695, 258053818962880481731105905, 474634971350859004824110566, 872989816367087788458319171
Generating function in Maple syntax:
(x^9-x^8+x^7+5*x^6+4*x^5-3*x^4+2*x^3-6*x^2+4*x-1)/(x^3+x^2+x-1)/(x-1)^4
Generating function in latex syntax:
\frac{x^{9}-x^{8}+x^{7}+5 x^{6}+4 x^{5}-3 x^{4}+2 x^{3}-6 x^{2}+4 x -1}{\left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{4}}
Generating function in sympy syntax:
(x**9 - x**8 + x**7 + 5*x**6 + 4*x**5 - 3*x**4 + 2*x**3 - 6*x**2 + 4*x - 1)/((x - 1)**4*(x**3 + x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
-(x^3+x^2+x-1)*(x-1)^4*F(x)+x^9-x^8+x^7+5*x^6+4*x^5-3*x^4+2*x^3-6*x^2+4*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x^{3}+x^{2}+x -1\right) \left(x -1\right)^{4} F \! \left(x \right)+x^{9}-x^{8}+x^{7}+5 x^{6}+4 x^{5}-3 x^{4}+2 x^{3}-6 x^{2}+4 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,n = 2,2,1/264*(((-19*11^(1/2)+77*I)*3^(1/2)-57*I*11^(1/2)+77)*(17+3*11^(1/2)*3^(1/2))^(1/3)+352+((23*11^(1/2)+143*I)*3^(1/2)-69*I*11^(1/2)-143)*(17+3*11^(1/2)*3^(1/2))^(2/3))*(1/24*((17*I+3*11^(1/2))*3^(1/2)-9*I*11^(1/2)-17)*(17+3*11^(1/2)*3^(1/2))^(2/3)-1/6*I*3^(1/2)*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/6*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3)^(-n)+1/264*(((23*11^(1/2)-143*I)*3^(1/2)+69*I*11^(1/2)-143)*(17+3*11^(1/2)*3^(1/2))^(2/3)+352+((-19*11^(1/2)-77*I)*3^(1/2)+57*I*11^(1/2)+77)*(17+3*11^(1/2)*3^(1/2))^(1/3))*(1/24*((-17*I+3*11^(1/2))*3^(1/2)+9*I*11^(1/2)-17)*(17+3*11^(1/2)*3^(1/2))^(2/3)+1/6*I*3^(1/2)*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/6*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3)^(-n)+1/264*((-46*11^(1/2)*3^(1/2)+286)*(17+3*11^(1/2)*3^(1/2))^(2/3)+38*(17+3*11^(1/2)*3^(1/2))^(1/3)*11^(1/2)*3^(1/2)-154*(17+3*11^(1/2)*3^(1/2))^(1/3)+352)*(1/3*(17+3*11^(1/2)*3^(1/2))^(1/3)-1/3+17/12*(17+3*11^(1/2)*3^(1/2))^(2/3)-1/4*(17+3*11^(1/2)*3^(1/2))^(2/3)*11^(1/2)*3^(1/2))^(-n)+1/2*n^3-7/2*n^2+4*n-7)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ 2 & n =2 \\ \frac{\left(\left(\left(-19 \sqrt{11}+77 \,\mathrm{I}\right) \sqrt{3}-57 \,\mathrm{I} \sqrt{11}+77\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+352+\left(\left(23 \sqrt{11}+143 \,\mathrm{I}\right) \sqrt{3}-69 \,\mathrm{I} \sqrt{11}-143\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}\right) \left(\frac{\left(\left(17 \,\mathrm{I}+3 \sqrt{11}\right) \sqrt{3}-9 \,\mathrm{I} \sqrt{11}-17\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{24}-\frac{\mathrm{I} \sqrt{3}\, \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{1}{3}\right)^{-n}}{264}\\+\\\frac{\left(\left(\left(23 \sqrt{11}-143 \,\mathrm{I}\right) \sqrt{3}+69 \,\mathrm{I} \sqrt{11}-143\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+352+\left(\left(-19 \sqrt{11}-77 \,\mathrm{I}\right) \sqrt{3}+57 \,\mathrm{I} \sqrt{11}+77\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}\right) \left(\frac{\left(\left(-17 \,\mathrm{I}+3 \sqrt{11}\right) \sqrt{3}+9 \,\mathrm{I} \sqrt{11}-17\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{24}+\frac{\mathrm{I} \sqrt{3}\, \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{6}-\frac{1}{3}\right)^{-n}}{264}\\+\\\frac{\left(\left(-46 \sqrt{11}\, \sqrt{3}+286\right) \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}+38 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}} \sqrt{11}\, \sqrt{3}-154 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}+352\right) \left(\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{1}{3}}}{3}-\frac{1}{3}+\frac{17 \left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}}}{12}-\frac{\left(17+3 \sqrt{11}\, \sqrt{3}\right)^{\frac{2}{3}} \sqrt{11}\, \sqrt{3}}{4}\right)^{-n}}{264}\\+\frac{n^{3}}{2}-\frac{7 n^{2}}{2}+4 n -7 & \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) = 51
a(6) = 115
a(7) = 234
a(8) = 449
a(9) = 831
a(n+3) = -n^3+7*n^2+a(n)+a(n+1)+a(n+2)-2*n+9, 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) = 19
a \! \left(5\right) = 51
a \! \left(6\right) = 115
a \! \left(7\right) = 234
a \! \left(8\right) = 449
a \! \left(9\right) = 831
a \! \left(n +3\right) = -n^{3}+7 n^{2}+a \! \left(n \right)+a \! \left(n +1\right)+a \! \left(n +2\right)-2 n +9, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://www.permpal.com/tree/20375/
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[17,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[11,x] = F[12,x]*F[4,x]
F[12,x] = F[13,x]+F[16,x]
F[13,x] = F[1,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[4,x]
F[16,x] = F[11,x]
F[17,x] = F[18,x]+F[37,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[13,x]+F[21,x]
F[21,x] = F[18,x]+F[22,x]
F[22,x] = F[23,x]+F[24,x]+F[32,x]
F[23,x] = 0
F[24,x] = F[25,x]*F[4,x]
F[25,x] = F[26,x]+F[29,x]
F[26,x] = F[14,x]+F[27,x]
F[27,x] = F[28,x]
F[28,x] = F[26,x]*F[4,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[18,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[18,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[26,x]
F[37,x] = F[23,x]+F[38,x]+F[70,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[52,x]
F[40,x] = F[41,x]+F[7,x]
F[41,x] = F[23,x]+F[42,x]+F[43,x]
F[42,x] = F[4,x]*F[40,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]+F[46,x]
F[45,x] = F[14,x]
F[46,x] = F[47,x]
F[47,x] = F[23,x]+F[28,x]+F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]+F[51,x]
F[50,x] = F[14,x]
F[51,x] = F[47,x]
F[52,x] = F[53,x]+F[61,x]
F[53,x] = F[54,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[18,x]
F[57,x] = F[58,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[31,x]+F[60,x]
F[60,x] = F[58,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[65,x]
F[64,x] = F[22,x]
F[65,x] = F[66,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]+F[69,x]
F[68,x] = F[22,x]
F[69,x] = F[66,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[72,x]+F[79,x]
F[72,x] = F[18,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[7,x]+F[77,x]
F[77,x] = F[78,x]
F[78,x] = F[4,x]*F[76,x]
F[79,x] = F[80,x]
F[80,x] = F[23,x]+F[24,x]+F[81,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[33,x]+F[83,x]
F[83,x] = F[80,x]
System of equations in latex syntax:
F_{0}\! \left(x \right) = F_{1}\! \left(x \right)+F_{2}\! \left(x \right)
F_{1}\! \left(x \right) = 1
F_{2}\! \left(x \right) = F_{3}\! \left(x \right)
F_{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_{17}\! \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_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{16}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{16}\! \left(x \right) = F_{11}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{37}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{4}\! \left(x \right)
F_{20}\! \left(x \right) = F_{13}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)+F_{32}\! \left(x \right)
F_{23}\! \left(x \right) = 0
F_{24}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{29}\! \left(x \right)
F_{26}\! \left(x \right) = F_{14}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \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_{18}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{18}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{26}\! \left(x \right)
F_{37}\! \left(x \right) = F_{23}\! \left(x \right)+F_{38}\! \left(x \right)+F_{70}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{52}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{7}\! \left(x \right)
F_{41}\! \left(x \right) = F_{23}\! \left(x \right)+F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{4}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{46}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{23}\! \left(x \right)+F_{28}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{51}\! \left(x \right)
F_{50}\! \left(x \right) = F_{14}\! \left(x \right)
F_{51}\! \left(x \right) = F_{47}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)+F_{61}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{18}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{31}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{65}\! \left(x \right)
F_{64}\! \left(x \right) = F_{22}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{22}\! \left(x \right)
F_{69}\! \left(x \right) = F_{66}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{79}\! \left(x \right)
F_{72}\! \left(x \right) = F_{18}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{7}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{4}\! \left(x \right) F_{76}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{33}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{80}\! \left(x \right)
System of equations in sympy syntax:
Eq(F_0(x), F_1(x) + F_2(x))
Eq(F_1(x), 1)
Eq(F_2(x), F_3(x))
Eq(F_3(x), F_4(x)*F_5(x))
Eq(F_4(x), x)
Eq(F_5(x), F_17(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))
Eq(F_11(x), F_12(x)*F_4(x))
Eq(F_12(x), F_13(x) + F_16(x))
Eq(F_13(x), F_1(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_4(x))
Eq(F_16(x), F_11(x))
Eq(F_17(x), F_18(x) + F_37(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_13(x) + F_21(x))
Eq(F_21(x), F_18(x) + F_22(x))
Eq(F_22(x), F_23(x) + F_24(x) + F_32(x))
Eq(F_23(x), 0)
Eq(F_24(x), F_25(x)*F_4(x))
Eq(F_25(x), F_26(x) + F_29(x))
Eq(F_26(x), F_14(x) + F_27(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_26(x)*F_4(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_18(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_18(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_26(x))
Eq(F_37(x), F_23(x) + F_38(x) + F_70(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_52(x))
Eq(F_40(x), F_41(x) + F_7(x))
Eq(F_41(x), F_23(x) + F_42(x) + F_43(x))
Eq(F_42(x), F_4(x)*F_40(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_46(x))
Eq(F_45(x), F_14(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_23(x) + F_28(x) + F_48(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_51(x))
Eq(F_50(x), F_14(x))
Eq(F_51(x), F_47(x))
Eq(F_52(x), F_53(x) + F_61(x))
Eq(F_53(x), F_54(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_18(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_31(x) + F_60(x))
Eq(F_60(x), F_58(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_65(x))
Eq(F_64(x), F_22(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_69(x))
Eq(F_68(x), F_22(x))
Eq(F_69(x), F_66(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_79(x))
Eq(F_72(x), F_18(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_7(x) + F_77(x))
Eq(F_77(x), F_78(x))
Eq(F_78(x), F_4(x)*F_76(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_23(x) + F_24(x) + F_81(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_33(x) + F_83(x))
Eq(F_83(x), F_80(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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"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": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [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": [3, 0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", 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