0132_0231_0321_2031_3120
Counting sequence:
1, 1, 2, 6, 19, 56, 154, 402, 1007, 2438, 5738, 13196, 29787, 66244, 145586, 316942, 684735, 1470122, 3140018, 6677432, 14146715, 29873208, 62900842, 132103946, 276804079, 578790126, 1207931354, 2516549252, 5234452667, 10871590988, 22548526338, 46707709606, 96636695807, 199715901394, 412316772066, 850403424752, 1752346544315, 3607772402432, 7421703346298, 15255723677922, 31336081216495, 64321430030678, 131941395118282, 270479860195836, 554153860138139, 1134695999578196, 2322168557548754, 4749890231648702, 9710886696142527, 19843985857692538, 40532396645889938, 82753643152450216, 168884986025870427, 344525371493276744, 702561541869185546, 1432144681503157562, 2918332558535370095, 5944751508128289342, 12105675798371070778, 24643697160970471412, 50152085450396897275, 102033553157704944348, 207525870829231372322, 421969270686104835926, 857773599427492915199, 1743217314965551311266, 3541774862152232508354, 7194230188746723638752, 14609821306377963294587, 29662364470524957315088, 60210172656587974688538, 122191232744252068011026, 247924240350656371713647, 502932030425617213136294, 1020031160299843363914026, 2068396519496904601227372, 4193461436788244947258075, 8500259669165361382010852, 17227192929508465736777458, 34907733041372417416705902, 70722160447455806717221055, 143257709624333557199430218, 290142196707511001926062962, 587537948332709778903608216, 1189583006500795107907103259, 2408180232672341316010741336, 4874388904686184832411146154, 9864834688055374065598039402, 19961783133476756932743812847, 40387793781685531468579146638, 81704042592835098143337194138, 165264995244598266699027848036, 334243810607052674222758065467, 675915261449817630094916104044, 1366685803371059823488627165506, 2763082167684968773574839026182, 5585585457255635800344841984255, 11290013158282668107080006126962, 22817710804108129226940650610338, 46110790583301844479442571709392, 93172319116774861010007677899835
Generating function in Maple syntax:
(2*x^8+2*x^7-9*x^6+27*x^5-48*x^4+48*x^3-27*x^2+8*x-1)/(2*x-1)^2/(x-1)^5
Generating function in latex syntax:
\frac{2 x^{8}+2 x^{7}-9 x^{6}+27 x^{5}-48 x^{4}+48 x^{3}-27 x^{2}+8 x -1}{\left(2 x -1\right)^{2} \left(x -1\right)^{5}}
Generating function in sympy syntax:
(2*x**8 + 2*x**7 - 9*x**6 + 27*x**5 - 48*x**4 + 48*x**3 - 27*x**2 + 8*x - 1)/((x - 1)**5*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
-(2*x-1)^2*(x-1)^5*F(x)+2*x^8+2*x^7-9*x^6+27*x^5-48*x^4+48*x^3-27*x^2+8*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right)^{2} \left(x -1\right)^{5} F \! \left(x \right)+2 x^{8}+2 x^{7}-9 x^{6}+27 x^{5}-48 x^{4}+48 x^{3}-27 x^{2}+8 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,-1+3/4*2^n*n-3*2^(-1+n)-1/12*n^4+2/3*n^3-35/12*n^2+16/3*n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ -1+\frac{3 \,2^{n} n}{4}-3 \,2^{-1+n}-\frac{n^{4}}{12}+\frac{2 n^{3}}{3}-\frac{35 n^{2}}{12}+\frac{16 n}{3} & \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) = 154
a(7) = 402
a(8) = 1007
a(n+2) = -4*a(n)+4*a(n+1)-1/12*(-1+n)*(n^3-15*n^2+68*n-120), 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) = 19
a \! \left(5\right) = 56
a \! \left(6\right) = 154
a \! \left(7\right) = 402
a \! \left(8\right) = 1007
a \! \left(n +2\right) = -4 a \! \left(n \right)+4 a \! \left(n +1\right)-\frac{\left(-1+n \right) \left(n^{3}-15 n^{2}+68 n -120\right)}{12}, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/21685/
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[16,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[16,x]*F[7,x]
F[7,x] = F[31,x]+F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[22,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[16,x]
F[13,x] = F[1,x]+F[14,x]+F[20,x]
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[16,x]*F[17,x]
F[16,x] = x
F[17,x] = F[1,x]+F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[16,x]*F[17,x]
F[20,x] = F[21,x]
F[21,x] = F[17,x]^2*F[16,x]
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[16,x]*F[22,x]
F[26,x] = F[24,x]+F[27,x]
F[27,x] = F[18,x]*F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[16,x]*F[30,x]
F[30,x] = F[1,x]+F[28,x]
F[31,x] = F[32,x]+F[70,x]
F[32,x] = F[18,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[16,x]*F[35,x]
F[35,x] = F[36,x]+F[50,x]
F[36,x] = F[18,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[16,x]*F[39,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[18,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[16,x]*F[40,x]
F[43,x] = F[44,x]+F[46,x]
F[44,x] = F[45,x]
F[45,x] = F[16,x]*F[18,x]
F[46,x] = 2*F[47,x]+F[48,x]+F[49,x]
F[47,x] = 0
F[48,x] = F[16,x]*F[41,x]
F[49,x] = F[16,x]*F[43,x]
F[50,x] = F[51,x]+F[54,x]
F[51,x] = F[52,x]
F[52,x] = F[16,x]*F[53,x]
F[53,x] = F[18,x]+F[51,x]
F[54,x] = 2*F[47,x]+F[55,x]+F[57,x]
F[55,x] = F[16,x]*F[56,x]
F[56,x] = F[37,x]+F[54,x]
F[57,x] = F[16,x]*F[58,x]
F[58,x] = F[59,x]+F[64,x]
F[59,x] = F[51,x]+F[60,x]
F[60,x] = 2*F[47,x]+F[61,x]+F[63,x]
F[61,x] = F[16,x]*F[62,x]
F[62,x] = F[41,x]+F[60,x]
F[63,x] = F[16,x]*F[59,x]
F[64,x] = F[65,x]+F[67,x]
F[65,x] = F[66,x]
F[66,x] = F[16,x]*F[51,x]
F[67,x] = 3*F[47,x]+F[68,x]+F[69,x]
F[68,x] = F[16,x]*F[60,x]
F[69,x] = F[16,x]*F[64,x]
F[70,x] = F[71,x]
F[71,x] = F[47,x]+F[72,x]+F[75,x]
F[72,x] = F[16,x]*F[73,x]
F[73,x] = F[28,x]+F[74,x]
F[74,x] = F[72,x]
F[75,x] = F[16,x]*F[76,x]
F[76,x] = F[77,x]+F[88,x]
F[77,x] = F[18,x]+F[78,x]
F[78,x] = F[47,x]+F[72,x]+F[79,x]
F[79,x] = F[16,x]*F[80,x]
F[80,x] = F[81,x]+F[84,x]
F[81,x] = F[18,x]+F[82,x]
F[82,x] = F[47,x]+F[72,x]+F[83,x]
F[83,x] = F[16,x]*F[81,x]
F[84,x] = F[44,x]+F[85,x]
F[85,x] = 2*F[47,x]+F[86,x]+F[87,x]
F[86,x] = F[16,x]*F[82,x]
F[87,x] = F[16,x]*F[84,x]
F[88,x] = F[89,x]+F[95,x]
F[89,x] = F[47,x]+F[90,x]+F[93,x]
F[90,x] = F[16,x]*F[91,x]
F[91,x] = F[16,x]+F[92,x]
F[92,x] = F[90,x]
F[93,x] = F[16,x]*F[94,x]
F[94,x] = F[18,x]+F[89,x]
F[95,x] = F[101,x]+F[103,x]+F[47,x]+F[96,x]
F[96,x] = F[16,x]*F[97,x]
F[97,x] = F[100,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[16,x]*F[28,x]
F[100,x] = F[96,x]
F[101,x] = F[102,x]*F[16,x]
F[102,x] = F[78,x]+F[95,x]
F[103,x] = F[104,x]*F[16,x]
F[104,x] = F[105,x]+F[110,x]
F[105,x] = F[106,x]+F[89,x]
F[106,x] = F[107,x]+F[109,x]+F[47,x]+F[96,x]
F[107,x] = F[108,x]*F[16,x]
F[108,x] = F[106,x]+F[82,x]
F[109,x] = F[105,x]*F[16,x]
F[110,x] = F[111,x]+F[113,x]
F[111,x] = F[112,x]
F[112,x] = F[16,x]*F[89,x]
F[113,x] = 3*F[47,x]+F[114,x]+F[115,x]
F[114,x] = F[106,x]*F[16,x]
F[115,x] = F[110,x]*F[16,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_{16}\! \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_{16}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{31}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{22}\! \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_{16}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)+F_{20}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right) F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = x
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{16}\! \left(x \right) F_{17}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{17} \left(x \right)^{2} F_{16}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{16}\! \left(x \right) F_{22}\! \left(x \right)
F_{26}\! \left(x \right) = F_{24}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{18}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{16}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{70}\! \left(x \right)
F_{32}\! \left(x \right) = F_{18}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{16}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{50}\! \left(x \right)
F_{36}\! \left(x \right) = F_{18}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{16}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{18}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{16}\! \left(x \right) F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{46}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{16}\! \left(x \right) F_{18}\! \left(x \right)
F_{46}\! \left(x \right) = 2 F_{47}\! \left(x \right)+F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{47}\! \left(x \right) = 0
F_{48}\! \left(x \right) = F_{16}\! \left(x \right) F_{41}\! \left(x \right)
F_{49}\! \left(x \right) = F_{16}\! \left(x \right) F_{43}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{54}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{16}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{18}\! \left(x \right)+F_{51}\! \left(x \right)
F_{54}\! \left(x \right) = 2 F_{47}\! \left(x \right)+F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{16}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{37}\! \left(x \right)+F_{54}\! \left(x \right)
F_{57}\! \left(x \right) = F_{16}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{64}\! \left(x \right)
F_{59}\! \left(x \right) = F_{51}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = 2 F_{47}\! \left(x \right)+F_{61}\! \left(x \right)+F_{63}\! \left(x \right)
F_{61}\! \left(x \right) = F_{16}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{41}\! \left(x \right)+F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{16}\! \left(x \right) F_{59}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{16}\! \left(x \right) F_{51}\! \left(x \right)
F_{67}\! \left(x \right) = 3 F_{47}\! \left(x \right)+F_{68}\! \left(x \right)+F_{69}\! \left(x \right)
F_{68}\! \left(x \right) = F_{16}\! \left(x \right) F_{60}\! \left(x \right)
F_{69}\! \left(x \right) = F_{16}\! \left(x \right) F_{64}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{47}\! \left(x \right)+F_{72}\! \left(x \right)+F_{75}\! \left(x \right)
F_{72}\! \left(x \right) = F_{16}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{28}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{16}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{88}\! \left(x \right)
F_{77}\! \left(x \right) = F_{18}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{47}\! \left(x \right)+F_{72}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{16}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{84}\! \left(x \right)
F_{81}\! \left(x \right) = F_{18}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{47}\! \left(x \right)+F_{72}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{16}\! \left(x \right) F_{81}\! \left(x \right)
F_{84}\! \left(x \right) = F_{44}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = 2 F_{47}\! \left(x \right)+F_{86}\! \left(x \right)+F_{87}\! \left(x \right)
F_{86}\! \left(x \right) = F_{16}\! \left(x \right) F_{82}\! \left(x \right)
F_{87}\! \left(x \right) = F_{16}\! \left(x \right) F_{84}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{95}\! \left(x \right)
F_{89}\! \left(x \right) = F_{47}\! \left(x \right)+F_{90}\! \left(x \right)+F_{93}\! \left(x \right)
F_{90}\! \left(x \right) = F_{16}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{16}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{90}\! \left(x \right)
F_{93}\! \left(x \right) = F_{16}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{18}\! \left(x \right)+F_{89}\! \left(x \right)
F_{95}\! \left(x \right) = F_{101}\! \left(x \right)+F_{103}\! \left(x \right)+F_{47}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{16}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{100}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{16}\! \left(x \right) F_{28}\! \left(x \right)
F_{100}\! \left(x \right) = F_{96}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{16}\! \left(x \right)
F_{102}\! \left(x \right) = F_{78}\! \left(x \right)+F_{95}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{16}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{110}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{89}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{109}\! \left(x \right)+F_{47}\! \left(x \right)+F_{96}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right) F_{16}\! \left(x \right)
F_{108}\! \left(x \right) = F_{106}\! \left(x \right)+F_{82}\! \left(x \right)
F_{109}\! \left(x \right) = F_{105}\! \left(x \right) F_{16}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{113}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right)
F_{112}\! \left(x \right) = F_{16}\! \left(x \right) F_{89}\! \left(x \right)
F_{113}\! \left(x \right) = 3 F_{47}\! \left(x \right)+F_{114}\! \left(x \right)+F_{115}\! \left(x \right)
F_{114}\! \left(x \right) = F_{106}\! \left(x \right) F_{16}\! \left(x \right)
F_{115}\! \left(x \right) = F_{110}\! \left(x \right) F_{16}\! \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_16(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_16(x)*F_7(x))
Eq(F_7(x), F_31(x) + F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_22(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_16(x))
Eq(F_13(x), F_1(x) + F_14(x) + F_20(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_16(x)*F_17(x))
Eq(F_16(x), x)
Eq(F_17(x), F_1(x) + F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_16(x)*F_17(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_16(x)*F_17(x)**2)
Eq(F_22(x), F_23(x) + F_26(x))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_16(x)*F_22(x))
Eq(F_26(x), F_24(x) + F_27(x))
Eq(F_27(x), F_18(x)*F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_16(x)*F_30(x))
Eq(F_30(x), F_1(x) + F_28(x))
Eq(F_31(x), F_32(x) + F_70(x))
Eq(F_32(x), F_18(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_16(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_50(x))
Eq(F_36(x), F_18(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_16(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_18(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_16(x)*F_40(x))
Eq(F_43(x), F_44(x) + F_46(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_16(x)*F_18(x))
Eq(F_46(x), 2*F_47(x) + F_48(x) + F_49(x))
Eq(F_47(x), 0)
Eq(F_48(x), F_16(x)*F_41(x))
Eq(F_49(x), F_16(x)*F_43(x))
Eq(F_50(x), F_51(x) + F_54(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_16(x)*F_53(x))
Eq(F_53(x), F_18(x) + F_51(x))
Eq(F_54(x), 2*F_47(x) + F_55(x) + F_57(x))
Eq(F_55(x), F_16(x)*F_56(x))
Eq(F_56(x), F_37(x) + F_54(x))
Eq(F_57(x), F_16(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_64(x))
Eq(F_59(x), F_51(x) + F_60(x))
Eq(F_60(x), 2*F_47(x) + F_61(x) + F_63(x))
Eq(F_61(x), F_16(x)*F_62(x))
Eq(F_62(x), F_41(x) + F_60(x))
Eq(F_63(x), F_16(x)*F_59(x))
Eq(F_64(x), F_65(x) + F_67(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_16(x)*F_51(x))
Eq(F_67(x), 3*F_47(x) + F_68(x) + F_69(x))
Eq(F_68(x), F_16(x)*F_60(x))
Eq(F_69(x), F_16(x)*F_64(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_47(x) + F_72(x) + F_75(x))
Eq(F_72(x), F_16(x)*F_73(x))
Eq(F_73(x), F_28(x) + F_74(x))
Eq(F_74(x), F_72(x))
Eq(F_75(x), F_16(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_88(x))
Eq(F_77(x), F_18(x) + F_78(x))
Eq(F_78(x), F_47(x) + F_72(x) + F_79(x))
Eq(F_79(x), F_16(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_84(x))
Eq(F_81(x), F_18(x) + F_82(x))
Eq(F_82(x), F_47(x) + F_72(x) + F_83(x))
Eq(F_83(x), F_16(x)*F_81(x))
Eq(F_84(x), F_44(x) + F_85(x))
Eq(F_85(x), 2*F_47(x) + F_86(x) + F_87(x))
Eq(F_86(x), F_16(x)*F_82(x))
Eq(F_87(x), F_16(x)*F_84(x))
Eq(F_88(x), F_89(x) + F_95(x))
Eq(F_89(x), F_47(x) + F_90(x) + F_93(x))
Eq(F_90(x), F_16(x)*F_91(x))
Eq(F_91(x), F_16(x) + F_92(x))
Eq(F_92(x), F_90(x))
Eq(F_93(x), F_16(x)*F_94(x))
Eq(F_94(x), F_18(x) + F_89(x))
Eq(F_95(x), F_101(x) + F_103(x) + F_47(x) + F_96(x))
Eq(F_96(x), F_16(x)*F_97(x))
Eq(F_97(x), F_100(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_16(x)*F_28(x))
Eq(F_100(x), F_96(x))
Eq(F_101(x), F_102(x)*F_16(x))
Eq(F_102(x), F_78(x) + F_95(x))
Eq(F_103(x), F_104(x)*F_16(x))
Eq(F_104(x), F_105(x) + F_110(x))
Eq(F_105(x), F_106(x) + F_89(x))
Eq(F_106(x), F_107(x) + F_109(x) + F_47(x) + F_96(x))
Eq(F_107(x), F_108(x)*F_16(x))
Eq(F_108(x), F_106(x) + F_82(x))
Eq(F_109(x), F_105(x)*F_16(x))
Eq(F_110(x), F_111(x) + F_113(x))
Eq(F_111(x), F_112(x))
Eq(F_112(x), F_16(x)*F_89(x))
Eq(F_113(x), F_114(x) + F_115(x) + 3*F_47(x))
Eq(F_114(x), F_106(x)*F_16(x))
Eq(F_115(x), F_110(x)*F_16(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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 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]]}], "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": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 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]]}], "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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "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": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 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]]}], "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": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 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]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": false, 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