0132_0213_0231_3012_3201
Counting sequence:
1, 1, 2, 6, 19, 52, 121, 252, 489, 910, 1659, 3010, 5495, 10160, 19077, 36368, 70253, 137146, 269847, 533926, 1060491, 2111724, 4211953, 8409796, 16802449, 33584262, 67143891, 134258602, 268482879, 536925640, 1073804669, 2147555480, 4295049045, 8590027250, 17179973807, 34359856078, 68719608723, 137439100996, 274878071337, 549755996556, 1099511830201, 2199023479294, 4398046757803, 8796093293586, 17592186342279, 35184372415072, 70368744534261, 140737488744352, 281474977134269, 562949953881770, 1125899907342279, 2251799814226550, 4503599627955995, 9007199255373340, 18014398510163937, 36028797019698388, 72057594038717793, 144115188076704246, 288230376152621827, 576460752304398586, 1152921504607890511, 2305843009214809464, 4611686018428579053, 9223372036856046376, 18446744073710905509, 36893488147420544482, 73786976294839739231, 147573952589678041502, 295147905179354554659, 590295810358707485300, 1180591620717413246489, 2361183241434824664220, 4722366482869647390345, 9444732965739292728430, 18889465931478583285467, 37778931862957164275298, 75557863725914326125463, 151115727451828649690896, 302231454903657296681317, 604462909807314590516016, 1208925819614629178033421, 2417851639229258352910234, 4835703278458516702499703, 9671406556917033401508166, 19342813113834066799348139, 38685626227668133594844492, 77371252455336267185646801, 154742504910672534367054052, 309485009821345068729664049, 618970019642690137454672230, 1237940039285380274904469299, 2475880078570760549803836490, 4951760157141521099602336095, 9903520314283042199199092520, 19807040628566084398392354397, 39614081257132168796778618808, 79228162514264337593550879733, 158456325028528675187095124946, 316912650057057350374183329807, 633825300114114700748359444846, 1267650600228229401496711370931
Generating function in Maple syntax:
-(2*x^8-5*x^7+2*x^6+7*x^5-12*x^4+18*x^3-15*x^2+6*x-1)/(2*x-1)/(x-1)^5
Generating function in latex syntax:
-\frac{2 x^{8}-5 x^{7}+2 x^{6}+7 x^{5}-12 x^{4}+18 x^{3}-15 x^{2}+6 x -1}{\left(2 x -1\right) \left(x -1\right)^{5}}
Generating function in sympy syntax:
(-2*x**8 + 5*x**7 - 2*x**6 - 7*x**5 + 12*x**4 - 18*x**3 + 15*x**2 - 6*x + 1)/((x - 1)**5*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x-1)^5*F(x)+2*x^8-5*x^7+2*x^6+7*x^5-12*x^4+18*x^3-15*x^2+6*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x -1\right)^{5} F \! \left(x \right)+2 x^{8}-5 x^{7}+2 x^{6}+7 x^{5}-12 x^{4}+18 x^{3}-15 x^{2}+6 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,5-1/12*n^2-17/6*n-1/6*n^3+1/12*n^4+2^n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ 5-\frac{n^{2}}{12}-\frac{17 n}{6}-\frac{n^{3}}{6}+\frac{n^{4}}{12}+2^{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) = 52
a(6) = 121
a(7) = 252
a(8) = 489
a(n+1) = 2*a(n)-1/12*(-2+n)*(n^3-4*n^2-9*n-48), 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) = 52
a \! \left(6\right) = 121
a \! \left(7\right) = 252
a \! \left(8\right) = 489
a \! \left(n +1\right) = 2 a \! \left(n \right)-\frac{\left(-2+n \right) \left(n^{3}-4 n^{2}-9 n -48\right)}{12}, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18225/
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[21,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[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]
F[14,x] = F[15,x]*F[4,x]
F[15,x] = F[16,x]+F[17,x]
F[16,x] = F[1,x]+F[4,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[4,x]
F[20,x] = F[1,x]+F[18,x]
F[21,x] = F[22,x]+F[33,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[20,x]+F[25,x]
F[25,x] = F[18,x]+F[26,x]
F[26,x] = F[27,x]+F[28,x]+F[30,x]
F[27,x] = 0
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[18,x]+F[26,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[18,x]+F[32,x]
F[32,x] = F[30,x]
F[33,x] = F[27,x]+F[34,x]+F[92,x]
F[34,x] = F[35,x]*F[4,x]
F[35,x] = F[36,x]+F[50,x]
F[36,x] = F[37,x]+F[7,x]
F[37,x] = F[27,x]+F[38,x]+F[40,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[11,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]+F[43,x]
F[42,x] = F[18,x]
F[43,x] = F[44,x]
F[44,x] = F[27,x]+F[45,x]+F[47,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[4,x]
F[47,x] = F[4,x]*F[48,x]
F[48,x] = F[17,x]+F[49,x]
F[49,x] = F[32,x]
F[50,x] = F[51,x]+F[71,x]
F[51,x] = F[27,x]+F[52,x]+F[54,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[51,x]+F[7,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[56,x]+F[61,x]
F[56,x] = F[18,x]+F[57,x]
F[57,x] = F[27,x]+F[58,x]+F[60,x]
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[11,x]+F[57,x]
F[60,x] = F[4,x]*F[56,x]
F[61,x] = F[62,x]
F[62,x] = F[27,x]+F[28,x]+F[63,x]
F[63,x] = F[4,x]*F[64,x]
F[64,x] = F[65,x]+F[70,x]
F[65,x] = F[18,x]+F[66,x]
F[66,x] = F[27,x]+F[67,x]+F[69,x]
F[67,x] = F[4,x]*F[68,x]
F[68,x] = F[4,x]+F[66,x]
F[69,x] = F[18,x]*F[4,x]
F[70,x] = F[32,x]
F[71,x] = F[27,x]+F[72,x]+F[74,x]+F[76,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[37,x]+F[71,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[57,x]
F[76,x] = F[4,x]*F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[26,x]
F[79,x] = F[80,x]
F[80,x] = F[27,x]+F[81,x]+F[87,x]+F[89,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[32,x]+F[83,x]
F[83,x] = 2*F[27,x]+F[81,x]+F[84,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[32,x]+F[86,x]
F[86,x] = F[84,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[66,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[70,x]+F[91,x]
F[91,x] = F[86,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[107,x]+F[94,x]
F[94,x] = F[22,x]+F[95,x]
F[95,x] = F[106,x]+F[27,x]+F[96,x]
F[96,x] = F[4,x]*F[97,x]
F[97,x] = F[101,x]+F[98,x]
F[98,x] = F[11,x]+F[99,x]
F[99,x] = F[100,x]+F[27,x]+F[38,x]
F[100,x] = F[4,x]*F[42,x]
F[101,x] = F[102,x]+F[57,x]
F[102,x] = F[103,x]+F[105,x]+F[27,x]+F[74,x]
F[103,x] = F[104,x]*F[4,x]
F[104,x] = F[102,x]+F[99,x]
F[105,x] = F[4,x]*F[78,x]
F[106,x] = F[4,x]*F[94,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]+F[27,x]+F[63,x]
F[109,x] = F[110,x]*F[4,x]
F[110,x] = F[111,x]+F[112,x]
F[111,x] = F[18,x]+F[32,x]
F[112,x] = F[26,x]+F[83,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_{21}\! \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_{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_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right) F_{4}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \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_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{33}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{20}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{18}\! \left(x \right)+F_{26}\! \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_{29}\! \left(x \right) F_{4}\! \left(x \right)
F_{29}\! \left(x \right) = F_{18}\! \left(x \right)+F_{26}\! \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_{32}\! \left(x \right) = F_{30}\! \left(x \right)
F_{33}\! \left(x \right) = F_{27}\! \left(x \right)+F_{34}\! \left(x \right)+F_{92}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{50}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)+F_{7}\! \left(x \right)
F_{37}\! \left(x \right) = F_{27}\! \left(x \right)+F_{38}\! \left(x \right)+F_{40}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{11}\! \left(x \right)
F_{40}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{43}\! \left(x \right)
F_{42}\! \left(x \right) = F_{18}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{27}\! \left(x \right)+F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{4}\! \left(x \right)
F_{47}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{17}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{32}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{71}\! \left(x \right)
F_{51}\! \left(x \right) = F_{27}\! \left(x \right)+F_{52}\! \left(x \right)+F_{54}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{51}\! \left(x \right)+F_{7}\! \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_{61}\! \left(x \right)
F_{56}\! \left(x \right) = F_{18}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{27}\! \left(x \right)+F_{58}\! \left(x \right)+F_{60}\! \left(x \right)
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{11}\! \left(x \right)+F_{57}\! \left(x \right)
F_{60}\! \left(x \right) = F_{4}\! \left(x \right) F_{56}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{70}\! \left(x \right)
F_{65}\! \left(x \right) = F_{18}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{27}\! \left(x \right)+F_{67}\! \left(x \right)+F_{69}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{4}\! \left(x \right)+F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{18}\! \left(x \right) F_{4}\! \left(x \right)
F_{70}\! \left(x \right) = F_{32}\! \left(x \right)
F_{71}\! \left(x \right) = F_{27}\! \left(x \right)+F_{72}\! \left(x \right)+F_{74}\! \left(x \right)+F_{76}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{37}\! \left(x \right)+F_{71}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{57}\! \left(x \right)
F_{76}\! \left(x \right) = F_{4}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{26}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{27}\! \left(x \right)+F_{81}\! \left(x \right)+F_{87}\! \left(x \right)+F_{89}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{32}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{81}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{32}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{84}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{66}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{70}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{86}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{107}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{22}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{106}\! \left(x \right)+F_{27}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{4}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{101}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{11}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{27}\! \left(x \right)+F_{38}\! \left(x \right)
F_{100}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{57}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{105}\! \left(x \right)+F_{27}\! \left(x \right)+F_{74}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{102}\! \left(x \right)+F_{99}\! \left(x \right)
F_{105}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{106}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{27}\! \left(x \right)+F_{63}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{4}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{112}\! \left(x \right)
F_{111}\! \left(x \right) = F_{18}\! \left(x \right)+F_{32}\! \left(x \right)
F_{112}\! \left(x \right) = F_{26}\! \left(x \right)+F_{83}\! \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_21(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_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x))
Eq(F_14(x), F_15(x)*F_4(x))
Eq(F_15(x), F_16(x) + F_17(x))
Eq(F_16(x), F_1(x) + F_4(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_4(x))
Eq(F_20(x), F_1(x) + F_18(x))
Eq(F_21(x), F_22(x) + F_33(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_20(x) + F_25(x))
Eq(F_25(x), F_18(x) + F_26(x))
Eq(F_26(x), F_27(x) + F_28(x) + F_30(x))
Eq(F_27(x), 0)
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_18(x) + F_26(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_18(x) + F_32(x))
Eq(F_32(x), F_30(x))
Eq(F_33(x), F_27(x) + F_34(x) + F_92(x))
Eq(F_34(x), F_35(x)*F_4(x))
Eq(F_35(x), F_36(x) + F_50(x))
Eq(F_36(x), F_37(x) + F_7(x))
Eq(F_37(x), F_27(x) + F_38(x) + F_40(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_11(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_43(x))
Eq(F_42(x), F_18(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_27(x) + F_45(x) + F_47(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_4(x))
Eq(F_47(x), F_4(x)*F_48(x))
Eq(F_48(x), F_17(x) + F_49(x))
Eq(F_49(x), F_32(x))
Eq(F_50(x), F_51(x) + F_71(x))
Eq(F_51(x), F_27(x) + F_52(x) + F_54(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_51(x) + F_7(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_61(x))
Eq(F_56(x), F_18(x) + F_57(x))
Eq(F_57(x), F_27(x) + F_58(x) + F_60(x))
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_11(x) + F_57(x))
Eq(F_60(x), F_4(x)*F_56(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_27(x) + F_28(x) + F_63(x))
Eq(F_63(x), F_4(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_70(x))
Eq(F_65(x), F_18(x) + F_66(x))
Eq(F_66(x), F_27(x) + F_67(x) + F_69(x))
Eq(F_67(x), F_4(x)*F_68(x))
Eq(F_68(x), F_4(x) + F_66(x))
Eq(F_69(x), F_18(x)*F_4(x))
Eq(F_70(x), F_32(x))
Eq(F_71(x), F_27(x) + F_72(x) + F_74(x) + F_76(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_37(x) + F_71(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_57(x))
Eq(F_76(x), F_4(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_26(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_27(x) + F_81(x) + F_87(x) + F_89(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_32(x) + F_83(x))
Eq(F_83(x), 2*F_27(x) + F_81(x) + F_84(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_32(x) + F_86(x))
Eq(F_86(x), F_84(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_66(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_70(x) + F_91(x))
Eq(F_91(x), F_86(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_107(x) + F_94(x))
Eq(F_94(x), F_22(x) + F_95(x))
Eq(F_95(x), F_106(x) + F_27(x) + F_96(x))
Eq(F_96(x), F_4(x)*F_97(x))
Eq(F_97(x), F_101(x) + F_98(x))
Eq(F_98(x), F_11(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_27(x) + F_38(x))
Eq(F_100(x), F_4(x)*F_42(x))
Eq(F_101(x), F_102(x) + F_57(x))
Eq(F_102(x), F_103(x) + F_105(x) + F_27(x) + F_74(x))
Eq(F_103(x), F_104(x)*F_4(x))
Eq(F_104(x), F_102(x) + F_99(x))
Eq(F_105(x), F_4(x)*F_78(x))
Eq(F_106(x), F_4(x)*F_94(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x) + F_27(x) + F_63(x))
Eq(F_109(x), F_110(x)*F_4(x))
Eq(F_110(x), F_111(x) + F_112(x))
Eq(F_111(x), F_18(x) + F_32(x))
Eq(F_112(x), F_26(x) + F_83(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "maxreqlen": 1, "one_cell_only": false, "strategy_class": "CellInsertionFactory"}, {"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "point_only": false, "strategy_class": "PatternPlacementFactory"}]], "inferral_strats": [{"class_module": "tilings.strategies.row_and_col_separation", "ignore_parent": true, "inferrable": true, "possibly_empty": false, "strategy_class": "RowColumnSeparationStrategy", "workable": true}, {"class_module": "tilings.strategies.obstruction_inferral", "strategy_class": "ObstructionTransitivityFactory"}], "initial_strats": [{"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "point_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": false, "strategy_class": "LocallyFactorableVerificationStrategy", "symmetry": false}]}
Specification JSON:
{"root": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 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": true, "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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 2, 0, 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", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 0], [1, 2], [1, 2]]}, {"patt": [3, 0, 1, 2], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 2, 0, 1], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 1], "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], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 0]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 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