0123_0213_0231_1032_3021
Counting sequence:
1, 1, 2, 6, 19, 55, 152, 412, 1105, 2944, 7808, 20641, 54436, 143308, 376769, 989560, 2597032, 6811777, 17858780, 46805524, 122639713, 321277456, 841520336, 2203938913, 5771607124, 15113503900, 39574147457, 103619424232, 271305096760, 710337809089, 1859792216588, 4869206612836, 12748163166241, 33375953974528, 87381040934624, 228769853183905, 598933887326212, 1568042546212972, 4105215226149185, 10747646081907544, 28137808918919368, 73665952473542401, 192860392099091516, 504915911018499508, 1321888715345941729, 3460752983798395120, 9060375733607382512, 23720385212140030177, 62100801893045263540, 162582064447460871484, 425645479410267572993, 1114354549705202291656, 2917418521549060190296, 7637901718629420055873, 19996288041714083530604, 52350965221262597642500, 137056613251573243610017, 358818885792456201613792, 939400066643793498083840, 2459381359174920566342689, 6438744100952960748354148, 16856851123827946773539596, 44131809630818849761904321, 115538578489204542891452728, 302483927277946659671012584, 791913206226939197638702465, 2073255697167478456279329692, 5427853896804711217267756372, 14210306016305085287660878945, 37203064198227404829988759504, 97398886670610849570853157648, 254993595998072584619666229601, 667581901692541785762336563476, 1747752109817422535615725525468, 4575674429235465346981604142209, 11979271180840452557122615159720, 31362139119188850427973297854072, 82107146188532014933971391436737, 214959299470019026788289102524620, 562770752268748730259592368274084, 1473352957430674493647880906571553, 3857288120212169409998836159988416, 10098511403583623054978199190489376, 26438246091294278392194904645671073, 69216226871810369396124801214906564, 181210434527159144345216071935814060, 474415076715711692737596560466066497, 1242034795632065192063719901209447192, 3251689310204662399845855726656398600, 8513033135030279040258432445747995649, 22287410094982888786498611944564082428, 58349197150111815450375744055897239796, 152760181355739413826905301559033613281, 399931346917880138554893523293015552688, 1047033859399448426886881993663636950064, 2741170231283559992203965908385143108065, 7176476834457421249921442632866287995252, 18788260272101083157953215792962712119932, 49188303981870587024723912351519830849025, 128776651673560195517789936472592745396104, 337141651038909034731788727488250335277208
Generating function in Maple syntax:
(x^7-3*x^5-3*x^3+8*x^2-5*x+1)/(x-1)/(2*x-1)/(x^2-3*x+1)
Generating function in latex syntax:
\frac{x^{7}-3 x^{5}-3 x^{3}+8 x^{2}-5 x +1}{\left(x -1\right) \left(2 x -1\right) \left(x^{2}-3 x +1\right)}
Generating function in sympy syntax:
(x**7 - 3*x**5 - 3*x**3 + 8*x**2 - 5*x + 1)/((x - 1)*(2*x - 1)*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
-(x-1)*(2*x-1)*(x^2-3*x+1)*F(x)+x^7-3*x^5-3*x^3+8*x^2-5*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x -1\right) \left(2 x -1\right) \left(x^{2}-3 x +1\right) F \! \left(x \right)+x^{7}-3 x^{5}-3 x^{3}+8 x^{2}-5 x +1 = 0
Explicit closed form in Maple syntax:
1/2*piecewise(n = 0,213/8,n = 1,45/4,n = 2,9/2,n = 3,1,0)-1+27/10*(3/2-1/2*5^(1/2))^(-n)*5^(1/2)-27/10*(3/2+1/2*5^(1/2))^(-n)*5^(1/2)-5/16*2^n-11/2*(3/2-1/2*5^(1/2))^(-n)-11/2*(3/2+1/2*5^(1/2))^(-n)
Explicit closed form in latex syntax:
\frac{\left(\left\{\begin{array}{cc}\frac{213}{8} & n =0 \\ \frac{45}{4} & n =1 \\ \frac{9}{2} & n =2 \\ 1 & n =3 \\ 0 & \mathit{\text{otherwise}} \end{array}\right.\right)}{2}-1+\frac{27 \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}}{10}-\frac{27 \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}}{10}-\frac{5 \,2^{n}}{16}-\frac{11 \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{2}-\frac{11 \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{2}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 55
a(6) = 152
a(7) = 412
a(n+3) = 2*a(n)-7*a(n+1)+5*a(n+2)-1, 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) = 55
a \! \left(6\right) = 152
a \! \left(7\right) = 412
a \! \left(n +3\right) = 2 a \! \left(n \right)-7 a \! \left(n +1\right)+5 a \! \left(n +2\right)-1, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/16714/
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[18,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[14,x]
F[18,x] = F[19,x]+F[56,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[1,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[16,x]*F[4,x]
F[25,x] = F[19,x]+F[26,x]
F[26,x] = F[27,x]+F[28,x]+F[54,x]
F[27,x] = 0
F[28,x] = F[29,x]*F[4,x]
F[29,x] = F[30,x]+F[34,x]
F[30,x] = F[23,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[4,x]
F[34,x] = F[26,x]+F[35,x]
F[35,x] = 2*F[27,x]+F[36,x]+F[40,x]
F[36,x] = F[37,x]*F[4,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[31,x]
F[39,x] = F[35,x]
F[40,x] = F[4,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[27,x]+F[43,x]+F[53,x]
F[43,x] = F[4,x]*F[44,x]
F[44,x] = F[45,x]+F[47,x]
F[45,x] = F[4,x]+F[46,x]
F[46,x] = F[32,x]
F[47,x] = F[42,x]+F[48,x]
F[48,x] = 2*F[27,x]+F[40,x]+F[49,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[46,x]
F[52,x] = F[48,x]
F[53,x] = F[19,x]*F[4,x]
F[54,x] = F[4,x]*F[55,x]
F[55,x] = F[19,x]+F[42,x]
F[56,x] = F[27,x]+F[57,x]+F[99,x]
F[57,x] = F[4,x]*F[58,x]
F[58,x] = F[59,x]+F[67,x]
F[59,x] = F[23,x]+F[60,x]
F[60,x] = F[27,x]+F[61,x]+F[65,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[4,x]+F[63,x]
F[63,x] = F[64,x]
F[64,x] = x^2
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[23,x]
F[67,x] = F[68,x]+F[91,x]
F[68,x] = F[27,x]+F[57,x]+F[69,x]
F[69,x] = F[4,x]*F[70,x]
F[70,x] = F[19,x]+F[71,x]
F[71,x] = F[27,x]+F[53,x]+F[72,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[74,x]+F[77,x]
F[74,x] = F[4,x]+F[75,x]
F[75,x] = F[27,x]+F[61,x]+F[76,x]
F[76,x] = F[23,x]*F[4,x]
F[77,x] = F[71,x]+F[78,x]
F[78,x] = F[27,x]+F[79,x]+F[86,x]+F[90,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[81,x]+F[82,x]
F[81,x] = F[46,x]
F[82,x] = F[83,x]
F[83,x] = 2*F[27,x]+F[79,x]+F[84,x]
F[84,x] = F[4,x]*F[85,x]
F[85,x] = F[71,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[71,x]+F[88,x]
F[88,x] = F[89,x]
F[89,x] = F[4,x]*F[42,x]
F[90,x] = F[26,x]*F[4,x]
F[91,x] = F[27,x]+F[86,x]+F[92,x]+F[97,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[94,x]+F[95,x]
F[94,x] = F[31,x]
F[95,x] = F[96,x]
F[96,x] = 2*F[27,x]+F[84,x]+F[92,x]
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[26,x]
F[99,x] = F[100,x]*F[4,x]
F[100,x] = F[101,x]+F[106,x]
F[101,x] = F[102,x]+F[19,x]
F[102,x] = F[103,x]+F[27,x]+F[72,x]
F[103,x] = F[104,x]*F[4,x]
F[104,x] = F[105,x]+F[19,x]
F[105,x] = F[103,x]+F[27,x]+F[43,x]
F[106,x] = F[107,x]
F[107,x] = F[108,x]+F[27,x]+F[28,x]
F[108,x] = F[109,x]*F[4,x]
F[109,x] = F[110,x]+F[55,x]
F[110,x] = F[107,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_{18}\! \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_{14}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{56}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{25}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{16}\! \left(x \right) F_{4}\! \left(x \right)
F_{25}\! \left(x \right) = F_{19}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)+F_{54}\! \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_{30}\! \left(x \right)+F_{34}\! \left(x \right)
F_{30}\! \left(x \right) = F_{23}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{26}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{36}\! \left(x \right)+F_{40}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{31}\! \left(x \right)
F_{39}\! \left(x \right) = F_{35}\! \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_{42}\! \left(x \right) = F_{27}\! \left(x \right)+F_{43}\! \left(x \right)+F_{53}\! \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_{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_{32}\! \left(x \right)
F_{47}\! \left(x \right) = F_{42}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{40}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{46}\! \left(x \right)
F_{52}\! \left(x \right) = F_{48}\! \left(x \right)
F_{53}\! \left(x \right) = F_{19}\! \left(x \right) F_{4}\! \left(x \right)
F_{54}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{19}\! \left(x \right)+F_{42}\! \left(x \right)
F_{56}\! \left(x \right) = F_{27}\! \left(x \right)+F_{57}\! \left(x \right)+F_{99}\! \left(x \right)
F_{57}\! \left(x \right) = F_{4}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{67}\! \left(x \right)
F_{59}\! \left(x \right) = F_{23}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{27}\! \left(x \right)+F_{61}\! \left(x \right)+F_{65}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \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_{64}\! \left(x \right) = x^{2}
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{23}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{91}\! \left(x \right)
F_{68}\! \left(x \right) = F_{27}\! \left(x \right)+F_{57}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{4}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{19}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{27}\! \left(x \right)+F_{53}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{77}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{27}\! \left(x \right)+F_{61}\! \left(x \right)+F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{23}\! \left(x \right) F_{4}\! \left(x \right)
F_{77}\! \left(x \right) = F_{71}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{27}\! \left(x \right)+F_{79}\! \left(x \right)+F_{86}\! \left(x \right)+F_{90}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)+F_{82}\! \left(x \right)
F_{81}\! \left(x \right) = F_{46}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{79}\! \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_{71}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{71}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{90}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{91}\! \left(x \right) = F_{27}\! \left(x \right)+F_{86}\! \left(x \right)+F_{92}\! \left(x \right)+F_{97}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{95}\! \left(x \right)
F_{94}\! \left(x \right) = F_{31}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = 2 F_{27}\! \left(x \right)+F_{84}\! \left(x \right)+F_{92}\! \left(x \right)
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{26}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{4}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{106}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{19}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{27}\! \left(x \right)+F_{72}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right) F_{4}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{19}\! \left(x \right)
F_{105}\! \left(x \right) = F_{103}\! \left(x \right)+F_{27}\! \left(x \right)+F_{43}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{55}\! \left(x \right)
F_{110}\! \left(x \right) = F_{107}\! \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_18(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_14(x))
Eq(F_18(x), F_19(x) + F_56(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_16(x)*F_4(x))
Eq(F_25(x), F_19(x) + F_26(x))
Eq(F_26(x), F_27(x) + F_28(x) + F_54(x))
Eq(F_27(x), 0)
Eq(F_28(x), F_29(x)*F_4(x))
Eq(F_29(x), F_30(x) + F_34(x))
Eq(F_30(x), F_23(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_4(x))
Eq(F_34(x), F_26(x) + F_35(x))
Eq(F_35(x), 2*F_27(x) + F_36(x) + F_40(x))
Eq(F_36(x), F_37(x)*F_4(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_31(x))
Eq(F_39(x), F_35(x))
Eq(F_40(x), F_4(x)*F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_27(x) + F_43(x) + F_53(x))
Eq(F_43(x), F_4(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_47(x))
Eq(F_45(x), F_4(x) + F_46(x))
Eq(F_46(x), F_32(x))
Eq(F_47(x), F_42(x) + F_48(x))
Eq(F_48(x), 2*F_27(x) + F_40(x) + F_49(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_46(x))
Eq(F_52(x), F_48(x))
Eq(F_53(x), F_19(x)*F_4(x))
Eq(F_54(x), F_4(x)*F_55(x))
Eq(F_55(x), F_19(x) + F_42(x))
Eq(F_56(x), F_27(x) + F_57(x) + F_99(x))
Eq(F_57(x), F_4(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_67(x))
Eq(F_59(x), F_23(x) + F_60(x))
Eq(F_60(x), F_27(x) + F_61(x) + F_65(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_4(x) + F_63(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), x**2)
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_23(x))
Eq(F_67(x), F_68(x) + F_91(x))
Eq(F_68(x), F_27(x) + F_57(x) + F_69(x))
Eq(F_69(x), F_4(x)*F_70(x))
Eq(F_70(x), F_19(x) + F_71(x))
Eq(F_71(x), F_27(x) + F_53(x) + F_72(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_77(x))
Eq(F_74(x), F_4(x) + F_75(x))
Eq(F_75(x), F_27(x) + F_61(x) + F_76(x))
Eq(F_76(x), F_23(x)*F_4(x))
Eq(F_77(x), F_71(x) + F_78(x))
Eq(F_78(x), F_27(x) + F_79(x) + F_86(x) + F_90(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_81(x) + F_82(x))
Eq(F_81(x), F_46(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), 2*F_27(x) + F_79(x) + F_84(x))
Eq(F_84(x), F_4(x)*F_85(x))
Eq(F_85(x), F_71(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_71(x) + F_88(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_4(x)*F_42(x))
Eq(F_90(x), F_26(x)*F_4(x))
Eq(F_91(x), F_27(x) + F_86(x) + F_92(x) + F_97(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_95(x))
Eq(F_94(x), F_31(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), 2*F_27(x) + F_84(x) + F_92(x))
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_26(x))
Eq(F_99(x), F_100(x)*F_4(x))
Eq(F_100(x), F_101(x) + F_106(x))
Eq(F_101(x), F_102(x) + F_19(x))
Eq(F_102(x), F_103(x) + F_27(x) + F_72(x))
Eq(F_103(x), F_104(x)*F_4(x))
Eq(F_104(x), F_105(x) + F_19(x))
Eq(F_105(x), F_103(x) + F_27(x) + F_43(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_108(x) + F_27(x) + F_28(x))
Eq(F_108(x), F_109(x)*F_4(x))
Eq(F_109(x), F_110(x) + F_55(x))
Eq(F_110(x), F_107(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, 2, 3], "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": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 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, 2, 3], "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": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 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, 2, 3], "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": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 2, 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, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [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": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [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, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"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", "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, 2], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [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": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [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, 2], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[1, 2], [1, 0], [1, 2], [1, 0]]}, {"patt": [3, 0, 2, 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, 1, 2], "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, 2, 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, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [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": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [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, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 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, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [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": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [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, 1], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 1], "pos": [[0, 1], [0, 0], [0, 1], [0, 0]]}, {"patt": [3, 0, 2, 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, 1, 2], "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, 2, 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, 2], "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, 2, 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": 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