0132_0213_1032_1302_3120
Counting sequence:
1, 1, 2, 6, 19, 53, 135, 323, 740, 1646, 3590, 7730, 16505, 35043, 74105, 156229, 328530, 689324, 1443424, 3016828, 6294287, 13110825, 27267547, 56628791, 117447504, 243278138, 503326730, 1040199638, 2147498165, 4429202111, 9126825485, 18790505145, 38654732510, 79456925848, 163208792580, 335007489344, 687194813035, 1408749324709, 2886218081039, 5909875064523, 12094627978492, 24739011706310, 50577534968142, 103354093111226, 211106232643889, 431008558210523, 879609302355425, 1794402976678253, 3659174697400490, 7459086883009476, 15199648742568680, 30962247438382660, 63050394783415815, 128352589380307553, 261208778387757955, 531424756030009759, 1080863910569233640, 2197756618157141394, 4467570830351897554, 9079256848779313118, 18446744073709973997, 37469948899722979895, 76092819304052386037, 154491481617318014561, 313594649253062933174, 636412670542980124208, 1291272085159669246220, 2619437658466757004168, 5312662293228351583715, 10772898539046378907741, 21840944983272109925175, 44272185776902924740275, 89724963174523259974420, 181811109590481341696158, 368344585663832327694230, 746133904293403944849474, 1511157274518286469530345, 3060093480899530099687379, 6195744825524974521648969, 12542605378501777688926613, 25387442211907212670252802, 51379347333621739926511580, 103967620486858109026309232, 210353092612945476400534796, 425541888504349469498319359, 860755183565615972392631193, 1740853180245066011578819115, 3520391986717800156746405383, 7118155225890936580672083840, 14391052956692545695704540906, 29091590923206436460131746970, 58802151866055563057710837990, 118842243771396506390318476325, 240160367621363773330432767663, 485272495399869067760459485405, 980448511114021177720109300489, 1980704062856608439838601803150, 4001022206970349048473972670664, 8081272576454962434541486251284, 16321001477938453544270057229008, 32958915605933964438914286946907
Generating function in Maple syntax:
-(6*x^8-12*x^7+17*x^6-30*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{6 x^{8}-12 x^{7}+17 x^{6}-30 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:
(-6*x**8 + 12*x**7 - 17*x**6 + 30*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)+6*x^8-12*x^7+17*x^6-30*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)+6 x^{8}-12 x^{7}+17 x^{6}-30 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),1,6-95/12*n+59/24*n^2-7/12*n^3+1/24*n^4+1/4*2^n*n+2^n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 6-\frac{95 n}{12}+\frac{59 n^{2}}{24}-\frac{7 n^{3}}{12}+\frac{n^{4}}{24}+\frac{2^{n} n}{4}+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) = 53
a(6) = 135
a(7) = 323
a(8) = 740
a(n+2) = -4*a(n)+4*a(n+1)+1/24*(n^2-17*n+48)*(n^2-5*n+10), 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) = 53
a \! \left(6\right) = 135
a \! \left(7\right) = 323
a \! \left(8\right) = 740
a \! \left(n +2\right) = -4 a \! \left(n \right)+4 a \! \left(n +1\right)+\frac{\left(n^{2}-17 n +48\right) \left(n^{2}-5 n +10\right)}{24}, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/21615/
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[10,x]*F[4,x]
F[4,x] = F[19,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[10,x]*F[8,x]
F[8,x] = F[5,x]+F[9,x]
F[9,x] = F[10,x]*F[11,x]*F[13,x]
F[10,x] = x
F[11,x] = 2*F[12,x]+F[1,x]
F[12,x] = F[10,x]*F[11,x]
F[13,x] = F[1,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[10,x]*F[13,x]*F[16,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[10,x]*F[16,x]
F[19,x] = F[20,x]
F[20,x] = F[10,x]*F[21,x]
F[21,x] = F[22,x]+F[39,x]
F[22,x] = F[23,x]
F[23,x] = F[13,x]*F[24,x]
F[24,x] = F[25,x]+F[26,x]
F[25,x] = F[1,x]+F[12,x]
F[26,x] = F[27,x]+F[29,x]
F[27,x] = F[28,x]
F[28,x] = F[10,x]*F[24,x]
F[29,x] = F[10,x]*F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[10,x]*F[32,x]
F[32,x] = F[16,x]+F[33,x]
F[33,x] = F[34,x]+F[37,x]
F[34,x] = F[35,x]
F[35,x] = F[10,x]*F[36,x]
F[36,x] = F[1,x]+F[34,x]
F[37,x] = F[38,x]
F[38,x] = F[10,x]*F[33,x]
F[39,x] = F[16,x]*F[40,x]
F[40,x] = F[41,x]+F[83,x]
F[41,x] = F[10,x]+F[42,x]
F[42,x] = F[29,x]+F[43,x]+F[44,x]
F[43,x] = 0
F[44,x] = F[10,x]*F[45,x]
F[45,x] = F[46,x]+F[60,x]
F[46,x] = F[10,x]+F[47,x]
F[47,x] = F[43,x]+F[48,x]+F[49,x]
F[48,x] = F[10,x]*F[17,x]
F[49,x] = F[10,x]*F[50,x]
F[50,x] = F[51,x]+F[54,x]
F[51,x] = F[10,x]+F[52,x]
F[52,x] = F[43,x]+F[48,x]+F[53,x]
F[53,x] = F[10,x]*F[51,x]
F[54,x] = F[55,x]+F[58,x]
F[55,x] = F[56,x]
F[56,x] = F[10,x]*F[57,x]
F[57,x] = F[10,x]+F[55,x]
F[58,x] = F[59,x]
F[59,x] = F[10,x]*F[54,x]
F[60,x] = F[61,x]+F[65,x]
F[61,x] = F[43,x]+F[62,x]+F[63,x]
F[62,x] = F[10,x]*F[34,x]
F[63,x] = F[10,x]*F[64,x]
F[64,x] = F[10,x]+F[61,x]
F[65,x] = F[43,x]+F[66,x]+F[70,x]+F[75,x]
F[66,x] = F[10,x]*F[67,x]
F[67,x] = F[38,x]+F[43,x]+F[68,x]
F[68,x] = F[10,x]*F[69,x]
F[69,x] = F[17,x]+F[37,x]
F[70,x] = F[10,x]*F[71,x]
F[71,x] = F[52,x]+F[72,x]
F[72,x] = F[43,x]+F[66,x]+F[70,x]+F[73,x]
F[73,x] = F[10,x]*F[74,x]
F[74,x] = F[61,x]+F[72,x]
F[75,x] = F[10,x]*F[76,x]
F[76,x] = F[74,x]+F[77,x]
F[77,x] = F[78,x]+F[81,x]
F[78,x] = F[79,x]
F[79,x] = F[10,x]*F[80,x]
F[80,x] = F[61,x]+F[78,x]
F[81,x] = F[82,x]
F[82,x] = F[10,x]*F[77,x]
F[83,x] = F[84,x]
F[84,x] = F[43,x]+F[48,x]+F[85,x]
F[85,x] = F[10,x]*F[86,x]
F[86,x] = F[51,x]+F[87,x]
F[87,x] = F[88,x]+F[92,x]
F[88,x] = F[43,x]+F[89,x]+F[90,x]
F[89,x] = x^2
F[90,x] = F[10,x]*F[91,x]
F[91,x] = F[10,x]+F[88,x]
F[92,x] = F[43,x]+F[93,x]+F[95,x]+F[97,x]
F[93,x] = F[10,x]*F[94,x]
F[94,x] = F[48,x]
F[95,x] = F[10,x]*F[96,x]
F[96,x] = F[52,x]+F[92,x]
F[97,x] = F[10,x]*F[87,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_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{19}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{10}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{5}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right) F_{13}\! \left(x \right)
F_{10}\! \left(x \right) = x
F_{11}\! \left(x \right) = 2 F_{12}\! \left(x \right)+F_{1}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \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_{10}\! \left(x \right) F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{10}\! \left(x \right) F_{16}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{10}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{39}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{13}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{26}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{29}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{10}\! \left(x \right) F_{24}\! \left(x \right)
F_{29}\! \left(x \right) = F_{10}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{10}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{16}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{10}\! \left(x \right) F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{1}\! \left(x \right)+F_{34}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{10}\! \left(x \right) F_{33}\! \left(x \right)
F_{39}\! \left(x \right) = F_{16}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{83}\! \left(x \right)
F_{41}\! \left(x \right) = F_{10}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{29}\! \left(x \right)+F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = 0
F_{44}\! \left(x \right) = F_{10}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{60}\! \left(x \right)
F_{46}\! \left(x \right) = F_{10}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{43}\! \left(x \right)+F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = F_{10}\! \left(x \right) F_{17}\! \left(x \right)
F_{49}\! \left(x \right) = F_{10}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{54}\! \left(x \right)
F_{51}\! \left(x \right) = F_{10}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{43}\! \left(x \right)+F_{48}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{10}\! \left(x \right) F_{51}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{58}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{10}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{10}\! \left(x \right)+F_{55}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{10}\! \left(x \right) F_{54}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{65}\! \left(x \right)
F_{61}\! \left(x \right) = F_{43}\! \left(x \right)+F_{62}\! \left(x \right)+F_{63}\! \left(x \right)
F_{62}\! \left(x \right) = F_{10}\! \left(x \right) F_{34}\! \left(x \right)
F_{63}\! \left(x \right) = F_{10}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{10}\! \left(x \right)+F_{61}\! \left(x \right)
F_{65}\! \left(x \right) = F_{43}\! \left(x \right)+F_{66}\! \left(x \right)+F_{70}\! \left(x \right)+F_{75}\! \left(x \right)
F_{66}\! \left(x \right) = F_{10}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{38}\! \left(x \right)+F_{43}\! \left(x \right)+F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{10}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{17}\! \left(x \right)+F_{37}\! \left(x \right)
F_{70}\! \left(x \right) = F_{10}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{52}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{43}\! \left(x \right)+F_{66}\! \left(x \right)+F_{70}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{10}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{61}\! \left(x \right)+F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{10}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{74}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{81}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{10}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{61}\! \left(x \right)+F_{78}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{10}\! \left(x \right) F_{77}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{43}\! \left(x \right)+F_{48}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{10}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{51}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)+F_{92}\! \left(x \right)
F_{88}\! \left(x \right) = F_{43}\! \left(x \right)+F_{89}\! \left(x \right)+F_{90}\! \left(x \right)
F_{89}\! \left(x \right) = x^{2}
F_{90}\! \left(x \right) = F_{10}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{10}\! \left(x \right)+F_{88}\! \left(x \right)
F_{92}\! \left(x \right) = F_{43}\! \left(x \right)+F_{93}\! \left(x \right)+F_{95}\! \left(x \right)+F_{97}\! \left(x \right)
F_{93}\! \left(x \right) = F_{10}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{48}\! \left(x \right)
F_{95}\! \left(x \right) = F_{10}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{52}\! \left(x \right)+F_{92}\! \left(x \right)
F_{97}\! \left(x \right) = F_{10}\! \left(x \right) F_{87}\! \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_10(x)*F_4(x))
Eq(F_4(x), F_19(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_10(x)*F_8(x))
Eq(F_8(x), F_5(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_11(x)*F_13(x))
Eq(F_10(x), x)
Eq(F_11(x), F_1(x) + 2*F_12(x))
Eq(F_12(x), F_10(x)*F_11(x))
Eq(F_13(x), F_1(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_10(x)*F_13(x)*F_16(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_10(x)*F_16(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_10(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_39(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_13(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_26(x))
Eq(F_25(x), F_1(x) + F_12(x))
Eq(F_26(x), F_27(x) + F_29(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_10(x)*F_24(x))
Eq(F_29(x), F_10(x)*F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_10(x)*F_32(x))
Eq(F_32(x), F_16(x) + F_33(x))
Eq(F_33(x), F_34(x) + F_37(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_10(x)*F_36(x))
Eq(F_36(x), F_1(x) + F_34(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_10(x)*F_33(x))
Eq(F_39(x), F_16(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_83(x))
Eq(F_41(x), F_10(x) + F_42(x))
Eq(F_42(x), F_29(x) + F_43(x) + F_44(x))
Eq(F_43(x), 0)
Eq(F_44(x), F_10(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_60(x))
Eq(F_46(x), F_10(x) + F_47(x))
Eq(F_47(x), F_43(x) + F_48(x) + F_49(x))
Eq(F_48(x), F_10(x)*F_17(x))
Eq(F_49(x), F_10(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_54(x))
Eq(F_51(x), F_10(x) + F_52(x))
Eq(F_52(x), F_43(x) + F_48(x) + F_53(x))
Eq(F_53(x), F_10(x)*F_51(x))
Eq(F_54(x), F_55(x) + F_58(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_10(x)*F_57(x))
Eq(F_57(x), F_10(x) + F_55(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_10(x)*F_54(x))
Eq(F_60(x), F_61(x) + F_65(x))
Eq(F_61(x), F_43(x) + F_62(x) + F_63(x))
Eq(F_62(x), F_10(x)*F_34(x))
Eq(F_63(x), F_10(x)*F_64(x))
Eq(F_64(x), F_10(x) + F_61(x))
Eq(F_65(x), F_43(x) + F_66(x) + F_70(x) + F_75(x))
Eq(F_66(x), F_10(x)*F_67(x))
Eq(F_67(x), F_38(x) + F_43(x) + F_68(x))
Eq(F_68(x), F_10(x)*F_69(x))
Eq(F_69(x), F_17(x) + F_37(x))
Eq(F_70(x), F_10(x)*F_71(x))
Eq(F_71(x), F_52(x) + F_72(x))
Eq(F_72(x), F_43(x) + F_66(x) + F_70(x) + F_73(x))
Eq(F_73(x), F_10(x)*F_74(x))
Eq(F_74(x), F_61(x) + F_72(x))
Eq(F_75(x), F_10(x)*F_76(x))
Eq(F_76(x), F_74(x) + F_77(x))
Eq(F_77(x), F_78(x) + F_81(x))
Eq(F_78(x), F_79(x))
Eq(F_79(x), F_10(x)*F_80(x))
Eq(F_80(x), F_61(x) + F_78(x))
Eq(F_81(x), F_82(x))
Eq(F_82(x), F_10(x)*F_77(x))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_43(x) + F_48(x) + F_85(x))
Eq(F_85(x), F_10(x)*F_86(x))
Eq(F_86(x), F_51(x) + F_87(x))
Eq(F_87(x), F_88(x) + F_92(x))
Eq(F_88(x), F_43(x) + F_89(x) + F_90(x))
Eq(F_89(x), x**2)
Eq(F_90(x), F_10(x)*F_91(x))
Eq(F_91(x), F_10(x) + F_88(x))
Eq(F_92(x), F_43(x) + F_93(x) + F_95(x) + F_97(x))
Eq(F_93(x), F_10(x)*F_94(x))
Eq(F_94(x), F_48(x))
Eq(F_95(x), F_10(x)*F_96(x))
Eq(F_96(x), F_52(x) + F_92(x))
Eq(F_97(x), F_10(x)*F_87(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, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 0], [0, 1], [0, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 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0], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 3]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 0], [0, 3]]}, {"patt": [1, 0, 2], "pos": [[0, 2], [0, 2], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 3], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 0], [0, 3], [0, 3]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 3], [0, 3], [0, 0], [0, 3]]}], "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": [[0, 3]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 4]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0], "pos": [[2, 4]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 4], [0, 2]]}, {"patt": [1, 0], "pos": [[1, 3], [1, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 4]]}, {"patt": [0, 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