0213_1230_1320

Counting sequence:
1, 1, 2, 6, 21, 75, 261, 876, 2840, 8934, 27399, 82259, 242599, 704816, 2021818, 5737262, 16130049, 44987495, 124605577, 343054192, 939500948, 2561068834, 6953035595, 18808871815, 50718209107, 136374159436, 365764426574, 978789473778, 2613956517357, 6968175570675, 18545187443853, 49283931344148, 130798876407056, 346723177338174, 918103211701071, 2428701777860891, 6419046922545535, 16951811414923976, 44734520570570530, 117972093593260694, 310922023159513305, 818997800019855455, 2156225335433460049, 5674202316987727384, 14925609084244973324, 39245655660931403194, 103156752370749175187, 271058636625179254927, 712033062129365904043, 1869903291387424483876, 4909418029493845534646, 12886699703183935537050, 33819127709522917085253, 88735941071528270239275, 232787688952011150275925, 610590434500841838425340, 1601309356034526131061512, 4198952690999474759578134, 11009105113673341607831703, 28861091599714484267454563, 75653186215352838237531991, 198289233595431843124138976, 519675073422373080390655882, 1361847889658610439099631486, 3568552998425144360293565361, 9350291891592858738262268375, 24497968807974514797372162841, 64181387899755222907583035456, 168137388403397353955547803780, 440450939011792605506509076434, 1153746948203129342303223119579, 3022073111827698216952285442839, 7915570330231792271027181780739, 20732116993137528205076944142716, 54298836865534800111834197235998, 142207985241350292069875095349442, 372430358534809216576236694303389, 975337161726614010701877618208995, 2554194509803977899353070261302557, 6688727206896793248497489047542372, 17515562175566166465005870006175488, 45866590294644011634644111946317934, 120105045735423965139994527242711775, 314498851966276056342410453539524395, 823512957351742455945875916813574447, 2156333219625452534476039185733769336, 5646194547998726789754699236238874354, 14783959317285829934096603589713104358, 38709809037033505443547192268000527497, 101355427954839469351236579829591098575, 265380520786268288563503309476813080033, 694844186489752477678992752576082545128, 1819292188827892488567857736688008383996, 4763370732398919833486093219865178868074, 12471636863383181168793528489293732534051, 32653511920304327015972900029830878672671, 85493659877894156969885028264095056022875, 223838961737150785673837316460921507605076, 586050974362458192734125345399419355128710, 1534380953433796930777175874521540537408874, 4017253619139019505065402493231630846157045

Generating function in Maple syntax:
-(7*x^5+3*x^4-25*x^3+23*x^2-8*x+1)/(x^2+2*x-1)/(x^2-3*x+1)/(2*x-1)^2

Generating function in latex syntax:
-\frac{7 x^{5}+3 x^{4}-25 x^{3}+23 x^{2}-8 x +1}{\left(x^{2}+2 x -1\right) \left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2}}

Generating function in sympy syntax:
(-7*x**5 - 3*x**4 + 25*x**3 - 23*x**2 + 8*x - 1)/((2*x - 1)**2*(x**2 - 3*x + 1)*(x**2 + 2*x - 1))

Implicit equation for the generating function in Maple syntax:
(x^2+2*x-1)*(x^2-3*x+1)*(2*x-1)^2*F(x)+7*x^5+3*x^4-25*x^3+23*x^2-8*x+1 = 0

Implicit equation for the generating function in latex syntax:
\left(x^{2}+2 x -1\right) \left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} F \! \left(x \right)+7 x^{5}+3 x^{4}-25 x^{3}+23 x^{2}-8 x +1 = 0

Explicit closed form in Maple syntax:
1/20*(26*5^(1/2)+70)*(3/2-1/2*5^(1/2))^(-n)+1/20*(-26*5^(1/2)+70)*(3/2+1/2*5^(1/2))^(-n)+1/20*(85*2^(1/2)-120)*(-1-2^(1/2))^(-n)+1/20*(-85*2^(1/2)-120)*(2^(1/2)-1)^(-n)+2^(n-1)*n+6*2^n

Explicit closed form in latex syntax:
\frac{\left(26 \sqrt{5}+70\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{20}+\frac{\left(-26 \sqrt{5}+70\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{20}+\frac{\left(85 \sqrt{2}-120\right) \left(-1-\sqrt{2}\right)^{-n}}{20}+\frac{\left(-85 \sqrt{2}-120\right) \left(\sqrt{2}-1\right)^{-n}}{20}+2^{n -1} n +6 \,2^{n}

Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 75
a(n+6) = 4*a(n)-8*a(n+1)-19*a(n+2)+43*a(n+3)-30*a(n+4)+9*a(n+5), n >= 6

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) = 21
a \! \left(5\right) = 75
a \! \left(n +6\right) = 4 a \! \left(n \right)-8 a \! \left(n +1\right)-19 a \! \left(n +2\right)+43 a \! \left(n +3\right)-30 a \! \left(n +4\right)+9 a \! \left(n +5\right), \quad n \geq 6

Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/328/
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[19,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[19,x]*F[7,x]
F[7,x] = F[103,x]+F[8,x]
F[8,x] = F[4,x]+F[9,x]
F[9,x] = F[10,x]*F[95,x]
F[10,x] = F[11,x]+F[21,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[19,x]
F[14,x] = F[11,x]+F[15,x]
F[15,x] = F[12,x]+F[16,x]
F[16,x] = F[12,x]*F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[20,x]
F[19,x] = x
F[20,x] = F[1,x]+F[18,x]
F[21,x] = F[12,x]+F[22,x]
F[22,x] = F[23,x]+F[24,x]+F[65,x]
F[23,x] = 0
F[24,x] = F[19,x]*F[25,x]
F[25,x] = F[26,x]+F[32,x]
F[26,x] = F[27,x]+F[30,x]
F[27,x] = F[28,x]
F[28,x] = F[19,x]*F[29,x]
F[29,x] = F[1,x]+F[27,x]
F[30,x] = F[31,x]
F[31,x] = F[19,x]*F[26,x]
F[32,x] = F[33,x]+F[51,x]
F[33,x] = F[23,x]+F[34,x]+F[46,x]
F[34,x] = F[19,x]*F[35,x]
F[35,x] = F[36,x]+F[39,x]
F[36,x] = F[27,x]+F[37,x]
F[37,x] = F[38,x]
F[38,x] = F[19,x]*F[27,x]
F[39,x] = F[33,x]+F[40,x]
F[40,x] = 2*F[23,x]+F[41,x]+F[45,x]
F[41,x] = F[19,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[37,x]
F[44,x] = F[40,x]
F[45,x] = F[19,x]*F[33,x]
F[46,x] = F[19,x]*F[47,x]
F[47,x] = F[17,x]+F[48,x]
F[48,x] = F[23,x]+F[46,x]+F[49,x]
F[49,x] = F[19,x]*F[50,x]
F[50,x] = F[27,x]+F[48,x]
F[51,x] = 2*F[23,x]+F[52,x]+F[64,x]
F[52,x] = F[19,x]*F[53,x]
F[53,x] = F[54,x]+F[57,x]
F[54,x] = F[30,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[19,x]*F[30,x]
F[57,x] = F[51,x]+F[58,x]
F[58,x] = 3*F[23,x]+F[59,x]+F[63,x]
F[59,x] = F[19,x]*F[60,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[55,x]
F[62,x] = F[58,x]
F[63,x] = F[19,x]*F[51,x]
F[64,x] = F[19,x]*F[32,x]
F[65,x] = F[19,x]*F[66,x]
F[66,x] = F[47,x]+F[67,x]
F[67,x] = F[68,x]+F[81,x]
F[68,x] = F[69,x]
F[69,x] = F[19,x]*F[70,x]
F[70,x] = F[71,x]+F[74,x]
F[71,x] = F[17,x]+F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[17,x]*F[19,x]
F[74,x] = F[68,x]+F[75,x]
F[75,x] = 2*F[23,x]+F[76,x]+F[80,x]
F[76,x] = F[19,x]*F[77,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[72,x]
F[79,x] = F[75,x]
F[80,x] = F[19,x]*F[68,x]
F[81,x] = 2*F[23,x]+F[82,x]+F[94,x]
F[82,x] = F[19,x]*F[83,x]
F[83,x] = F[84,x]+F[87,x]
F[84,x] = F[48,x]+F[85,x]
F[85,x] = F[86,x]
F[86,x] = F[19,x]*F[48,x]
F[87,x] = F[81,x]+F[88,x]
F[88,x] = 3*F[23,x]+F[89,x]+F[93,x]
F[89,x] = F[19,x]*F[90,x]
F[90,x] = F[91,x]+F[92,x]
F[91,x] = F[85,x]
F[92,x] = F[88,x]
F[93,x] = F[19,x]*F[81,x]
F[94,x] = F[19,x]*F[67,x]
F[95,x] = F[96,x]
F[96,x] = F[19,x]*F[97,x]
F[97,x] = F[98,x]+F[99,x]
F[98,x] = F[1,x]+F[95,x]
F[99,x] = F[100,x]+F[95,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[19,x]
F[102,x] = F[95,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[15,x]
F[105,x] = F[95,x]+F[98,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_{19}\! \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_{19}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{103}\! \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_{95}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{21}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{14}\! \left(x \right) = F_{11}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{20}\! \left(x \right)
F_{19}\! \left(x \right) = x
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{18}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right)+F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{24}\! \left(x \right)+F_{65}\! \left(x \right)
F_{23}\! \left(x \right) = 0
F_{24}\! \left(x \right) = F_{19}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{32}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{30}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{19}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{19}\! \left(x \right) F_{26}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{51}\! \left(x \right)
F_{33}\! \left(x \right) = F_{23}\! \left(x \right)+F_{34}\! \left(x \right)+F_{46}\! \left(x \right)
F_{34}\! \left(x \right) = F_{19}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{27}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{19}\! \left(x \right) F_{27}\! \left(x \right)
F_{39}\! \left(x \right) = F_{33}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{41}\! \left(x \right)+F_{45}\! \left(x \right)
F_{41}\! \left(x \right) = F_{19}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{37}\! \left(x \right)
F_{44}\! \left(x \right) = F_{40}\! \left(x \right)
F_{45}\! \left(x \right) = F_{19}\! \left(x \right) F_{33}\! \left(x \right)
F_{46}\! \left(x \right) = F_{19}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{17}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{23}\! \left(x \right)+F_{46}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{19}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{27}\! \left(x \right)+F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{52}\! \left(x \right)+F_{64}\! \left(x \right)
F_{52}\! \left(x \right) = F_{19}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{57}\! \left(x \right)
F_{54}\! \left(x \right) = F_{30}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{19}\! \left(x \right) F_{30}\! \left(x \right)
F_{57}\! \left(x \right) = F_{51}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = 3 F_{23}\! \left(x \right)+F_{59}\! \left(x \right)+F_{63}\! \left(x \right)
F_{59}\! \left(x \right) = F_{19}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{55}\! \left(x \right)
F_{62}\! \left(x \right) = F_{58}\! \left(x \right)
F_{63}\! \left(x \right) = F_{19}\! \left(x \right) F_{51}\! \left(x \right)
F_{64}\! \left(x \right) = F_{19}\! \left(x \right) F_{32}\! \left(x \right)
F_{65}\! \left(x \right) = F_{19}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{47}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{81}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{19}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{74}\! \left(x \right)
F_{71}\! \left(x \right) = F_{17}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{17}\! \left(x \right) F_{19}\! \left(x \right)
F_{74}\! \left(x \right) = F_{68}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{76}\! \left(x \right)+F_{80}\! \left(x \right)
F_{76}\! \left(x \right) = F_{19}\! \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_{72}\! \left(x \right)
F_{79}\! \left(x \right) = F_{75}\! \left(x \right)
F_{80}\! \left(x \right) = F_{19}\! \left(x \right) F_{68}\! \left(x \right)
F_{81}\! \left(x \right) = 2 F_{23}\! \left(x \right)+F_{82}\! \left(x \right)+F_{94}\! \left(x \right)
F_{82}\! \left(x \right) = F_{19}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{87}\! \left(x \right)
F_{84}\! \left(x \right) = F_{48}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{19}\! \left(x \right) F_{48}\! \left(x \right)
F_{87}\! \left(x \right) = F_{81}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = 3 F_{23}\! \left(x \right)+F_{89}\! \left(x \right)+F_{93}\! \left(x \right)
F_{89}\! \left(x \right) = F_{19}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{91}\! \left(x \right) = F_{85}\! \left(x \right)
F_{92}\! \left(x \right) = F_{88}\! \left(x \right)
F_{93}\! \left(x \right) = F_{19}\! \left(x \right) F_{81}\! \left(x \right)
F_{94}\! \left(x \right) = F_{19}\! \left(x \right) F_{67}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{19}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)+F_{99}\! \left(x \right)
F_{98}\! \left(x \right) = F_{1}\! \left(x \right)+F_{95}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{95}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{19}\! \left(x \right)
F_{102}\! \left(x \right) = F_{95}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{15}\! \left(x \right)
F_{105}\! \left(x \right) = F_{95}\! \left(x \right)+F_{98}\! \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_19(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_19(x)*F_7(x))
Eq(F_7(x), F_103(x) + F_8(x))
Eq(F_8(x), F_4(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_95(x))
Eq(F_10(x), F_11(x) + F_21(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_19(x))
Eq(F_14(x), F_11(x) + F_15(x))
Eq(F_15(x), F_12(x) + F_16(x))
Eq(F_16(x), F_12(x)*F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_20(x))
Eq(F_19(x), x)
Eq(F_20(x), F_1(x) + F_18(x))
Eq(F_21(x), F_12(x) + F_22(x))
Eq(F_22(x), F_23(x) + F_24(x) + F_65(x))
Eq(F_23(x), 0)
Eq(F_24(x), F_19(x)*F_25(x))
Eq(F_25(x), F_26(x) + F_32(x))
Eq(F_26(x), F_27(x) + F_30(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_19(x)*F_29(x))
Eq(F_29(x), F_1(x) + F_27(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_19(x)*F_26(x))
Eq(F_32(x), F_33(x) + F_51(x))
Eq(F_33(x), F_23(x) + F_34(x) + F_46(x))
Eq(F_34(x), F_19(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_39(x))
Eq(F_36(x), F_27(x) + F_37(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_19(x)*F_27(x))
Eq(F_39(x), F_33(x) + F_40(x))
Eq(F_40(x), 2*F_23(x) + F_41(x) + F_45(x))
Eq(F_41(x), F_19(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_37(x))
Eq(F_44(x), F_40(x))
Eq(F_45(x), F_19(x)*F_33(x))
Eq(F_46(x), F_19(x)*F_47(x))
Eq(F_47(x), F_17(x) + F_48(x))
Eq(F_48(x), F_23(x) + F_46(x) + F_49(x))
Eq(F_49(x), F_19(x)*F_50(x))
Eq(F_50(x), F_27(x) + F_48(x))
Eq(F_51(x), 2*F_23(x) + F_52(x) + F_64(x))
Eq(F_52(x), F_19(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_57(x))
Eq(F_54(x), F_30(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_19(x)*F_30(x))
Eq(F_57(x), F_51(x) + F_58(x))
Eq(F_58(x), 3*F_23(x) + F_59(x) + F_63(x))
Eq(F_59(x), F_19(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_55(x))
Eq(F_62(x), F_58(x))
Eq(F_63(x), F_19(x)*F_51(x))
Eq(F_64(x), F_19(x)*F_32(x))
Eq(F_65(x), F_19(x)*F_66(x))
Eq(F_66(x), F_47(x) + F_67(x))
Eq(F_67(x), F_68(x) + F_81(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_19(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_74(x))
Eq(F_71(x), F_17(x) + F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_17(x)*F_19(x))
Eq(F_74(x), F_68(x) + F_75(x))
Eq(F_75(x), 2*F_23(x) + F_76(x) + F_80(x))
Eq(F_76(x), F_19(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_72(x))
Eq(F_79(x), F_75(x))
Eq(F_80(x), F_19(x)*F_68(x))
Eq(F_81(x), 2*F_23(x) + F_82(x) + F_94(x))
Eq(F_82(x), F_19(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_87(x))
Eq(F_84(x), F_48(x) + F_85(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_19(x)*F_48(x))
Eq(F_87(x), F_81(x) + F_88(x))
Eq(F_88(x), 3*F_23(x) + F_89(x) + F_93(x))
Eq(F_89(x), F_19(x)*F_90(x))
Eq(F_90(x), F_91(x) + F_92(x))
Eq(F_91(x), F_85(x))
Eq(F_92(x), F_88(x))
Eq(F_93(x), F_19(x)*F_81(x))
Eq(F_94(x), F_19(x)*F_67(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_19(x)*F_97(x))
Eq(F_97(x), F_98(x) + F_99(x))
Eq(F_98(x), F_1(x) + F_95(x))
Eq(F_99(x), F_100(x) + F_95(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_19(x))
Eq(F_102(x), F_95(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_15(x))
Eq(F_105(x), F_95(x) + F_98(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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 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"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[2, 0], [2, 0], [2, 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}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 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1], [3, 1], [3, 1], [3, 1]]}], "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, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0], "pos": [[3, 2]]}, {"patt": [0], "pos": [[4, 0]]}, {"patt": [0], "pos": [[4, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[0, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [3, 0], [4, 2]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[4, 2], [4, 2], [4, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [2, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [3, 0], [4, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [3, 0], [3, 0], [4, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[3, 0], [3, 0], [3, 0], [4, 2]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[3, 0], [3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 3, 0], 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