0132_0213_1230_1320
Counting sequence:
1, 1, 2, 6, 20, 65, 198, 567, 1549, 4097, 10617, 27196, 69291, 176322, 449254, 1147708, 2941586, 7564515, 19513804, 50479193, 130893499, 340084051, 885032087, 2306209766, 6015750345, 15704955580, 41026310348, 107227335942, 280360755464, 733262355077, 1918236803682, 5019061996011, 13134165660121, 34373849482517, 89968181924709, 235492246252288, 616431578579031, 1613648406488550, 4224205270227874, 11058350331719488, 28949611044153134, 75788012572198551, 198409484812544872, 519430555875837101, 1359862407163147495, 3560117108367540295, 9320409793832292323, 24400954009357493642, 63882135681523967829, 167244819889051949632, 437851057627404404072, 1146305820170073730026, 3001061337064106582276, 7856868059105657888537, 20569522575967987963614, 53851659139497677174943, 140985373782741212451301, 369104300087244853911785, 966327202232935119242769, 2529876658114434582175108, 6623301475108011304929219, 17340025173191769747271626, 45396768856410418346493982, 118850271019891390751077636, 311154023450912009044408970, 814611757828051255517069835, 2132681167023509548856151748, 5583431577222777635689172417, 14617613232605043062505528019, 38269407456512174837373403387, 100190607808770131112682914287, 262302413313473904795745712366, 686716626819000345925605118881, 1797847456518220435313015488132, 4706825721485040731768087227844, 12322629665435650247621136198798, 32261063189819389097566453800896, 84460559734017446273352440724845, 221120615672222761345582602489114, 578901286602630385231454088694803, 1515583242775627366673315664286129, 3967848439004169461047858716043901, 10387962068796716187987704474881917, 27196037756505648926559148868439496, 71200151178959569398585248995142895, 186404415736851735523204336569187950, 488013095944552987478867680884625498, 1277634871922721923969119714419680392, 3344891519475442172779799090302778534, 8757039685807263361752799591594331967, 22926227536553665432163416145198889952, 60021642921068367949706760935195941781, 157138701221080708407414942403039709311, 411394460731032297189573348489244546927, 1077044680949733262892014249785620019899, 2819739582073601650780645407329770856978, 7382174065181940007767670280438589760941, 19326782613293955008720016058786682521480, 50598173774343398290079229449164302178784, 132467738709023186403745079707164278611698, 346805042351300054003756079124858484866364
Generating function in Maple syntax:
-(x^8+3*x^7-14*x^6+5*x^5+20*x^4-36*x^3+25*x^2-8*x+1)/(2*x-1)/(x^2-3*x+1)/(x^2+x-1)/(x-1)^3
Generating function in latex syntax:
-\frac{x^{8}+3 x^{7}-14 x^{6}+5 x^{5}+20 x^{4}-36 x^{3}+25 x^{2}-8 x +1}{\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x^{2}+x -1\right) \left(x -1\right)^{3}}
Generating function in sympy syntax:
(-x**8 - 3*x**7 + 14*x**6 - 5*x**5 - 20*x**4 + 36*x**3 - 25*x**2 + 8*x - 1)/((x - 1)**3*(2*x - 1)*(x**2 - 3*x + 1)*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x^2-3*x+1)*(x^2+x-1)*(x-1)^3*F(x)+x^8+3*x^7-14*x^6+5*x^5+20*x^4-36*x^3+25*x^2-8*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x^{2}-3 x +1\right) \left(x^{2}+x -1\right) \left(x -1\right)^{3} F \! \left(x \right)+x^{8}+3 x^{7}-14 x^{6}+5 x^{5}+20 x^{4}-36 x^{3}+25 x^{2}-8 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/10*(-2*5^(1/2)+10)*(3/2-1/2*5^(1/2))^(-n)+1/10*(2*5^(1/2)+10)*(3/2+1/2*5^(1/2))^(-n)+1/10*(47*5^(1/2)-105)*(-1/2*5^(1/2)-1/2)^(-n)+1/10*(-47*5^(1/2)-105)*(1/2*5^(1/2)-1/2)^(-n)+3/2*n^2+13/2*n+9*2^(n-1)+16)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(-2 \sqrt{5}+10\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{10}+\frac{\left(2 \sqrt{5}+10\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{10}+\\\frac{\left(47 \sqrt{5}-105\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{10}+\frac{\left(-47 \sqrt{5}-105\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{10}+\frac{3 n^{2}}{2}+\\\frac{13 n}{2}+9 \,2^{n -1}+16 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 65
a(6) = 198
a(7) = 567
a(8) = 1549
a(n+5) = -3/2*n^2-11*a(n+3)+6*a(n+4)-2*a(n)+5*a(n+1)+4*a(n+2)-7/2*n+1, 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) = 20
a \! \left(5\right) = 65
a \! \left(6\right) = 198
a \! \left(7\right) = 567
a \! \left(8\right) = 1549
a \! \left(n +5\right) = -\frac{3 n^{2}}{2}-11 a \! \left(n +3\right)+6 a \! \left(n +4\right)-2 a \! \left(n \right)+5 a \! \left(n +1\right)+4 a \! \left(n +2\right)-\frac{7 n}{2}+1, \quad n \geq 9
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15277/
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[12,x]*F[4,x]
F[4,x] = F[23,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[12,x]*F[8,x]
F[8,x] = F[13,x]+F[9,x]
F[9,x] = F[1,x]+F[10,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[9,x]
F[12,x] = x
F[13,x] = F[14,x]+F[21,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[18,x]
F[17,x] = F[1,x]+F[12,x]
F[18,x] = F[14,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]*F[14,x]
F[21,x] = F[22,x]
F[22,x] = F[12,x]*F[13,x]
F[23,x] = F[24,x]+F[35,x]
F[24,x] = F[25,x]
F[25,x] = F[12,x]*F[26,x]
F[26,x] = F[17,x]+F[27,x]
F[27,x] = F[24,x]+F[28,x]
F[28,x] = F[29,x]+F[30,x]+F[34,x]
F[29,x] = 0
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[12,x]
F[33,x] = F[28,x]
F[34,x] = F[12,x]*F[24,x]
F[35,x] = F[102,x]+F[29,x]+F[36,x]
F[36,x] = F[12,x]*F[37,x]
F[37,x] = F[38,x]+F[59,x]
F[38,x] = F[39,x]+F[6,x]
F[39,x] = F[29,x]+F[40,x]+F[41,x]
F[40,x] = F[10,x]*F[12,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[43,x]+F[46,x]
F[43,x] = F[12,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[12,x]*F[43,x]
F[46,x] = F[47,x]+F[57,x]
F[47,x] = F[29,x]+F[48,x]+F[49,x]
F[48,x] = x^2
F[49,x] = F[12,x]*F[50,x]
F[50,x] = F[51,x]+F[54,x]
F[51,x] = F[12,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = x^2
F[54,x] = F[47,x]+F[55,x]
F[55,x] = F[56,x]
F[56,x] = F[12,x]*F[47,x]
F[57,x] = F[58,x]
F[58,x] = F[12,x]*F[46,x]
F[59,x] = F[35,x]+F[60,x]
F[60,x] = F[29,x]+F[61,x]+F[65,x]+F[86,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[63,x]+F[64,x]
F[63,x] = F[39,x]
F[64,x] = F[60,x]
F[65,x] = F[12,x]*F[66,x]
F[66,x] = F[29,x]+F[67,x]+F[84,x]
F[67,x] = F[12,x]*F[68,x]
F[68,x] = F[69,x]+F[71,x]
F[69,x] = F[10,x]+F[70,x]
F[70,x] = F[29,x]+F[40,x]+F[45,x]
F[71,x] = F[66,x]+F[72,x]
F[72,x] = F[29,x]+F[65,x]+F[73,x]+F[77,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[75,x]+F[76,x]
F[75,x] = F[70,x]
F[76,x] = F[72,x]
F[77,x] = F[12,x]*F[78,x]
F[78,x] = F[28,x]+F[79,x]
F[79,x] = 2*F[29,x]+F[77,x]+F[80,x]
F[80,x] = F[12,x]*F[81,x]
F[81,x] = F[82,x]+F[83,x]
F[82,x] = F[44,x]
F[83,x] = F[79,x]
F[84,x] = F[12,x]*F[85,x]
F[85,x] = F[24,x]+F[66,x]
F[86,x] = F[12,x]*F[87,x]
F[87,x] = F[78,x]+F[88,x]
F[88,x] = F[100,x]+F[89,x]
F[89,x] = F[29,x]+F[90,x]+F[91,x]+F[92,x]
F[90,x] = 0
F[91,x] = F[12,x]*F[28,x]
F[92,x] = F[12,x]*F[93,x]
F[93,x] = F[94,x]+F[97,x]
F[94,x] = F[28,x]+F[95,x]
F[95,x] = F[96,x]
F[96,x] = F[12,x]*F[28,x]
F[97,x] = F[89,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[12,x]*F[89,x]
F[100,x] = F[101,x]
F[101,x] = F[12,x]*F[88,x]
F[102,x] = F[103,x]*F[12,x]
F[103,x] = F[104,x]+F[85,x]
F[104,x] = F[105,x]+F[111,x]
F[105,x] = F[106,x]+F[29,x]+F[30,x]
F[106,x] = F[107,x]*F[12,x]
F[107,x] = F[108,x]+F[27,x]
F[108,x] = F[105,x]+F[109,x]
F[109,x] = F[110,x]
F[110,x] = F[105,x]*F[12,x]
F[111,x] = 2*F[29,x]+F[112,x]+F[80,x]
F[112,x] = F[104,x]*F[12,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{23}\! \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_{12}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{9}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{21}\! \left(x \right)
F_{14}\! \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_{17}\! \left(x \right)+F_{18}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{35}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{17}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{24}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)+F_{34}\! \left(x \right)
F_{29}\! \left(x \right) = 0
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right)
F_{33}\! \left(x \right) = F_{28}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{35}\! \left(x \right) = F_{102}\! \left(x \right)+F_{29}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)+F_{59}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{6}\! \left(x \right)
F_{39}\! \left(x \right) = F_{29}\! \left(x \right)+F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{57}\! \left(x \right)
F_{47}\! \left(x \right) = F_{29}\! \left(x \right)+F_{48}\! \left(x \right)+F_{49}\! \left(x \right)
F_{48}\! \left(x \right) = x^{2}
F_{49}\! \left(x \right) = F_{12}\! \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_{12}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = x^{2}
F_{54}\! \left(x \right) = F_{47}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{59}\! \left(x \right) = F_{35}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{29}\! \left(x \right)+F_{61}\! \left(x \right)+F_{65}\! \left(x \right)+F_{86}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{64}\! \left(x \right)
F_{63}\! \left(x \right) = F_{39}\! \left(x \right)
F_{64}\! \left(x \right) = F_{60}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{29}\! \left(x \right)+F_{67}\! \left(x \right)+F_{84}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{71}\! \left(x \right)
F_{69}\! \left(x \right) = F_{10}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{29}\! \left(x \right)+F_{40}\! \left(x \right)+F_{45}\! \left(x \right)
F_{71}\! \left(x \right) = F_{66}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{29}\! \left(x \right)+F_{65}\! \left(x \right)+F_{73}\! \left(x \right)+F_{77}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)+F_{76}\! \left(x \right)
F_{75}\! \left(x \right) = F_{70}\! \left(x \right)
F_{76}\! \left(x \right) = F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{28}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{29}\! \left(x \right)+F_{77}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{83}\! \left(x \right)
F_{82}\! \left(x \right) = F_{44}\! \left(x \right)
F_{83}\! \left(x \right) = F_{79}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{24}\! \left(x \right)+F_{66}\! \left(x \right)
F_{86}\! \left(x \right) = F_{12}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{78}\! \left(x \right)+F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{100}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{29}\! \left(x \right)+F_{90}\! \left(x \right)+F_{91}\! \left(x \right)+F_{92}\! \left(x \right)
F_{90}\! \left(x \right) = 0
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)+F_{97}\! \left(x \right)
F_{94}\! \left(x \right) = F_{28}\! \left(x \right)+F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{97}\! \left(x \right) = F_{89}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right) F_{12}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{85}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{111}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{12}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{27}\! \left(x \right)
F_{108}\! \left(x \right) = F_{105}\! \left(x \right)+F_{109}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{105}\! \left(x \right) F_{12}\! \left(x \right)
F_{111}\! \left(x \right) = 2 F_{29}\! \left(x \right)+F_{112}\! \left(x \right)+F_{80}\! \left(x \right)
F_{112}\! \left(x \right) = F_{104}\! \left(x \right) F_{12}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_23(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_12(x)*F_8(x))
Eq(F_8(x), F_13(x) + F_9(x))
Eq(F_9(x), F_1(x) + F_10(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_9(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_21(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_18(x))
Eq(F_17(x), F_1(x) + F_12(x))
Eq(F_18(x), F_14(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)*F_14(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_12(x)*F_13(x))
Eq(F_23(x), F_24(x) + F_35(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_12(x)*F_26(x))
Eq(F_26(x), F_17(x) + F_27(x))
Eq(F_27(x), F_24(x) + F_28(x))
Eq(F_28(x), F_29(x) + F_30(x) + F_34(x))
Eq(F_29(x), 0)
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_12(x))
Eq(F_33(x), F_28(x))
Eq(F_34(x), F_12(x)*F_24(x))
Eq(F_35(x), F_102(x) + F_29(x) + F_36(x))
Eq(F_36(x), F_12(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_59(x))
Eq(F_38(x), F_39(x) + F_6(x))
Eq(F_39(x), F_29(x) + F_40(x) + F_41(x))
Eq(F_40(x), F_10(x)*F_12(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_46(x))
Eq(F_43(x), F_12(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_12(x)*F_43(x))
Eq(F_46(x), F_47(x) + F_57(x))
Eq(F_47(x), F_29(x) + F_48(x) + F_49(x))
Eq(F_48(x), x**2)
Eq(F_49(x), F_12(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_54(x))
Eq(F_51(x), F_12(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), x**2)
Eq(F_54(x), F_47(x) + F_55(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_12(x)*F_47(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_12(x)*F_46(x))
Eq(F_59(x), F_35(x) + F_60(x))
Eq(F_60(x), F_29(x) + F_61(x) + F_65(x) + F_86(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_64(x))
Eq(F_63(x), F_39(x))
Eq(F_64(x), F_60(x))
Eq(F_65(x), F_12(x)*F_66(x))
Eq(F_66(x), F_29(x) + F_67(x) + F_84(x))
Eq(F_67(x), F_12(x)*F_68(x))
Eq(F_68(x), F_69(x) + F_71(x))
Eq(F_69(x), F_10(x) + F_70(x))
Eq(F_70(x), F_29(x) + F_40(x) + F_45(x))
Eq(F_71(x), F_66(x) + F_72(x))
Eq(F_72(x), F_29(x) + F_65(x) + F_73(x) + F_77(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_75(x) + F_76(x))
Eq(F_75(x), F_70(x))
Eq(F_76(x), F_72(x))
Eq(F_77(x), F_12(x)*F_78(x))
Eq(F_78(x), F_28(x) + F_79(x))
Eq(F_79(x), 2*F_29(x) + F_77(x) + F_80(x))
Eq(F_80(x), F_12(x)*F_81(x))
Eq(F_81(x), F_82(x) + F_83(x))
Eq(F_82(x), F_44(x))
Eq(F_83(x), F_79(x))
Eq(F_84(x), F_12(x)*F_85(x))
Eq(F_85(x), F_24(x) + F_66(x))
Eq(F_86(x), F_12(x)*F_87(x))
Eq(F_87(x), F_78(x) + F_88(x))
Eq(F_88(x), F_100(x) + F_89(x))
Eq(F_89(x), F_29(x) + F_90(x) + F_91(x) + F_92(x))
Eq(F_90(x), 0)
Eq(F_91(x), F_12(x)*F_28(x))
Eq(F_92(x), F_12(x)*F_93(x))
Eq(F_93(x), F_94(x) + F_97(x))
Eq(F_94(x), F_28(x) + F_95(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_12(x)*F_28(x))
Eq(F_97(x), F_89(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_12(x)*F_89(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_12(x)*F_88(x))
Eq(F_102(x), F_103(x)*F_12(x))
Eq(F_103(x), F_104(x) + F_85(x))
Eq(F_104(x), F_105(x) + F_111(x))
Eq(F_105(x), F_106(x) + F_29(x) + F_30(x))
Eq(F_106(x), F_107(x)*F_12(x))
Eq(F_107(x), F_108(x) + F_27(x))
Eq(F_108(x), F_105(x) + F_109(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_105(x)*F_12(x))
Eq(F_111(x), F_112(x) + 2*F_29(x) + F_80(x))
Eq(F_112(x), F_104(x)*F_12(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": [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, 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, 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, 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, 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": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"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, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "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, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 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, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 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], "pos": [[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, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 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], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 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": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"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, 0], [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, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, 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