0132_1032_1320_2103
Counting sequence:
1, 1, 2, 6, 20, 64, 191, 542, 1494, 4053, 10889, 29049, 77045, 203318, 534203, 1398209, 3647276, 9485428, 24602038, 63653846, 164329373, 423377148, 1088767880, 2795142167, 7164579007, 18337774499, 46872405435, 119658416692, 305113401905, 777149171491, 1977436247798, 5026697785874, 12766445891304, 32395659000252, 82139855363771, 208108773286266, 526882419515786, 1333030403070713, 3370422732484517, 8516487516647549, 21507073573876241, 54282362727893650, 136931671092892135, 345244842247378421, 870038190834069728, 2191524544413427488, 5517721473121223018, 13886302006702055474, 34932875672198216473, 87843580435446287384, 220810808746667491740, 554844784538369544571, 1393700607929388840827, 3499611778552967100871, 8784720414451523573687, 22044422634087831126608, 55301508579290548447965, 138690657240751814062455, 347723223609600343024490, 871566492620886085277406, 2183994635099397558140156, 5471299807568845111274360, 13703164791665706978953399, 34311999205805796398520662, 85895248857574563976231550, 214977641974788868004435869, 537924596687990048331669889, 1345724814005207341284298049, 3365894828022234296164710509, 8416989923800355938665652590, 21043962087878276104215625235, 52603544009851173966974287337, 131468450765665415496281159188, 328510533159996223441602219404, 820730071781598027498246380382, 2050107744152929078629984465358, 5120121186248735567152683118229, 12785356946008724708308359782836, 31920987377248005153843866105840, 79684220880713484864860730565727, 198885238306026528822063719528439, 496327758438728055766749606386859, 1238431268284825869150460955613683, 3089683974597298702945493924568300, 7707196772585280178202553309511817, 19222968180011164898266222693353611, 47938825646798910213587443920442718, 119535957500352469679379093480973418, 298026725433238476736091006780989520, 742948194795129109054416286072885108, 1851866559866966907426781361315439283, 4615404922457944161893265497359420850, 11501645531659051256943584220903391922, 28659014623778995319257633800921954753, 71402703481635409837713476359121929757, 177877563933559339528957891104756233669, 443079611223429956236685204187967081993, 1103563592752604944283040458205374536394, 2748329949483693626659847762017192465215, 6843797640670242149146398497876592397213, 17040529342129723978766747688713166380744
Generating function in Maple syntax:
(2*x^9-4*x^8-12*x^7+53*x^6-97*x^5+107*x^4-77*x^3+35*x^2-9*x+1)/(x-1)^2/(3*x^3-5*x^2+4*x-1)^2
Generating function in latex syntax:
\frac{2 x^{9}-4 x^{8}-12 x^{7}+53 x^{6}-97 x^{5}+107 x^{4}-77 x^{3}+35 x^{2}-9 x +1}{\left(x -1\right)^{2} \left(3 x^{3}-5 x^{2}+4 x -1\right)^{2}}
Generating function in sympy syntax:
(2*x**9 - 4*x**8 - 12*x**7 + 53*x**6 - 97*x**5 + 107*x**4 - 77*x**3 + 35*x**2 - 9*x + 1)/((x - 1)**2*(3*x**3 - 5*x**2 + 4*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
-(x-1)^2*(3*x^3-5*x^2+4*x-1)^2*F(x)+2*x^9-4*x^8-12*x^7+53*x^6-97*x^5+107*x^4-77*x^3+35*x^2-9*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x -1\right)^{2} \left(3 x^{3}-5 x^{2}+4 x -1\right)^{2} F \! \left(x \right)+2 x^{9}-4 x^{8}-12 x^{7}+53 x^{6}-97 x^{5}+107 x^{4}-77 x^{3}+35 x^{2}-9 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,n = 1,1,1/37675044*(-18817*2^(1/3)*(((-39/607*n+26565/18817)*31^(1/2)+I*n-1199/607*I)*3^(1/2)+(-117/607*I*n+79695/18817*I)*31^(1/2)+n-1199/607)*(47+9*31^(1/2)*3^(1/2))^(2/3)+5797*(((-15/17*n-3777/527)*31^(1/2)+I*n-2731/17*I)*3^(1/2)+(45/17*I*n+11331/527*I)*31^(1/2)-n+2731/17)*2^(2/3)*(47+9*31^(1/2)*3^(1/2))^(1/3)+2670712*n+3255868)*(47/8712*2^(1/3)*((I-9/47*31^(1/2))*3^(1/2)-27/47*I*31^(1/2)+1)*(47+9*31^(1/2)*3^(1/2))^(2/3)-1/36*I*3^(1/2)*(188+36*31^(1/2)*3^(1/2))^(1/3)+1/36*(188+36*31^(1/2)*3^(1/2))^(1/3)+5/9)^(-n)+1/37675044*(-5797*(((15/17*n+3777/527)*31^(1/2)+I*n-2731/17*I)*3^(1/2)+(45/17*I*n+11331/527*I)*31^(1/2)+n-2731/17)*2^(2/3)*(47+9*31^(1/2)*3^(1/2))^(1/3)+18817*(((39/607*n-26565/18817)*31^(1/2)+I*n-1199/607*I)*3^(1/2)+(-117/607*I*n+79695/18817*I)*31^(1/2)-n+1199/607)*2^(1/3)*(47+9*31^(1/2)*3^(1/2))^(2/3)+2670712*n+3255868)*(-47/8712*2^(1/3)*((I+9/47*31^(1/2))*3^(1/2)-27/47*I*31^(1/2)-1)*(47+9*31^(1/2)*3^(1/2))^(2/3)+1/36*I*3^(1/2)*(188+36*31^(1/2)*3^(1/2))^(1/3)+1/36*(188+36*31^(1/2)*3^(1/2))^(1/3)+5/9)^(-n)+1/37675044*(10230*(3^(1/2)*(n+1259/155)*31^(1/2)+17/15*n-2731/15)*2^(2/3)*(47+9*31^(1/2)*3^(1/2))^(1/3)-2418*2^(1/3)*(3^(1/2)*(n-8855/403)*31^(1/2)-607/39*n+1199/39)*(47+9*31^(1/2)*3^(1/2))^(2/3)+2670712*n+3255868)*(1/4356*2^(1/3)*(9*31^(1/2)*3^(1/2)-47)*(47+9*31^(1/2)*3^(1/2))^(2/3)-1/18*(188+36*31^(1/2)*3^(1/2))^(1/3)+5/9)^(-n)-n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ 1 & n =1 \\ \frac{\left(-18817 \,2^{\frac{1}{3}} \left(\left(\left(-\frac{39 n}{607}+\frac{26565}{18817}\right) \sqrt{31}+\mathrm{I} n -\frac{1199 \,\mathrm{I}}{607}\right) \sqrt{3}+\left(-\frac{117 \,\mathrm{I} n}{607}+\frac{79695 \,\mathrm{I}}{18817}\right) \sqrt{31}+n -\frac{1199}{607}\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}+5797 \left(\left(\left(-\frac{15 n}{17}-\frac{3777}{527}\right) \sqrt{31}+\mathrm{I} n -\frac{2731 \,\mathrm{I}}{17}\right) \sqrt{3}+\left(\frac{45 \,\mathrm{I} n}{17}+\frac{11331 \,\mathrm{I}}{527}\right) \sqrt{31}-n +\frac{2731}{17}\right) 2^{\frac{2}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}+2670712 n +3255868\right) \left(\frac{47 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}-\frac{9 \sqrt{31}}{47}\right) \sqrt{3}-\frac{27 \,\mathrm{I} \sqrt{31}}{47}+1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{8712}-\frac{\mathrm{I} \sqrt{3}\, \left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{\left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{5}{9}\right)^{-n}}{37675044}\\+\\\frac{\left(-5797 \left(\left(\left(\frac{15 n}{17}+\frac{3777}{527}\right) \sqrt{31}+\mathrm{I} n -\frac{2731 \,\mathrm{I}}{17}\right) \sqrt{3}+\left(\frac{45 \,\mathrm{I} n}{17}+\frac{11331 \,\mathrm{I}}{527}\right) \sqrt{31}+n -\frac{2731}{17}\right) 2^{\frac{2}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}+18817 \left(\left(\left(\frac{39 n}{607}-\frac{26565}{18817}\right) \sqrt{31}+\mathrm{I} n -\frac{1199 \,\mathrm{I}}{607}\right) \sqrt{3}+\left(-\frac{117 \,\mathrm{I} n}{607}+\frac{79695 \,\mathrm{I}}{18817}\right) \sqrt{31}-n +\frac{1199}{607}\right) 2^{\frac{1}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}+2670712 n +3255868\right) \left(-\frac{47 \,2^{\frac{1}{3}} \left(\left(\mathrm{I}+\frac{9 \sqrt{31}}{47}\right) \sqrt{3}-\frac{27 \,\mathrm{I} \sqrt{31}}{47}-1\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{8712}+\frac{\mathrm{I} \sqrt{3}\, \left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{\left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{36}+\frac{5}{9}\right)^{-n}}{37675044}\\+\\\frac{\left(10230 \left(\sqrt{3}\, \left(n +\frac{1259}{155}\right) \sqrt{31}+\frac{17 n}{15}-\frac{2731}{15}\right) 2^{\frac{2}{3}} \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}-2418 \,2^{\frac{1}{3}} \left(\sqrt{3}\, \left(n -\frac{8855}{403}\right) \sqrt{31}-\frac{607 n}{39}+\frac{1199}{39}\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}+2670712 n +3255868\right) \left(\frac{2^{\frac{1}{3}} \left(9 \sqrt{31}\, \sqrt{3}-47\right) \left(47+9 \sqrt{31}\, \sqrt{3}\right)^{\frac{2}{3}}}{4356}-\frac{\left(188+36 \sqrt{31}\, \sqrt{3}\right)^{\frac{1}{3}}}{18}+\frac{5}{9}\right)^{-n}}{37675044}\\-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) = 20
a(5) = 64
a(6) = 191
a(7) = 542
a(8) = 1494
a(9) = 4053
a(n+6) = -9*a(n)+30*a(n+1)-49*a(n+2)+46*a(n+3)-26*a(n+4)+8*a(n+5)-n, n >= 10
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) = 64
a \! \left(6\right) = 191
a \! \left(7\right) = 542
a \! \left(8\right) = 1494
a \! \left(9\right) = 4053
a \! \left(n +6\right) = -9 a \! \left(n \right)+30 a \! \left(n +1\right)-49 a \! \left(n +2\right)+46 a \! \left(n +3\right)-26 a \! \left(n +4\right)+8 a \! \left(n +5\right)-n, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15528/
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[28,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[7,x]
F[14,x] = F[15,x]+F[16,x]+F[27,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[11,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[18,x]*F[4,x]
F[21,x] = F[22,x]+F[25,x]
F[22,x] = F[23,x]
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[22,x]+F[7,x]
F[25,x] = F[26,x]
F[26,x] = F[21,x]*F[4,x]
F[27,x] = F[13,x]*F[4,x]
F[28,x] = F[2,x]+F[29,x]
F[29,x] = F[15,x]+F[30,x]+F[59,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[11,x]+F[14,x]
F[33,x] = F[34,x]+F[37,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]*F[4,x]
F[36,x] = F[2,x]+F[34,x]
F[37,x] = 2*F[15,x]+F[38,x]+F[56,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[34,x]+F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[4,x]*F[40,x]
F[43,x] = F[44,x]+F[54,x]
F[44,x] = F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[44,x]+F[47,x]
F[47,x] = F[48,x]
F[48,x] = F[4,x]*F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[11,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = F[4,x]*F[53,x]
F[53,x] = F[18,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[43,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[47,x]+F[58,x]
F[58,x] = F[56,x]
F[59,x] = F[4,x]*F[60,x]
F[60,x] = F[61,x]+F[64,x]
F[61,x] = F[2,x]+F[62,x]
F[62,x] = F[15,x]+F[30,x]+F[63,x]
F[63,x] = F[4,x]*F[61,x]
F[64,x] = F[47,x]+F[65,x]
F[65,x] = 2*F[15,x]+F[66,x]+F[75,x]
F[66,x] = F[4,x]*F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[19,x]+F[69,x]
F[69,x] = F[70,x]
F[70,x] = F[4,x]*F[71,x]
F[71,x] = F[72,x]
F[72,x] = F[19,x]+F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[72,x]
F[75,x] = F[4,x]*F[64,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_{28}\! \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_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{27}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{11}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{18}\! \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_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{22}\! \left(x \right)+F_{7}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{2}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{15}\! \left(x \right)+F_{30}\! \left(x \right)+F_{59}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{11}\! \left(x \right)+F_{14}\! \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_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{2}\! \left(x \right)+F_{34}\! \left(x \right)
F_{37}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{38}\! \left(x \right)+F_{56}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{34}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{54}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{4}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{44}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{4}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{4}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{18}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{43}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{47}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{56}\! \left(x \right)
F_{59}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{64}\! \left(x \right)
F_{61}\! \left(x \right) = F_{2}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{15}\! \left(x \right)+F_{30}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{4}\! \left(x \right) F_{61}\! \left(x \right)
F_{64}\! \left(x \right) = F_{47}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{66}\! \left(x \right)+F_{75}\! \left(x \right)
F_{66}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{19}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{4}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{19}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{75}\! \left(x \right) = F_{4}\! \left(x \right) F_{64}\! \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_28(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) + F_7(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_27(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_11(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_18(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_25(x))
Eq(F_22(x), F_23(x))
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_22(x) + F_7(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_21(x)*F_4(x))
Eq(F_27(x), F_13(x)*F_4(x))
Eq(F_28(x), F_2(x) + F_29(x))
Eq(F_29(x), F_15(x) + F_30(x) + F_59(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_11(x) + F_14(x))
Eq(F_33(x), F_34(x) + F_37(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x)*F_4(x))
Eq(F_36(x), F_2(x) + F_34(x))
Eq(F_37(x), 2*F_15(x) + F_38(x) + F_56(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_34(x) + F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_4(x)*F_40(x))
Eq(F_43(x), F_44(x) + F_54(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_44(x) + F_47(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_4(x)*F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_11(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_4(x)*F_53(x))
Eq(F_53(x), F_18(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_43(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_47(x) + F_58(x))
Eq(F_58(x), F_56(x))
Eq(F_59(x), F_4(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_64(x))
Eq(F_61(x), F_2(x) + F_62(x))
Eq(F_62(x), F_15(x) + F_30(x) + F_63(x))
Eq(F_63(x), F_4(x)*F_61(x))
Eq(F_64(x), F_47(x) + F_65(x))
Eq(F_65(x), 2*F_15(x) + F_66(x) + F_75(x))
Eq(F_66(x), F_4(x)*F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_19(x) + F_69(x))
Eq(F_69(x), F_70(x))
Eq(F_70(x), F_4(x)*F_71(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_19(x) + F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_4(x)*F_72(x))
Eq(F_75(x), F_4(x)*F_64(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:
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1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "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, 2, 1], "pos": [[1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [2, 1, 0], "pos": [[1, 2], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 3, 2, 0], "pos": [[1, 0], [1, 2], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 0, 3], "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": [], 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true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "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, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 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"pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "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": [1, 0], "pos": [[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, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [2, 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