0231_0312_1032_2130
Counting sequence:
1, 1, 2, 6, 20, 64, 197, 596, 1793, 5385, 16163, 48499, 145508, 436535, 1309616, 3928860, 11786594, 35359798, 106079411, 318238250, 954714767, 2864144319, 8592432977, 25777298953, 77331896882, 231995690669, 695987072030, 2087961216114, 6263883648368, 18791650945132, 56374952835425, 169124858506304, 507374575518941, 1522123726556853, 4566371179670591, 13699113539011807, 41097340617035456, 123292021851106403, 369876065553319244, 1109628196659957768, 3328884589979873342, 9986653769939620066, 29959961309818860239, 89879883929456580758, 269639651788369742315, 808918955365109226987, 2426756866095327681005, 7280270598285983043061, 21840811794857949129230, 65522435384573847387737, 196567306153721542163258, 589701918461164626489822, 1769105755383493879469516, 5307317266150481638408600, 15921951798451444915225853, 47765855395354334745677612, 143297566186063004237032889, 429892698558189012711098721, 1289678095674567038133296219, 3869034287023701114399888715, 11607102861071103343199666204, 34821308583213310029598998671, 104463925749639930088796996072, 313391777248919790266390988276, 940175331746759370799172964890, 2820525995240278112397518894734, 8461577985720834337192556684267, 25384733957162503011577670052866, 76154201871487509034733010158663, 228462605614462527104199030476055, 685387816843387581312597091428233, 2056163450530162743937791274284769, 6168490351590488231813373822854378, 18505471054771464695440121468563205, 55516413164314394086320364405689686, 166549239492943182258961093217069130, 499647718478829546776883279651207464, 1498943155436488640330649838953622468, 4496829466309465920991949516860867481, 13490488398928397762975848550582602520, 40471465196785193288927545651747807637, 121414395590355579866782636955243422989, 364243186771066739600347910865730269047, 1092729560313200218801043732597190807223, 3278188680939600656403131197791572421752, 9834566042818801969209393593374717265339, 29503698128456405907628180780124151796100, 88511094385369217722884542340372455388384, 265533283156107653168653627021117366165238, 796599849468322959505960881063352098495802, 2389799548404968878517882643190056295487495, 7169398645214906635553647929570168886462574, 21508195935644719906660943788710506659387811, 64524587806934159719982831366131519978163523, 193573763420802479159948494098394559934490661, 580721290262407437479845482295183679803472077, 1742163870787222312439536446885551039410416326, 5226491612361666937318609340656653118231249073, 15679474837085000811955828021969959354693747314, 47038424511255002435867484065909878064081242038, 141115273533765007307602452197729634192243726212
Generating function in Maple syntax:
(x^5-5*x^4+8*x^3-9*x^2+5*x-1)/(3*x-1)/(x^2-x+1)/(x-1)^2
Generating function in latex syntax:
\frac{x^{5}-5 x^{4}+8 x^{3}-9 x^{2}+5 x -1}{\left(3 x -1\right) \left(x^{2}-x +1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(x**5 - 5*x**4 + 8*x**3 - 9*x**2 + 5*x - 1)/((x - 1)**2*(3*x - 1)*(x**2 - x + 1))
Implicit equation for the generating function in Maple syntax:
(3*x-1)*(x^2-x+1)*(x-1)^2*F(x)-x^5+5*x^4-8*x^3+9*x^2-5*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(3 x -1\right) \left(x^{2}-x +1\right) \left(x -1\right)^{2} F \! \left(x \right)-x^{5}+5 x^{4}-8 x^{3}+9 x^{2}-5 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/84*(10*I*3^(1/2)+6)*(1/2+1/2*I*3^(1/2))^(-n)-5/42*I*(1/2-1/2*I*3^(1/2))^(-n)*3^(1/2)-1/2*n+23/84*3^n+1/14*(1/2-1/2*I*3^(1/2))^(-n)+1/4)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(10 \,\mathrm{I} \sqrt{3}+6\right) \left(\frac{1}{2}+\frac{\mathrm{I} \sqrt{3}}{2}\right)^{-n}}{84}-\frac{5 \,\mathrm{I} \left(\frac{1}{2}-\frac{\mathrm{I} \sqrt{3}}{2}\right)^{-n} \sqrt{3}}{42}-\frac{n}{2}+\frac{23 \,3^{n}}{84}+\\\frac{\left(\frac{1}{2}-\frac{\mathrm{I} \sqrt{3}}{2}\right)^{-n}}{14}+\frac{1}{4} & \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(n+3) = 3*a(n)-4*a(n+1)+4*a(n+2)+n, 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) = 20
a \! \left(5\right) = 64
a \! \left(n +3\right) = 3 a \! \left(n \right)-4 a \! \left(n +1\right)+4 a \! \left(n +2\right)+n, \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15776/
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[13,x]*F[4,x]
F[4,x] = F[21,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[13,x]*F[8,x]
F[8,x] = F[5,x]+F[9,x]
F[9,x] = F[10,x]+F[14,x]
F[10,x] = F[11,x]
F[11,x] = F[12,x]*F[13,x]
F[12,x] = F[1,x]+F[10,x]
F[13,x] = x
F[14,x] = F[15,x]
F[15,x] = F[13,x]*F[16,x]
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[18,x]
F[18,x] = F[13,x]*F[19,x]
F[19,x] = F[1,x]+F[17,x]
F[20,x] = F[15,x]
F[21,x] = F[22,x]+F[38,x]
F[22,x] = F[23,x]
F[23,x] = F[13,x]*F[24,x]
F[24,x] = F[25,x]+F[30,x]
F[25,x] = F[1,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[13,x]*F[28,x]
F[28,x] = F[25,x]+F[29,x]
F[29,x] = F[10,x]
F[30,x] = F[22,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[13,x]*F[33,x]
F[33,x] = F[30,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[13,x]*F[37,x]
F[37,x] = F[22,x]+F[35,x]
F[38,x] = F[39,x]+F[40,x]+F[62,x]
F[39,x] = 0
F[40,x] = F[13,x]*F[41,x]
F[41,x] = F[42,x]+F[49,x]
F[42,x] = F[17,x]+F[43,x]
F[43,x] = F[39,x]+F[44,x]+F[47,x]
F[44,x] = F[13,x]*F[45,x]
F[45,x] = F[42,x]+F[46,x]
F[46,x] = F[20,x]
F[47,x] = F[13,x]*F[48,x]
F[48,x] = F[10,x]+F[20,x]
F[49,x] = F[50,x]+F[53,x]
F[50,x] = F[39,x]+F[40,x]+F[51,x]
F[51,x] = F[13,x]*F[52,x]
F[52,x] = F[22,x]+F[50,x]
F[53,x] = 2*F[39,x]+F[54,x]+F[60,x]
F[54,x] = F[13,x]*F[55,x]
F[55,x] = F[49,x]+F[56,x]
F[56,x] = F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[13,x]*F[59,x]
F[59,x] = F[50,x]+F[57,x]
F[60,x] = F[13,x]*F[61,x]
F[61,x] = F[35,x]+F[57,x]
F[62,x] = F[13,x]*F[63,x]
F[63,x] = F[21,x]+F[64,x]
F[64,x] = F[65,x]+F[82,x]
F[65,x] = F[39,x]+F[66,x]+F[80,x]
F[66,x] = F[13,x]*F[67,x]
F[67,x] = F[68,x]+F[73,x]
F[68,x] = F[13,x]+F[69,x]
F[69,x] = F[39,x]+F[70,x]+F[72,x]
F[70,x] = F[13,x]*F[71,x]
F[71,x] = F[68,x]
F[72,x] = F[10,x]*F[13,x]
F[73,x] = F[74,x]+F[76,x]
F[74,x] = F[75,x]
F[75,x] = F[13,x]*F[22,x]
F[76,x] = 2*F[39,x]+F[77,x]+F[79,x]
F[77,x] = F[13,x]*F[78,x]
F[78,x] = F[73,x]
F[79,x] = F[13,x]*F[35,x]
F[80,x] = F[13,x]*F[81,x]
F[81,x] = F[22,x]+F[65,x]
F[82,x] = 2*F[39,x]+F[83,x]+F[99,x]
F[83,x] = F[13,x]*F[84,x]
F[84,x] = F[85,x]+F[92,x]
F[85,x] = F[86,x]+F[88,x]
F[86,x] = F[87,x]
F[87,x] = F[13,x]*F[17,x]
F[88,x] = 2*F[39,x]+F[89,x]+F[91,x]
F[89,x] = F[13,x]*F[90,x]
F[90,x] = F[85,x]
F[91,x] = F[13,x]*F[20,x]
F[92,x] = F[93,x]+F[95,x]
F[93,x] = F[94,x]
F[94,x] = F[13,x]*F[50,x]
F[95,x] = 3*F[39,x]+F[96,x]+F[98,x]
F[96,x] = F[13,x]*F[97,x]
F[97,x] = F[92,x]
F[98,x] = F[13,x]*F[57,x]
F[99,x] = F[100,x]*F[13,x]
F[100,x] = F[101,x]+F[50,x]
F[101,x] = 2*F[39,x]+F[83,x]+F[99,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_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{21}\! \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_{13}\! \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_{14}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{10}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{13}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{20}\! \left(x \right) = F_{15}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{38}\! \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_{30}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{13}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{25}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{10}\! \left(x \right)
F_{30}\! \left(x \right) = F_{22}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{13}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{30}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{13}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{22}\! \left(x \right)+F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)+F_{62}\! \left(x \right)
F_{39}\! \left(x \right) = 0
F_{40}\! \left(x \right) = F_{13}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{49}\! \left(x \right)
F_{42}\! \left(x \right) = F_{17}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{39}\! \left(x \right)+F_{44}\! \left(x \right)+F_{47}\! \left(x \right)
F_{44}\! \left(x \right) = F_{13}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{42}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{20}\! \left(x \right)
F_{47}\! \left(x \right) = F_{13}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{10}\! \left(x \right)+F_{20}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{53}\! \left(x \right)
F_{50}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)+F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{13}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{22}\! \left(x \right)+F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = 2 F_{39}\! \left(x \right)+F_{54}\! \left(x \right)+F_{60}\! \left(x \right)
F_{54}\! \left(x \right) = F_{13}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{49}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{13}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{50}\! \left(x \right)+F_{57}\! \left(x \right)
F_{60}\! \left(x \right) = F_{13}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{35}\! \left(x \right)+F_{57}\! \left(x \right)
F_{62}\! \left(x \right) = F_{13}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{21}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{82}\! \left(x \right)
F_{65}\! \left(x \right) = F_{39}\! \left(x \right)+F_{66}\! \left(x \right)+F_{80}\! \left(x \right)
F_{66}\! \left(x \right) = F_{13}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{73}\! \left(x \right)
F_{68}\! \left(x \right) = F_{13}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{39}\! \left(x \right)+F_{70}\! \left(x \right)+F_{72}\! \left(x \right)
F_{70}\! \left(x \right) = F_{13}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{68}\! \left(x \right)
F_{72}\! \left(x \right) = F_{10}\! \left(x \right) F_{13}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{76}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right)
F_{76}\! \left(x \right) = 2 F_{39}\! \left(x \right)+F_{77}\! \left(x \right)+F_{79}\! \left(x \right)
F_{77}\! \left(x \right) = F_{13}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{73}\! \left(x \right)
F_{79}\! \left(x \right) = F_{13}\! \left(x \right) F_{35}\! \left(x \right)
F_{80}\! \left(x \right) = F_{13}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{22}\! \left(x \right)+F_{65}\! \left(x \right)
F_{82}\! \left(x \right) = 2 F_{39}\! \left(x \right)+F_{83}\! \left(x \right)+F_{99}\! \left(x \right)
F_{83}\! \left(x \right) = F_{13}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{92}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{88}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{13}\! \left(x \right) F_{17}\! \left(x \right)
F_{88}\! \left(x \right) = 2 F_{39}\! \left(x \right)+F_{89}\! \left(x \right)+F_{91}\! \left(x \right)
F_{89}\! \left(x \right) = F_{13}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{85}\! \left(x \right)
F_{91}\! \left(x \right) = F_{13}\! \left(x \right) F_{20}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{95}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{13}\! \left(x \right) F_{50}\! \left(x \right)
F_{95}\! \left(x \right) = 3 F_{39}\! \left(x \right)+F_{96}\! \left(x \right)+F_{98}\! \left(x \right)
F_{96}\! \left(x \right) = F_{13}\! \left(x \right) F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{92}\! \left(x \right)
F_{98}\! \left(x \right) = F_{13}\! \left(x \right) F_{57}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{13}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{50}\! \left(x \right)
F_{101}\! \left(x \right) = 2 F_{39}\! \left(x \right)+F_{83}\! \left(x \right)+F_{99}\! \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_13(x)*F_4(x))
Eq(F_4(x), F_21(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_13(x)*F_8(x))
Eq(F_8(x), F_5(x) + F_9(x))
Eq(F_9(x), F_10(x) + F_14(x))
Eq(F_10(x), F_11(x))
Eq(F_11(x), F_12(x)*F_13(x))
Eq(F_12(x), F_1(x) + F_10(x))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_13(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_13(x)*F_19(x))
Eq(F_19(x), F_1(x) + F_17(x))
Eq(F_20(x), F_15(x))
Eq(F_21(x), F_22(x) + F_38(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_30(x))
Eq(F_25(x), F_1(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_13(x)*F_28(x))
Eq(F_28(x), F_25(x) + F_29(x))
Eq(F_29(x), F_10(x))
Eq(F_30(x), F_22(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_13(x)*F_33(x))
Eq(F_33(x), F_30(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_13(x)*F_37(x))
Eq(F_37(x), F_22(x) + F_35(x))
Eq(F_38(x), F_39(x) + F_40(x) + F_62(x))
Eq(F_39(x), 0)
Eq(F_40(x), F_13(x)*F_41(x))
Eq(F_41(x), F_42(x) + F_49(x))
Eq(F_42(x), F_17(x) + F_43(x))
Eq(F_43(x), F_39(x) + F_44(x) + F_47(x))
Eq(F_44(x), F_13(x)*F_45(x))
Eq(F_45(x), F_42(x) + F_46(x))
Eq(F_46(x), F_20(x))
Eq(F_47(x), F_13(x)*F_48(x))
Eq(F_48(x), F_10(x) + F_20(x))
Eq(F_49(x), F_50(x) + F_53(x))
Eq(F_50(x), F_39(x) + F_40(x) + F_51(x))
Eq(F_51(x), F_13(x)*F_52(x))
Eq(F_52(x), F_22(x) + F_50(x))
Eq(F_53(x), 2*F_39(x) + F_54(x) + F_60(x))
Eq(F_54(x), F_13(x)*F_55(x))
Eq(F_55(x), F_49(x) + F_56(x))
Eq(F_56(x), F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_13(x)*F_59(x))
Eq(F_59(x), F_50(x) + F_57(x))
Eq(F_60(x), F_13(x)*F_61(x))
Eq(F_61(x), F_35(x) + F_57(x))
Eq(F_62(x), F_13(x)*F_63(x))
Eq(F_63(x), F_21(x) + F_64(x))
Eq(F_64(x), F_65(x) + F_82(x))
Eq(F_65(x), F_39(x) + F_66(x) + F_80(x))
Eq(F_66(x), F_13(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_73(x))
Eq(F_68(x), F_13(x) + F_69(x))
Eq(F_69(x), F_39(x) + F_70(x) + F_72(x))
Eq(F_70(x), F_13(x)*F_71(x))
Eq(F_71(x), F_68(x))
Eq(F_72(x), F_10(x)*F_13(x))
Eq(F_73(x), F_74(x) + F_76(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_13(x)*F_22(x))
Eq(F_76(x), 2*F_39(x) + F_77(x) + F_79(x))
Eq(F_77(x), F_13(x)*F_78(x))
Eq(F_78(x), F_73(x))
Eq(F_79(x), F_13(x)*F_35(x))
Eq(F_80(x), F_13(x)*F_81(x))
Eq(F_81(x), F_22(x) + F_65(x))
Eq(F_82(x), 2*F_39(x) + F_83(x) + F_99(x))
Eq(F_83(x), F_13(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_92(x))
Eq(F_85(x), F_86(x) + F_88(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_13(x)*F_17(x))
Eq(F_88(x), 2*F_39(x) + F_89(x) + F_91(x))
Eq(F_89(x), F_13(x)*F_90(x))
Eq(F_90(x), F_85(x))
Eq(F_91(x), F_13(x)*F_20(x))
Eq(F_92(x), F_93(x) + F_95(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_13(x)*F_50(x))
Eq(F_95(x), 3*F_39(x) + F_96(x) + F_98(x))
Eq(F_96(x), F_13(x)*F_97(x))
Eq(F_97(x), F_92(x))
Eq(F_98(x), F_13(x)*F_57(x))
Eq(F_99(x), F_100(x)*F_13(x))
Eq(F_100(x), F_101(x) + F_50(x))
Eq(F_101(x), 2*F_39(x) + F_83(x) + F_99(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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 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": [2, 1, 3, 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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 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": [2, 1, 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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 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": [2, 1, 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, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 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, 2, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 3, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 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": [], 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[]}, "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": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "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], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 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{"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": []}, {"assumptions": [], 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