0132_0231_0321_1203_1230
Counting sequence:
1, 1, 2, 6, 19, 58, 171, 492, 1391, 3880, 10705, 29268, 79413, 214102, 574169, 1532994, 4078075, 10815934, 28615503, 75554880, 199163267, 524294236, 1378700197, 3622292136, 9510196329, 24954434218, 65449575341, 171595618422, 449756710351, 1178546927890, 3087696012675, 8088299206548, 21184986235223, 55482765626512, 145296596640889, 380475743772924, 996272368598685, 2608633419799294, 6830229186220673, 17883291089444010, 46822186702750627, 122588491699039846, 320954008632739767, 840295524431735016, 2199977644639204139, 5759729768462610628, 15079400776748605261, 39478859589876182352, 103357969641251940561, 270596667814995725650, 708435341134711586645, 1854716110988580090078, 4855726784104887505783, 12712492388823753492922, 33281807803261621946859, 87133048114551423980604, 228117575231172900631295, 597220163967727033926904, 1563543907463926222658593, 4093413576036684696031140, 10716700927928988027327237, 28056697566431187785591206, 73453408776956768280439337, 192303563352084255261136146, 503457351607507778520634699, 1318068634432705651549793038, 3450748842226828337054182431, 9034178482543589718318406032, 23651787804442305609021890771, 61921187365753544838408079660, 162111779236545740660362181365, 424414160378912453240674543608, 1111130722265397076437006433593, 2908978047737985501179740377082, 7615803504770564498038417240829, 19938432636578901376242739038534, 52199494749698892880173900474655, 136660052311428016728986454012514, 357780663601295102167679025671763, 936681941363656111358794912930020, 2452265166307628738804108616391847, 6420113569346256846296165389630816, 16808075565607426737473313752947657, 44004113175833056150708942857459276, 115204264059814733103438477970630509, 301608679201874977576405675706245198, 789621773947173571737835435150555601, 2067256643452043888418131435147971962, 5412148158053097208192454547893759731, 14169187834034211591738691697324703670, 37095415350780836530637875788844339335, 97117058231925638432314118693098680888, 254255759372540244640404191406957217403, 665650219941402397256740567898233561492, 1742694900564319490704787117303563771549, 4562434481979337042086130754593896610464, 11944608545834205330167766608740600271265, 31271391156454209857959775038352045619874, 81869564925410093103425336524162205408933, 214337303623579021253000922738624680223150, 561142345953012102419461072438285598443207
Generating function in Maple syntax:
(x^6-6*x^5+25*x^4-37*x^3+25*x^2-8*x+1)/(x^2-3*x+1)/(2*x-1)^2/(-1+x)^2
Generating function in latex syntax:
\frac{x^{6}-6 x^{5}+25 x^{4}-37 x^{3}+25 x^{2}-8 x +1}{\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} \left(-1+x \right)^{2}}
Generating function in sympy syntax:
(x**6 - 6*x**5 + 25*x**4 - 37*x**3 + 25*x**2 - 8*x + 1)/((x - 1)**2*(2*x - 1)**2*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
(x^2-3*x+1)*(2*x-1)^2*(-1+x)^2*F(x)-x^6+6*x^5-25*x^4+37*x^3-25*x^2+8*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} \left(-1+x \right)^{2} F \! \left(x \right)-x^{6}+6 x^{5}-25 x^{4}+37 x^{3}-25 x^{2}+8 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,2/5*(3/2-1/2*5^(1/2))^(-n)*5^(1/2)-2/5*(3/2+1/2*5^(1/2))^(-n)*5^(1/2)+1/20*(-5*n-5)*2^n-n+1)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{2 \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}}{5}-\frac{2 \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n} \sqrt{5}}{5}+\frac{\left(-5 n -5\right) 2^{n}}{20}-n +1 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 58
a(6) = 171
a(n+4) = -4*a(n)+16*a(n+1)-17*a(n+2)+7*a(n+3)+n-2, n >= 7
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 58
a \! \left(6\right) = 171
a \! \left(n +4\right) = -4 a \! \left(n \right)+16 a \! \left(n +1\right)-17 a \! \left(n +2\right)+7 a \! \left(n +3\right)+n -2, \quad n \geq 7
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18659/
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[18,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[12,x]+F[14,x]
F[14,x] = F[15,x]+F[16,x]+F[17,x]
F[15,x] = 0
F[16,x] = F[10,x]*F[12,x]
F[17,x] = F[12,x]*F[13,x]
F[18,x] = F[19,x]+F[58,x]
F[19,x] = F[20,x]
F[20,x] = F[12,x]*F[21,x]
F[21,x] = F[22,x]+F[26,x]
F[22,x] = F[1,x]+F[23,x]
F[23,x] = F[24,x]
F[24,x] = F[12,x]*F[25,x]
F[25,x] = F[1,x]+F[12,x]
F[26,x] = F[19,x]+F[27,x]
F[27,x] = F[15,x]+F[28,x]+F[56,x]
F[28,x] = F[12,x]*F[29,x]
F[29,x] = F[30,x]+F[34,x]
F[30,x] = F[23,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[12,x]*F[33,x]
F[33,x] = F[12,x]
F[34,x] = F[27,x]+F[35,x]
F[35,x] = 2*F[15,x]+F[36,x]+F[40,x]
F[36,x] = F[12,x]*F[37,x]
F[37,x] = F[38,x]+F[39,x]
F[38,x] = F[31,x]
F[39,x] = F[35,x]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[42,x]
F[42,x] = F[15,x]+F[43,x]+F[55,x]
F[43,x] = F[12,x]*F[44,x]
F[44,x] = F[45,x]+F[48,x]
F[45,x] = F[12,x]+F[46,x]
F[46,x] = F[47,x]
F[47,x] = x^2
F[48,x] = F[42,x]+F[49,x]
F[49,x] = 2*F[15,x]+F[50,x]+F[54,x]
F[50,x] = F[12,x]*F[51,x]
F[51,x] = F[52,x]+F[53,x]
F[52,x] = F[46,x]
F[53,x] = F[49,x]
F[54,x] = F[12,x]*F[42,x]
F[55,x] = F[12,x]*F[19,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[19,x]+F[42,x]
F[58,x] = F[15,x]+F[59,x]+F[83,x]
F[59,x] = F[12,x]*F[60,x]
F[60,x] = F[61,x]+F[68,x]
F[61,x] = F[6,x]+F[62,x]
F[62,x] = F[63,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[12,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[12,x]*F[65,x]
F[68,x] = F[58,x]+F[69,x]
F[69,x] = 2*F[15,x]+F[70,x]+F[74,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[62,x]
F[73,x] = F[69,x]
F[74,x] = F[12,x]*F[75,x]
F[75,x] = F[76,x]
F[76,x] = F[42,x]+F[77,x]
F[77,x] = 2*F[15,x]+F[78,x]+F[82,x]
F[78,x] = F[12,x]*F[79,x]
F[79,x] = F[80,x]+F[81,x]
F[80,x] = F[66,x]
F[81,x] = F[77,x]
F[82,x] = F[12,x]*F[76,x]
F[83,x] = F[12,x]*F[84,x]
F[84,x] = F[85,x]+F[98,x]
F[85,x] = F[19,x]+F[86,x]
F[86,x] = F[15,x]+F[87,x]+F[97,x]
F[87,x] = F[12,x]*F[88,x]
F[88,x] = F[89,x]+F[91,x]
F[89,x] = F[10,x]+F[90,x]
F[90,x] = F[67,x]
F[91,x] = F[86,x]+F[92,x]
F[92,x] = 2*F[15,x]+F[82,x]+F[93,x]
F[93,x] = F[12,x]*F[94,x]
F[94,x] = F[95,x]+F[96,x]
F[95,x] = F[90,x]
F[96,x] = F[92,x]
F[97,x] = F[12,x]*F[85,x]
F[98,x] = F[42,x]+F[99,x]
F[99,x] = F[100,x]+F[101,x]+F[15,x]+F[78,x]
F[100,x] = F[12,x]*F[86,x]
F[101,x] = F[12,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_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{18}\! \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_{12}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{17}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{17}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{58}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{26}\! \left(x \right)
F_{22}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{26}\! \left(x \right) = F_{19}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{15}\! \left(x \right)+F_{28}\! \left(x \right)+F_{56}\! \left(x \right)
F_{28}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{34}\! \left(x \right)
F_{30}\! \left(x \right) = F_{23}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right)
F_{34}\! \left(x \right) = F_{27}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{36}\! \left(x \right)+F_{40}\! \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_{39}\! \left(x \right)
F_{38}\! \left(x \right) = F_{31}\! \left(x \right)
F_{39}\! \left(x \right) = F_{35}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{15}\! \left(x \right)+F_{43}\! \left(x \right)+F_{55}\! \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_{48}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = x^{2}
F_{48}\! \left(x \right) = F_{42}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{50}\! \left(x \right)+F_{54}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{53}\! \left(x \right)
F_{52}\! \left(x \right) = F_{46}\! \left(x \right)
F_{53}\! \left(x \right) = F_{49}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{19}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{19}\! \left(x \right)+F_{42}\! \left(x \right)
F_{58}\! \left(x \right) = F_{15}\! \left(x \right)+F_{59}\! \left(x \right)+F_{83}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{68}\! \left(x \right)
F_{61}\! \left(x \right) = F_{6}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right)+F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{68}\! \left(x \right) = F_{58}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{70}\! \left(x \right)+F_{74}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{62}\! \left(x \right)
F_{73}\! \left(x \right) = F_{69}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{42}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{78}\! \left(x \right)+F_{82}\! \left(x \right)
F_{78}\! \left(x \right) = F_{12}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{81}\! \left(x \right)
F_{80}\! \left(x \right) = F_{66}\! \left(x \right)
F_{81}\! \left(x \right) = F_{77}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{76}\! \left(x \right)
F_{83}\! \left(x \right) = F_{12}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{98}\! \left(x \right)
F_{85}\! \left(x \right) = F_{19}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{15}\! \left(x \right)+F_{87}\! \left(x \right)+F_{97}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)+F_{91}\! \left(x \right)
F_{89}\! \left(x \right) = F_{10}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{67}\! \left(x \right)
F_{91}\! \left(x \right) = F_{86}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{82}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{96}\! \left(x \right)
F_{95}\! \left(x \right) = F_{90}\! \left(x \right)
F_{96}\! \left(x \right) = F_{92}\! \left(x \right)
F_{97}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{98}\! \left(x \right) = F_{42}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{101}\! \left(x \right)+F_{15}\! \left(x \right)+F_{78}\! \left(x \right)
F_{100}\! \left(x \right) = F_{12}\! \left(x \right) F_{86}\! \left(x \right)
F_{101}\! \left(x \right) = F_{12}\! \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_12(x)*F_4(x))
Eq(F_4(x), F_18(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_12(x) + F_14(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_17(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_10(x)*F_12(x))
Eq(F_17(x), F_12(x)*F_13(x))
Eq(F_18(x), F_19(x) + F_58(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_12(x)*F_21(x))
Eq(F_21(x), F_22(x) + F_26(x))
Eq(F_22(x), F_1(x) + F_23(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_12(x)*F_25(x))
Eq(F_25(x), F_1(x) + F_12(x))
Eq(F_26(x), F_19(x) + F_27(x))
Eq(F_27(x), F_15(x) + F_28(x) + F_56(x))
Eq(F_28(x), F_12(x)*F_29(x))
Eq(F_29(x), F_30(x) + F_34(x))
Eq(F_30(x), F_23(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_12(x)*F_33(x))
Eq(F_33(x), F_12(x))
Eq(F_34(x), F_27(x) + F_35(x))
Eq(F_35(x), 2*F_15(x) + F_36(x) + F_40(x))
Eq(F_36(x), F_12(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_39(x))
Eq(F_38(x), F_31(x))
Eq(F_39(x), F_35(x))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_42(x))
Eq(F_42(x), F_15(x) + F_43(x) + F_55(x))
Eq(F_43(x), F_12(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_48(x))
Eq(F_45(x), F_12(x) + F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), x**2)
Eq(F_48(x), F_42(x) + F_49(x))
Eq(F_49(x), 2*F_15(x) + F_50(x) + F_54(x))
Eq(F_50(x), F_12(x)*F_51(x))
Eq(F_51(x), F_52(x) + F_53(x))
Eq(F_52(x), F_46(x))
Eq(F_53(x), F_49(x))
Eq(F_54(x), F_12(x)*F_42(x))
Eq(F_55(x), F_12(x)*F_19(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_19(x) + F_42(x))
Eq(F_58(x), F_15(x) + F_59(x) + F_83(x))
Eq(F_59(x), F_12(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_68(x))
Eq(F_61(x), F_6(x) + F_62(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_12(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_12(x)*F_65(x))
Eq(F_68(x), F_58(x) + F_69(x))
Eq(F_69(x), 2*F_15(x) + F_70(x) + F_74(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_62(x))
Eq(F_73(x), F_69(x))
Eq(F_74(x), F_12(x)*F_75(x))
Eq(F_75(x), F_76(x))
Eq(F_76(x), F_42(x) + F_77(x))
Eq(F_77(x), 2*F_15(x) + F_78(x) + F_82(x))
Eq(F_78(x), F_12(x)*F_79(x))
Eq(F_79(x), F_80(x) + F_81(x))
Eq(F_80(x), F_66(x))
Eq(F_81(x), F_77(x))
Eq(F_82(x), F_12(x)*F_76(x))
Eq(F_83(x), F_12(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_98(x))
Eq(F_85(x), F_19(x) + F_86(x))
Eq(F_86(x), F_15(x) + F_87(x) + F_97(x))
Eq(F_87(x), F_12(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_91(x))
Eq(F_89(x), F_10(x) + F_90(x))
Eq(F_90(x), F_67(x))
Eq(F_91(x), F_86(x) + F_92(x))
Eq(F_92(x), 2*F_15(x) + F_82(x) + F_93(x))
Eq(F_93(x), F_12(x)*F_94(x))
Eq(F_94(x), F_95(x) + F_96(x))
Eq(F_95(x), F_90(x))
Eq(F_96(x), F_92(x))
Eq(F_97(x), F_12(x)*F_85(x))
Eq(F_98(x), F_42(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_101(x) + F_15(x) + F_78(x))
Eq(F_100(x), F_12(x)*F_86(x))
Eq(F_101(x), F_12(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": 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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"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": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[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": 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