0132_1203_1320
Counting sequence:
1, 1, 2, 6, 21, 75, 261, 876, 2839, 8923, 27329, 81923, 241257, 700150, 2007431, 5698047, 16039035, 44832531, 124582797, 344485968, 948551863, 2602532611, 7118674037, 19420197251, 52858164561, 143582327530, 389337126791, 1054082755431, 2849847221679, 7695355162323, 20756236255029, 55927588961988, 150556434480247, 404949676033195, 1088327518633001, 2922803260252547, 7844088432202425, 21038134640583646, 56391103066478087, 151066266230196303, 404474676913144803, 1082415968753687571, 2895256259219560797, 7740691811070538296, 20686243886649031351, 55258745186751738835, 147552200288970163421, 393842763538166321411, 1050846483226745924769, 2802858514960739039698, 7473334866536025379079, 19919782266289125074103, 53078274175163885342487, 141389106363565336277715, 376518805063927559804421, 1002382156970096146188972, 2667841688452314872573815, 7098568545047562629183611, 18882923546438833513656977, 50217948433900169783874563, 133519087024096881757449993, 354916032777824087938168006, 943210945714289239513398407, 2506085761699849994337119391, 6657171016856851500327042891, 17680431826112788514302052115, 46947012284319844867723673901, 124634261662652938884412278816, 330813850049711835412857458359, 877907854112120606374587317923, 2329353311655199964580301948229, 6179382271772976792886463872643, 16390040391423886959610389652977, 43465249198508782872355146241210, 115247990841340678100551096749191, 305531063194198453963233843645447, 809859933173532080584150674019455, 2146340596595281598600490550308051, 5687522696493432836910375683925717, 15069018138918808152291780521945748, 39919542791084074885145661706456183, 105736852744510045514582934265033291, 280032731786702449654538548082490617, 741539248901315935644659797377377411, 1963377016944307802112757599655566681, 5197789900730921297635481741054269870, 13758794977577459417456868410217428231, 36415803806005060846096565536605548271, 96371440461548247407186252705244843699, 255009780850414047442356608432324655123, 674708867847967522068709699540005311229, 1784958456622974315871445499156802777608, 4721640437900613418067962990088445942967, 12488543030480416534019540695232395165555, 33028255237235827983543177360967347526061, 87340442257623325093713832128657797241347, 230941463678495249035816961828038898049345, 610584905624669382140554878348857714754466, 1614167731582079768479228328554593622796807, 4266880767412007344137817450143032352112983, 11278007527092824452787460626598308898139623
Generating function in Maple syntax:
-(x^9+17*x^8-109*x^7+300*x^6-451*x^5+403*x^4-220*x^3+72*x^2-13*x+1)/(x-1)^2/(x^2-3*x+1)^2/(2*x-1)^3
Generating function in latex syntax:
-\frac{x^{9}+17 x^{8}-109 x^{7}+300 x^{6}-451 x^{5}+403 x^{4}-220 x^{3}+72 x^{2}-13 x +1}{\left(x -1\right)^{2} \left(x^{2}-3 x +1\right)^{2} \left(2 x -1\right)^{3}}
Generating function in sympy syntax:
(-x**9 - 17*x**8 + 109*x**7 - 300*x**6 + 451*x**5 - 403*x**4 + 220*x**3 - 72*x**2 + 13*x - 1)/((x - 1)**2*(2*x - 1)**3*(x**2 - 3*x + 1)**2)
Implicit equation for the generating function in Maple syntax:
(x-1)^2*(x^2-3*x+1)^2*(2*x-1)^3*F(x)+x^9+17*x^8-109*x^7+300*x^6-451*x^5+403*x^4-220*x^3+72*x^2-13*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right)^{2} \left(x^{2}-3 x +1\right)^{2} \left(2 x -1\right)^{3} F \! \left(x \right)+x^{9}+17 x^{8}-109 x^{7}+300 x^{6}-451 x^{5}+403 x^{4}-220 x^{3}+72 x^{2}-13 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/80*((24*n+32)*5^(1/2)-40*n)*(3/2-1/2*5^(1/2))^(-n)+1/80*((-24*n-32)*5^(1/2)-40*n)*(3/2+1/2*5^(1/2))^(-n)+1/80*(-5*n^2-45*n+10)*2^n-n+1)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(\left(24 n +32\right) \sqrt{5}-40 n \right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{80}+\\\frac{\left(\left(-24 n -32\right) \sqrt{5}-40 n \right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{80}+\frac{\left(-5 n^{2}-45 n +10\right) 2^{n}}{80}-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) = 21
a(5) = 75
a(6) = 261
a(7) = 876
a(8) = 2839
a(9) = 8923
a(n+7) = 8*a(n)-60*a(n+1)+166*a(n+2)-217*a(n+3)+152*a(n+4)-59*a(n+5)+12*a(n+6)+n-2, 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) = 21
a \! \left(5\right) = 75
a \! \left(6\right) = 261
a \! \left(7\right) = 876
a \! \left(8\right) = 2839
a \! \left(9\right) = 8923
a \! \left(n +7\right) = 8 a \! \left(n \right)-60 a \! \left(n +1\right)+166 a \! \left(n +2\right)-217 a \! \left(n +3\right)+152 a \! \left(n +4\right)-59 a \! \left(n +5\right)+12 a \! \left(n +6\right)+n -2, \quad n \geq 10
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14715/
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[21,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[6,x]
F[14,x] = F[15,x]+F[16,x]+F[20,x]
F[15,x] = 0
F[16,x] = F[12,x]*F[17,x]
F[17,x] = F[18,x]+F[19,x]
F[18,x] = F[10,x]
F[19,x] = F[14,x]
F[20,x] = F[12,x]*F[13,x]
F[21,x] = F[22,x]+F[6,x]
F[22,x] = F[15,x]+F[23,x]+F[76,x]
F[23,x] = F[12,x]*F[24,x]
F[24,x] = F[25,x]+F[39,x]
F[25,x] = F[26,x]+F[6,x]
F[26,x] = F[27,x]
F[27,x] = F[12,x]*F[28,x]
F[28,x] = F[29,x]+F[32,x]
F[29,x] = F[10,x]+F[30,x]
F[30,x] = F[31,x]
F[31,x] = F[12,x]*F[29,x]
F[32,x] = F[26,x]+F[33,x]
F[33,x] = 2*F[15,x]+F[34,x]+F[38,x]
F[34,x] = F[12,x]*F[35,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[30,x]
F[37,x] = F[33,x]
F[38,x] = F[12,x]*F[32,x]
F[39,x] = F[22,x]+F[40,x]
F[40,x] = 2*F[15,x]+F[41,x]+F[45,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[26,x]
F[44,x] = F[40,x]
F[45,x] = F[12,x]*F[46,x]
F[46,x] = F[47,x]+F[54,x]
F[47,x] = F[14,x]+F[48,x]
F[48,x] = 2*F[15,x]+F[49,x]+F[53,x]
F[49,x] = F[12,x]*F[50,x]
F[50,x] = F[51,x]+F[52,x]
F[51,x] = F[30,x]
F[52,x] = F[48,x]
F[53,x] = F[12,x]*F[47,x]
F[54,x] = F[55,x]+F[69,x]
F[55,x] = F[56,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[58,x]+F[61,x]
F[58,x] = F[14,x]+F[59,x]
F[59,x] = F[60,x]
F[60,x] = F[12,x]*F[58,x]
F[61,x] = F[55,x]+F[62,x]
F[62,x] = 2*F[15,x]+F[63,x]+F[64,x]+F[68,x]
F[63,x] = 0
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[66,x]+F[67,x]
F[66,x] = F[59,x]
F[67,x] = F[62,x]
F[68,x] = F[12,x]*F[61,x]
F[69,x] = 2*F[15,x]+F[70,x]+F[71,x]+F[75,x]
F[70,x] = 0
F[71,x] = F[12,x]*F[72,x]
F[72,x] = F[73,x]+F[74,x]
F[73,x] = F[48,x]
F[74,x] = F[69,x]
F[75,x] = F[12,x]*F[54,x]
F[76,x] = F[12,x]*F[77,x]
F[77,x] = F[78,x]+F[85,x]
F[78,x] = F[6,x]+F[79,x]
F[79,x] = F[15,x]+F[80,x]+F[84,x]
F[80,x] = F[12,x]*F[81,x]
F[81,x] = F[82,x]+F[83,x]
F[82,x] = F[10,x]+F[30,x]
F[83,x] = F[48,x]+F[79,x]
F[84,x] = F[12,x]*F[78,x]
F[85,x] = F[86,x]+F[96,x]
F[86,x] = F[15,x]+F[16,x]+F[87,x]
F[87,x] = F[12,x]*F[88,x]
F[88,x] = F[13,x]+F[89,x]
F[89,x] = F[86,x]+F[90,x]
F[90,x] = F[15,x]+F[91,x]+F[92,x]+F[95,x]
F[91,x] = 0
F[92,x] = F[12,x]*F[93,x]
F[93,x] = F[19,x]+F[94,x]
F[94,x] = F[90,x]
F[95,x] = F[12,x]*F[89,x]
F[96,x] = F[101,x]+F[15,x]+F[49,x]+F[97,x]
F[97,x] = F[12,x]*F[98,x]
F[98,x] = F[100,x]+F[99,x]
F[99,x] = F[79,x]
F[100,x] = F[96,x]
F[101,x] = F[12,x]*F[85,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_{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_{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_{6}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{20}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)
F_{18}\! \left(x \right) = F_{10}\! \left(x \right)
F_{19}\! \left(x \right) = F_{14}\! \left(x \right)
F_{20}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{6}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)+F_{23}\! \left(x \right)+F_{76}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{39}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{6}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \left(x \right)
F_{29}\! \left(x \right) = F_{10}\! \left(x \right)+F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{26}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{34}\! \left(x \right)+F_{38}\! \left(x \right)
F_{34}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)
F_{37}\! \left(x \right) = F_{33}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right) F_{32}\! \left(x \right)
F_{39}\! \left(x \right) = F_{22}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{41}\! \left(x \right)+F_{45}\! \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_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{26}\! \left(x \right)
F_{44}\! \left(x \right) = F_{40}\! \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_{54}\! \left(x \right)
F_{47}\! \left(x \right) = F_{14}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{49}\! \left(x \right)+F_{53}\! \left(x \right)
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_{52}\! \left(x \right)
F_{51}\! \left(x \right) = F_{30}\! \left(x \right)
F_{52}\! \left(x \right) = F_{48}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{69}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{61}\! \left(x \right)
F_{58}\! \left(x \right) = F_{14}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{55}\! \left(x \right)+F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{63}\! \left(x \right)+F_{64}\! \left(x \right)+F_{68}\! \left(x \right)
F_{63}\! \left(x \right) = 0
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{67}\! \left(x \right)
F_{66}\! \left(x \right) = F_{59}\! \left(x \right)
F_{67}\! \left(x \right) = F_{62}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{69}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{70}\! \left(x \right)+F_{71}\! \left(x \right)+F_{75}\! \left(x \right)
F_{70}\! \left(x \right) = 0
F_{71}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = F_{48}\! \left(x \right)
F_{74}\! \left(x \right) = F_{69}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{76}\! \left(x \right) = F_{12}\! \left(x \right) F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{85}\! \left(x \right)
F_{78}\! \left(x \right) = F_{6}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{15}\! \left(x \right)+F_{80}\! \left(x \right)+F_{84}\! \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_{10}\! \left(x \right)+F_{30}\! \left(x \right)
F_{83}\! \left(x \right) = F_{48}\! \left(x \right)+F_{79}\! \left(x \right)
F_{84}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{96}\! \left(x \right)
F_{86}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{13}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{86}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{15}\! \left(x \right)+F_{91}\! \left(x \right)+F_{92}\! \left(x \right)+F_{95}\! \left(x \right)
F_{91}\! \left(x \right) = 0
F_{92}\! \left(x \right) = F_{12}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{19}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{90}\! \left(x \right)
F_{95}\! \left(x \right) = F_{12}\! \left(x \right) F_{89}\! \left(x \right)
F_{96}\! \left(x \right) = F_{101}\! \left(x \right)+F_{15}\! \left(x \right)+F_{49}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{12}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{100}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{79}\! \left(x \right)
F_{100}\! \left(x \right) = F_{96}\! \left(x \right)
F_{101}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \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_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_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_6(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_20(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_12(x)*F_17(x))
Eq(F_17(x), F_18(x) + F_19(x))
Eq(F_18(x), F_10(x))
Eq(F_19(x), F_14(x))
Eq(F_20(x), F_12(x)*F_13(x))
Eq(F_21(x), F_22(x) + F_6(x))
Eq(F_22(x), F_15(x) + F_23(x) + F_76(x))
Eq(F_23(x), F_12(x)*F_24(x))
Eq(F_24(x), F_25(x) + F_39(x))
Eq(F_25(x), F_26(x) + F_6(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_12(x)*F_28(x))
Eq(F_28(x), F_29(x) + F_32(x))
Eq(F_29(x), F_10(x) + F_30(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_12(x)*F_29(x))
Eq(F_32(x), F_26(x) + F_33(x))
Eq(F_33(x), 2*F_15(x) + F_34(x) + F_38(x))
Eq(F_34(x), F_12(x)*F_35(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_30(x))
Eq(F_37(x), F_33(x))
Eq(F_38(x), F_12(x)*F_32(x))
Eq(F_39(x), F_22(x) + F_40(x))
Eq(F_40(x), 2*F_15(x) + F_41(x) + F_45(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_26(x))
Eq(F_44(x), F_40(x))
Eq(F_45(x), F_12(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_54(x))
Eq(F_47(x), F_14(x) + F_48(x))
Eq(F_48(x), 2*F_15(x) + F_49(x) + F_53(x))
Eq(F_49(x), F_12(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_52(x))
Eq(F_51(x), F_30(x))
Eq(F_52(x), F_48(x))
Eq(F_53(x), F_12(x)*F_47(x))
Eq(F_54(x), F_55(x) + F_69(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_61(x))
Eq(F_58(x), F_14(x) + F_59(x))
Eq(F_59(x), F_60(x))
Eq(F_60(x), F_12(x)*F_58(x))
Eq(F_61(x), F_55(x) + F_62(x))
Eq(F_62(x), 2*F_15(x) + F_63(x) + F_64(x) + F_68(x))
Eq(F_63(x), 0)
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_67(x))
Eq(F_66(x), F_59(x))
Eq(F_67(x), F_62(x))
Eq(F_68(x), F_12(x)*F_61(x))
Eq(F_69(x), 2*F_15(x) + F_70(x) + F_71(x) + F_75(x))
Eq(F_70(x), 0)
Eq(F_71(x), F_12(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_74(x))
Eq(F_73(x), F_48(x))
Eq(F_74(x), F_69(x))
Eq(F_75(x), F_12(x)*F_54(x))
Eq(F_76(x), F_12(x)*F_77(x))
Eq(F_77(x), F_78(x) + F_85(x))
Eq(F_78(x), F_6(x) + F_79(x))
Eq(F_79(x), F_15(x) + F_80(x) + F_84(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_10(x) + F_30(x))
Eq(F_83(x), F_48(x) + F_79(x))
Eq(F_84(x), F_12(x)*F_78(x))
Eq(F_85(x), F_86(x) + F_96(x))
Eq(F_86(x), F_15(x) + F_16(x) + F_87(x))
Eq(F_87(x), F_12(x)*F_88(x))
Eq(F_88(x), F_13(x) + F_89(x))
Eq(F_89(x), F_86(x) + F_90(x))
Eq(F_90(x), F_15(x) + F_91(x) + F_92(x) + F_95(x))
Eq(F_91(x), 0)
Eq(F_92(x), F_12(x)*F_93(x))
Eq(F_93(x), F_19(x) + F_94(x))
Eq(F_94(x), F_90(x))
Eq(F_95(x), F_12(x)*F_89(x))
Eq(F_96(x), F_101(x) + F_15(x) + F_49(x) + F_97(x))
Eq(F_97(x), F_12(x)*F_98(x))
Eq(F_98(x), F_100(x) + F_99(x))
Eq(F_99(x), F_79(x))
Eq(F_100(x), F_96(x))
Eq(F_101(x), F_12(x)*F_85(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": [1, 2, 0, 3], "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": [1, 2, 0, 3], "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": [1, 2, 0, 3], "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], [1, 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, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "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], [2, 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, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "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, 2, 0, 3], "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], [1, 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, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "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], [1, 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, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "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": 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[{"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], [0, 0], [0, 0]]}, {"patt": [1, 2, 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, 1, 2], "pos": [[0, 0], [0, 0], [1, 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, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "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": 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[{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 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": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": 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