0123_0132_2130_3102
Counting sequence:
1, 1, 2, 6, 20, 58, 140, 317, 712, 1592, 3573, 8065, 18338, 42021, 97037, 225722, 528543, 1244808, 2946248, 7002017, 16696966, 39923368, 95664425, 229619127, 551872262, 1327740913, 3196914891, 7702163890, 18565095467, 44764860814, 107968422164, 260464219205, 628449019252, 1516514471768, 3659866628637, 8833172700445, 21320319912362, 51462477617373, 124223385932729, 299866823766890, 723874520696631, 1747454874059460, 4218469232286176, 10183775200408457, 24584803827706066, 59350986298513480, 143282043238380881, 345905708703562803, 835074906887799566, 2016018711827574889, 4867039213957805655, 11749951763636672098, 28366653442721543747, 68482682515038805930, 165330870373310354348, 399142134110962036205, 963610572199697898016, 2326354165812068566520, 5616300712306845450309, 13558919264470012591993, 32734066685419588260530, 79026907685275169147925, 190787592427556569342757, 460601513739836135314970, 1111989463071959682557391, 2684578127497780201294272, 6481141095448831670137592, 15646851076765261916162033, 37774824771758241095439070, 91196463675944731012829416, 220167678251872872303837305, 531531672464386505445984111, 1283230727797223786424684566, 3097992537370776380367045985, 7479214621294147076847251619, 18056419417689142954017487378, 43592048732498275698212554331, 105240507434946846991826912902, 254073044707929565136330775620, 613386559063571793593661481493, 1480846087263418805176396197004, 3575078582451782744357483593112, 8631002949897518051246425518957, 20837083877720832827917295827093, 50305169496308728061190154771130, 121447420452313124137779946172877, 293200005564944013942033771744593, 707847421910317790227800544847306, 1708894830041976453874980975030375, 4125637043307335825619461999185788, 9960168839283228527311165195617296, 24045974567127700158220917654391001, 58052117664047680713246504966287530, 140150209276243215741929097859869832, 338352534978577817407422963016017569, 816855276757491887006827635152767851, 1972063083541756979785958584572561950, 4760981433937412043597581650688217817, 11494025931609418980307163315371487151, 27749033257541968052511110633256937666, 66992092367464861020407903226624431219
Generating function in Maple syntax:
-(6*x^16+5*x^15-58*x^14-22*x^13+197*x^12-8*x^11-261*x^10+101*x^9+77*x^8-32*x^7+32*x^6-55*x^5-x^4+44*x^3-31*x^2+9*x-1)/(2*x-1)/(x^2+2*x-1)/(x-1)^3/(x^2+x-1)^3
Generating function in latex syntax:
-\frac{6 x^{16}+5 x^{15}-58 x^{14}-22 x^{13}+197 x^{12}-8 x^{11}-261 x^{10}+101 x^{9}+77 x^{8}-32 x^{7}+32 x^{6}-55 x^{5}-x^{4}+44 x^{3}-31 x^{2}+9 x -1}{\left(2 x -1\right) \left(x^{2}+2 x -1\right) \left(x -1\right)^{3} \left(x^{2}+x -1\right)^{3}}
Generating function in sympy syntax:
(-6*x**16 - 5*x**15 + 58*x**14 + 22*x**13 - 197*x**12 + 8*x**11 + 261*x**10 - 101*x**9 - 77*x**8 + 32*x**7 - 32*x**6 + 55*x**5 + x**4 - 44*x**3 + 31*x**2 - 9*x + 1)/((x - 1)**3*(2*x - 1)*(x**2 + x - 1)**3*(x**2 + 2*x - 1))
Implicit equation for the generating function in Maple syntax:
(2*x-1)*(x^2+2*x-1)*(x-1)^3*(x^2+x-1)^3*F(x)+6*x^16+5*x^15-58*x^14-22*x^13+197*x^12-8*x^11-261*x^10+101*x^9+77*x^8-32*x^7+32*x^6-55*x^5-x^4+44*x^3-31*x^2+9*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right) \left(x^{2}+2 x -1\right) \left(x -1\right)^{3} \left(x^{2}+x -1\right)^{3} F \! \left(x \right)+6 x^{16}+5 x^{15}-58 x^{14}-22 x^{13}+197 x^{12}-8 x^{11}-261 x^{10}+101 x^{9}+77 x^{8}-32 x^{7}+32 x^{6}-55 x^{5}-x^{4}+44 x^{3}-31 x^{2}+9 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 2,2,n = 3,6,n = 4,20,1/500*((-5*n^2+105*n+302)*5^(1/2)+25*n^2+235*n+750)*(-1/2*5^(1/2)-1/2)^(-n)+1/500*((5*n^2-105*n-302)*5^(1/2)+25*n^2+235*n+750)*(1/2*5^(1/2)-1/2)^(-n)+1/2*n^2-1/4*(-1-2^(1/2))^(-n)*2^(1/2)+1/4*(2^(1/2)-1)^(-n)*2^(1/2)-3/2*n+1/4*2^n-5)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 2 & n =2 \\ 6 & n =3 \\ 20 & n =4 \\ \frac{\left(\left(-5 n^{2}+105 n +302\right) \sqrt{5}+25 n^{2}+235 n +750\right) \left(-\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{500}+\\\frac{\left(\left(5 n^{2}-105 n -302\right) \sqrt{5}+25 n^{2}+235 n +750\right) \left(\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{-n}}{500}+\frac{n^{2}}{2}-\\\frac{\left(-1-\sqrt{2}\right)^{-n} \sqrt{2}}{4}+\frac{\left(\sqrt{2}-1\right)^{-n} \sqrt{2}}{4}-\frac{3 n}{2}+\frac{2^{n}}{4}-5 & \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) = 58
a(6) = 140
a(7) = 317
a(8) = 712
a(9) = 1592
a(10) = 3573
a(11) = 8065
a(12) = 18338
a(13) = 42021
a(14) = 97037
a(15) = 225722
a(16) = 528543
a(n+9) = -n^2+9*a(n+1)+5*a(n+2)-21*a(n+3)-12*a(n+4)+26*a(n+5)+2*a(n+6)-15*a(n+7)+7*a(n+8)+2*a(n)+11*n-3, n >= 17
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) = 58
a \! \left(6\right) = 140
a \! \left(7\right) = 317
a \! \left(8\right) = 712
a \! \left(9\right) = 1592
a \! \left(10\right) = 3573
a \! \left(11\right) = 8065
a \! \left(12\right) = 18338
a \! \left(13\right) = 42021
a \! \left(14\right) = 97037
a \! \left(15\right) = 225722
a \! \left(16\right) = 528543
a \! \left(n +9\right) = -n^{2}+9 a \! \left(n +1\right)+5 a \! \left(n +2\right)-21 a \! \left(n +3\right)-12 a \! \left(n +4\right)+26 a \! \left(n +5\right)+2 a \! \left(n +6\right)-15 a \! \left(n +7\right)+7 a \! \left(n +8\right)+2 a \! \left(n \right)+11 n -3, \quad n \geq 17
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14883/
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[25,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[11,x]
F[10,x] = F[1,x]+F[4,x]
F[11,x] = F[12,x]+F[18,x]
F[12,x] = F[13,x]
F[13,x] = F[14,x]*F[4,x]
F[14,x] = F[10,x]+F[15,x]
F[15,x] = F[12,x]+F[16,x]
F[16,x] = F[17,x]
F[17,x] = F[12,x]*F[4,x]
F[18,x] = F[17,x]+F[19,x]+F[20,x]
F[19,x] = 0
F[20,x] = F[21,x]*F[4,x]
F[21,x] = F[22,x]+F[23,x]
F[22,x] = F[4,x]
F[23,x] = F[24,x]
F[24,x] = F[20,x]
F[25,x] = F[26,x]+F[40,x]
F[26,x] = F[27,x]
F[27,x] = F[28,x]*F[4,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = F[1,x]+F[12,x]
F[30,x] = F[26,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[33,x]*F[4,x]
F[33,x] = F[34,x]+F[37,x]
F[34,x] = F[26,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[26,x]*F[4,x]
F[37,x] = F[31,x]+F[38,x]
F[38,x] = F[39,x]
F[39,x] = F[31,x]*F[4,x]
F[40,x] = F[19,x]+F[41,x]+F[81,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[43,x]+F[62,x]
F[43,x] = F[44,x]+F[7,x]
F[44,x] = F[19,x]+F[20,x]+F[45,x]
F[45,x] = F[4,x]*F[46,x]
F[46,x] = F[11,x]+F[47,x]
F[47,x] = F[48,x]+F[56,x]
F[48,x] = F[19,x]+F[49,x]+F[51,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[22,x]
F[51,x] = F[4,x]*F[52,x]
F[52,x] = F[15,x]+F[53,x]
F[53,x] = F[48,x]+F[54,x]
F[54,x] = F[55,x]
F[55,x] = F[4,x]*F[48,x]
F[56,x] = F[19,x]+F[55,x]+F[57,x]+F[58,x]
F[57,x] = 0
F[58,x] = F[4,x]*F[59,x]
F[59,x] = F[23,x]+F[60,x]
F[60,x] = F[61,x]
F[61,x] = F[58,x]
F[62,x] = F[63,x]+F[80,x]
F[63,x] = F[64,x]
F[64,x] = F[4,x]*F[65,x]
F[65,x] = F[66,x]+F[68,x]
F[66,x] = F[67,x]+F[7,x]
F[67,x] = F[20,x]
F[68,x] = F[63,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[79,x]
F[72,x] = F[73,x]
F[73,x] = F[74,x]
F[74,x] = F[4,x]*F[75,x]
F[75,x] = F[76,x]+F[77,x]
F[76,x] = F[24,x]+F[4,x]
F[77,x] = F[73,x]+F[78,x]
F[78,x] = F[70,x]
F[79,x] = F[78,x]
F[80,x] = F[70,x]
F[81,x] = F[4,x]*F[82,x]
F[82,x] = F[83,x]+F[90,x]
F[83,x] = F[26,x]+F[84,x]
F[84,x] = F[19,x]+F[36,x]+F[85,x]
F[85,x] = F[4,x]*F[86,x]
F[86,x] = F[87,x]+F[88,x]
F[87,x] = F[18,x]+F[4,x]
F[88,x] = F[73,x]+F[89,x]
F[89,x] = F[70,x]
F[90,x] = F[100,x]+F[91,x]
F[91,x] = F[19,x]+F[92,x]+F[95,x]
F[92,x] = F[4,x]*F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[12,x]+F[48,x]
F[95,x] = F[4,x]*F[96,x]
F[96,x] = F[34,x]+F[97,x]
F[97,x] = F[91,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[4,x]*F[91,x]
F[100,x] = F[101,x]+F[104,x]+F[19,x]+F[99,x]
F[101,x] = F[102,x]*F[4,x]
F[102,x] = F[103,x]
F[103,x] = F[18,x]+F[56,x]
F[104,x] = F[105,x]*F[4,x]
F[105,x] = F[106,x]+F[72,x]
F[106,x] = F[107,x]
F[107,x] = 2*F[19,x]+F[104,x]+F[108,x]
F[108,x] = F[109,x]*F[4,x]
F[109,x] = F[110,x]
F[110,x] = F[24,x]+F[61,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_{25}\! \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_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{18}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{14}\! \left(x \right) = F_{10}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{12}\! \left(x \right) F_{4}\! \left(x \right)
F_{18}\! \left(x \right) = F_{17}\! \left(x \right)+F_{19}\! \left(x \right)+F_{20}\! \left(x \right)
F_{19}\! \left(x \right) = 0
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)
F_{22}\! \left(x \right) = F_{4}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{20}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{40}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{30}\! \left(x \right) = F_{26}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right) F_{4}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{37}\! \left(x \right)
F_{34}\! \left(x \right) = F_{26}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{26}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{31}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{40}\! \left(x \right) = F_{19}\! \left(x \right)+F_{41}\! \left(x \right)+F_{81}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{62}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{7}\! \left(x \right)
F_{44}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \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_{11}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{56}\! \left(x \right)
F_{48}\! \left(x \right) = F_{19}\! \left(x \right)+F_{49}\! \left(x \right)+F_{51}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{22}\! \left(x \right)
F_{51}\! \left(x \right) = F_{4}\! \left(x \right) F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{15}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{48}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{4}\! \left(x \right) F_{48}\! \left(x \right)
F_{56}\! \left(x \right) = F_{19}\! \left(x \right)+F_{55}\! \left(x \right)+F_{57}\! \left(x \right)+F_{58}\! \left(x \right)
F_{57}\! \left(x \right) = 0
F_{58}\! \left(x \right) = F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{23}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{58}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{80}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{4}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{68}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{7}\! \left(x \right)
F_{67}\! \left(x \right) = F_{20}\! \left(x \right)
F_{68}\! \left(x \right) = F_{63}\! \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_{79}\! \left(x \right)
F_{72}\! \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_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{77}\! \left(x \right)
F_{76}\! \left(x \right) = F_{24}\! \left(x \right)+F_{4}\! \left(x \right)
F_{77}\! \left(x \right) = F_{73}\! \left(x \right)+F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{70}\! \left(x \right)
F_{79}\! \left(x \right) = F_{78}\! \left(x \right)
F_{80}\! \left(x \right) = F_{70}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{90}\! \left(x \right)
F_{83}\! \left(x \right) = F_{26}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{19}\! \left(x \right)+F_{36}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{4}\! \left(x \right) F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)+F_{88}\! \left(x \right)
F_{87}\! \left(x \right) = F_{18}\! \left(x \right)+F_{4}\! \left(x \right)
F_{88}\! \left(x \right) = F_{73}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{70}\! \left(x \right)
F_{90}\! \left(x \right) = F_{100}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{19}\! \left(x \right)+F_{92}\! \left(x \right)+F_{95}\! \left(x \right)
F_{92}\! \left(x \right) = F_{4}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right)+F_{48}\! \left(x \right)
F_{95}\! \left(x \right) = F_{4}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{34}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{91}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{4}\! \left(x \right) F_{91}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{104}\! \left(x \right)+F_{19}\! \left(x \right)+F_{99}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{4}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{18}\! \left(x \right)+F_{56}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{4}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{72}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)
F_{107}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{104}\! \left(x \right)+F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{4}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{24}\! \left(x \right)+F_{61}\! \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_25(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_11(x))
Eq(F_10(x), F_1(x) + F_4(x))
Eq(F_11(x), F_12(x) + F_18(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_14(x)*F_4(x))
Eq(F_14(x), F_10(x) + F_15(x))
Eq(F_15(x), F_12(x) + F_16(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_12(x)*F_4(x))
Eq(F_18(x), F_17(x) + F_19(x) + F_20(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_21(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_23(x))
Eq(F_22(x), F_4(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_20(x))
Eq(F_25(x), F_26(x) + F_40(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_28(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), F_1(x) + F_12(x))
Eq(F_30(x), F_26(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_33(x)*F_4(x))
Eq(F_33(x), F_34(x) + F_37(x))
Eq(F_34(x), F_26(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_26(x)*F_4(x))
Eq(F_37(x), F_31(x) + F_38(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_31(x)*F_4(x))
Eq(F_40(x), F_19(x) + F_41(x) + F_81(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_62(x))
Eq(F_43(x), F_44(x) + F_7(x))
Eq(F_44(x), F_19(x) + F_20(x) + F_45(x))
Eq(F_45(x), F_4(x)*F_46(x))
Eq(F_46(x), F_11(x) + F_47(x))
Eq(F_47(x), F_48(x) + F_56(x))
Eq(F_48(x), F_19(x) + F_49(x) + F_51(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_22(x))
Eq(F_51(x), F_4(x)*F_52(x))
Eq(F_52(x), F_15(x) + F_53(x))
Eq(F_53(x), F_48(x) + F_54(x))
Eq(F_54(x), F_55(x))
Eq(F_55(x), F_4(x)*F_48(x))
Eq(F_56(x), F_19(x) + F_55(x) + F_57(x) + F_58(x))
Eq(F_57(x), 0)
Eq(F_58(x), F_4(x)*F_59(x))
Eq(F_59(x), F_23(x) + F_60(x))
Eq(F_60(x), F_61(x))
Eq(F_61(x), F_58(x))
Eq(F_62(x), F_63(x) + F_80(x))
Eq(F_63(x), F_64(x))
Eq(F_64(x), F_4(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_68(x))
Eq(F_66(x), F_67(x) + F_7(x))
Eq(F_67(x), F_20(x))
Eq(F_68(x), F_63(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) + F_79(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_4(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_77(x))
Eq(F_76(x), F_24(x) + F_4(x))
Eq(F_77(x), F_73(x) + F_78(x))
Eq(F_78(x), F_70(x))
Eq(F_79(x), F_78(x))
Eq(F_80(x), F_70(x))
Eq(F_81(x), F_4(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_90(x))
Eq(F_83(x), F_26(x) + F_84(x))
Eq(F_84(x), F_19(x) + F_36(x) + F_85(x))
Eq(F_85(x), F_4(x)*F_86(x))
Eq(F_86(x), F_87(x) + F_88(x))
Eq(F_87(x), F_18(x) + F_4(x))
Eq(F_88(x), F_73(x) + F_89(x))
Eq(F_89(x), F_70(x))
Eq(F_90(x), F_100(x) + F_91(x))
Eq(F_91(x), F_19(x) + F_92(x) + F_95(x))
Eq(F_92(x), F_4(x)*F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_12(x) + F_48(x))
Eq(F_95(x), F_4(x)*F_96(x))
Eq(F_96(x), F_34(x) + F_97(x))
Eq(F_97(x), F_91(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_4(x)*F_91(x))
Eq(F_100(x), F_101(x) + F_104(x) + F_19(x) + F_99(x))
Eq(F_101(x), F_102(x)*F_4(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_18(x) + F_56(x))
Eq(F_104(x), F_105(x)*F_4(x))
Eq(F_105(x), F_106(x) + F_72(x))
Eq(F_106(x), F_107(x))
Eq(F_107(x), F_104(x) + F_108(x) + 2*F_19(x))
Eq(F_108(x), F_109(x)*F_4(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_24(x) + F_61(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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 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]]}, {"patt": [3, 1, 0, 2], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 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]]}, {"patt": [3, 1, 0, 2], "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, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 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]]}, {"patt": [3, 1, 0, 2], "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], "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": [0, 1, 2], "pos": [[0, 1], [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, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"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": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "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, 1, 2], "pos": [[1, 2], [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, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 1, 2, 3], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"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": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[1, 2], [1, 2], [1, 2], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 0], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "pos": [[1, 2], [1, 2], [1, 0], [1, 2]]}, {"patt": [3, 1, 0, 2], "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": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 0, 2], "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, 1], [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, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"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": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "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, 1], [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, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"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": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 1, 3, 0], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 0], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 0, 2], "pos": [[0, 1], 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