0132_0213_0231_1203_3120
Counting sequence:
1, 1, 2, 6, 19, 56, 154, 395, 950, 2166, 4742, 10090, 21081, 43592, 89718, 184441, 379468, 781918, 1613730, 3334560, 6895751, 14264640, 29505922, 61009895, 126080002, 260370038, 537282830, 1107816150, 2282351669, 4698427144, 9664669374, 19865437301, 40803662616, 83753639806, 171800823946, 352189861708, 721557524259, 1477472314848, 3023661167594, 6184757812323, 12644389438798, 25838529894326, 52776565817302, 107752148380994, 219902335734545, 448600755791880, 914793687623366, 1864771735866865, 3799912202805348, 7740561879033182, 15762598717810866, 32088147369818872, 65302194624754111, 132856189038700480, 270215977677225234, 549439154578282335, 1116892707631440410, 2269814212243181238, 4611686018481181918, 9367487224990249646, 19023204826078932205, 38622870404402220872, 78398662313345920142, 159103167635833315053, 322818021290014361648, 654859414616795779582, 1328165573307204660762, 2693224634761722533540, 5460236245818167184987, 11068046444225883693280, 22431240793630981268218, 45452777397620516483803, 92086146415958278846566, 186533476073351200138614, 377789318629571849516582, 765023370224882776535322, 1548936206381243902846921, 3135651344625444716902088, 6346860552976803485959702, 12844836833405435325319529, 25991905121714527627214972, 52588273153236369499453278, 106385472126087367804405442, 215188795891403993560405072, 435213295061266503391384311, 880097996679450039719822144, 1779538806472734145739994018, 3597763239173136424539177175, 7272897730801609115689473586, 14700537966513890765130280438, 29710560942849126598330880430, 60040091905340943333410921094, 121318123849967266940971970981, 245112127778505294430941827208, 495176015714152109960625520990, 1000255551742587262119532109669, 2020318144113740608636477822792, 4080250369484613386068691478398, 8239728901483491109729823563946, 16637914127995510894645560894972, 33592740906048079139664048926099
Generating function in Maple syntax:
-(2*x^10-14*x^9+31*x^8-54*x^7+111*x^6-171*x^5+171*x^4-110*x^3+44*x^2-10*x+1)/(2*x-1)^2/(x-1)^7
Generating function in latex syntax:
-\frac{2 x^{10}-14 x^{9}+31 x^{8}-54 x^{7}+111 x^{6}-171 x^{5}+171 x^{4}-110 x^{3}+44 x^{2}-10 x +1}{\left(2 x -1\right)^{2} \left(x -1\right)^{7}}
Generating function in sympy syntax:
(-2*x**10 + 14*x**9 - 31*x**8 + 54*x**7 - 111*x**6 + 171*x**5 - 171*x**4 + 110*x**3 - 44*x**2 + 10*x - 1)/((x - 1)**7*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^2*(x-1)^7*F(x)+2*x^10-14*x^9+31*x^8-54*x^7+111*x^6-171*x^5+171*x^4-110*x^3+44*x^2-10*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{2} \left(x -1\right)^{7} F \! \left(x \right)+2 x^{10}-14 x^{9}+31 x^{8}-54 x^{7}+111 x^{6}-171 x^{5}+171 x^{4}-110 x^{3}+44 x^{2}-10 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,-19/60*n+3*2^(-1+n)+1/240*n^5-25/144*n^4+13/16*n^3+1/720*n^6+1/4*2^n*n-419/180*n^2)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ -\frac{19 n}{60}+3 \,2^{-1+n}+\frac{n^{5}}{240}-\frac{25 n^{4}}{144}+\frac{13 n^{3}}{16}+\frac{n^{6}}{720}+\frac{2^{n} n}{4}-\frac{419 n^{2}}{180} & \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) = 56
a(6) = 154
a(7) = 395
a(8) = 950
a(9) = 2166
a(10) = 4742
a(n+2) = 1/720*n^6-1/80*n^5-31/144*n^4+37/16*n^3-2443/360*n^2-4*a(n)+4*a(n+1)+67/10*n+2, n >= 11
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) = 56
a \! \left(6\right) = 154
a \! \left(7\right) = 395
a \! \left(8\right) = 950
a \! \left(9\right) = 2166
a \! \left(10\right) = 4742
a \! \left(n +2\right) = \frac{n^{6}}{720}-\frac{n^{5}}{80}-\frac{31 n^{4}}{144}+\frac{37 n^{3}}{16}-\frac{2443 n^{2}}{360}-4 a \! \left(n \right)+4 a \! \left(n +1\right)+\frac{67 n}{10}+2, \quad n \geq 11
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18162/
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[19,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[17,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[1,x]+F[14,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[13,x]
F[19,x] = F[20,x]+F[34,x]
F[20,x] = F[21,x]
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[23,x]+F[28,x]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[12,x]*F[26,x]
F[26,x] = F[27,x]+F[9,x]
F[27,x] = F[14,x]
F[28,x] = F[20,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[32,x]+F[33,x]
F[32,x] = F[24,x]
F[33,x] = F[29,x]
F[34,x] = F[35,x]+F[36,x]+F[94,x]
F[35,x] = 0
F[36,x] = F[12,x]*F[37,x]
F[37,x] = F[38,x]+F[48,x]
F[38,x] = F[39,x]+F[6,x]
F[39,x] = F[40,x]
F[40,x] = F[12,x]*F[41,x]
F[41,x] = F[13,x]+F[42,x]
F[42,x] = F[43,x]+F[46,x]
F[43,x] = F[44,x]
F[44,x] = F[12,x]*F[45,x]
F[45,x] = F[14,x]+F[43,x]
F[46,x] = F[47,x]
F[47,x] = F[12,x]*F[42,x]
F[48,x] = F[34,x]+F[49,x]
F[49,x] = 2*F[35,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[39,x]
F[53,x] = F[49,x]
F[54,x] = F[12,x]*F[55,x]
F[55,x] = F[56,x]+F[68,x]
F[56,x] = F[57,x]+F[62,x]
F[57,x] = F[58,x]
F[58,x] = F[12,x]*F[59,x]
F[59,x] = F[60,x]+F[61,x]
F[60,x] = F[14,x]
F[61,x] = F[57,x]
F[62,x] = 2*F[35,x]+F[63,x]+F[67,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[65,x]+F[66,x]
F[65,x] = F[17,x]
F[66,x] = F[62,x]
F[67,x] = F[12,x]*F[56,x]
F[68,x] = F[69,x]+F[81,x]
F[69,x] = 2*F[35,x]+F[70,x]+F[79,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[43,x]
F[73,x] = F[74,x]
F[74,x] = F[75,x]
F[75,x] = F[12,x]*F[76,x]
F[76,x] = F[77,x]+F[78,x]
F[77,x] = F[43,x]
F[78,x] = F[74,x]
F[79,x] = F[12,x]*F[80,x]
F[80,x] = F[57,x]+F[69,x]
F[81,x] = 3*F[35,x]+F[82,x]+F[93,x]
F[82,x] = F[12,x]*F[83,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[46,x]
F[85,x] = F[86,x]
F[86,x] = 3*F[35,x]+F[87,x]+F[91,x]
F[87,x] = F[12,x]*F[88,x]
F[88,x] = F[89,x]+F[90,x]
F[89,x] = F[46,x]
F[90,x] = F[86,x]
F[91,x] = F[12,x]*F[92,x]
F[92,x] = F[74,x]+F[86,x]
F[93,x] = F[12,x]*F[68,x]
F[94,x] = F[12,x]*F[95,x]
F[95,x] = F[109,x]+F[96,x]
F[96,x] = F[20,x]+F[97,x]
F[97,x] = F[108,x]+F[35,x]+F[98,x]
F[98,x] = F[12,x]*F[99,x]
F[99,x] = F[100,x]+F[102,x]
F[100,x] = F[10,x]+F[101,x]
F[101,x] = F[18,x]
F[102,x] = F[103,x]+F[97,x]
F[103,x] = 2*F[35,x]+F[104,x]+F[67,x]
F[104,x] = F[105,x]*F[12,x]
F[105,x] = F[106,x]+F[107,x]
F[106,x] = F[101,x]
F[107,x] = F[103,x]
F[108,x] = F[12,x]*F[96,x]
F[109,x] = F[110,x]+F[123,x]
F[110,x] = F[111,x]+F[121,x]+F[35,x]
F[111,x] = F[112,x]*F[12,x]
F[112,x] = F[113,x]+F[115,x]
F[113,x] = F[114,x]+F[14,x]
F[114,x] = F[44,x]
F[115,x] = F[116,x]+F[57,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[12,x]
F[118,x] = F[119,x]+F[120,x]
F[119,x] = F[114,x]
F[120,x] = F[116,x]
F[121,x] = F[12,x]*F[122,x]
F[122,x] = F[110,x]+F[20,x]
F[123,x] = 2*F[35,x]+F[124,x]+F[134,x]
F[124,x] = F[12,x]*F[125,x]
F[125,x] = F[126,x]+F[128,x]
F[126,x] = F[127,x]+F[17,x]
F[127,x] = F[47,x]
F[128,x] = F[129,x]+F[62,x]
F[129,x] = 3*F[35,x]+F[130,x]+F[91,x]
F[130,x] = F[12,x]*F[131,x]
F[131,x] = F[132,x]+F[133,x]
F[132,x] = F[127,x]
F[133,x] = F[129,x]
F[134,x] = F[109,x]*F[12,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_{19}\! \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_{17}\! \left(x \right)
F_{14}\! \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_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{34}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{12}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{28}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{12}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{9}\! \left(x \right)
F_{27}\! \left(x \right) = F_{14}\! \left(x \right)
F_{28}\! \left(x \right) = F_{20}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{12}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)
F_{32}\! \left(x \right) = F_{24}\! \left(x \right)
F_{33}\! \left(x \right) = F_{29}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)+F_{94}\! \left(x \right)
F_{35}\! \left(x \right) = 0
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_{48}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{6}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{12}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{13}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{46}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right)+F_{43}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{48}\! \left(x \right) = F_{34}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = 2 F_{35}\! \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_{39}\! \left(x \right)
F_{53}\! \left(x \right) = F_{49}\! \left(x \right)
F_{54}\! \left(x \right) = F_{12}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{68}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{62}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{61}\! \left(x \right)
F_{60}\! \left(x \right) = F_{14}\! \left(x \right)
F_{61}\! \left(x \right) = F_{57}\! \left(x \right)
F_{62}\! \left(x \right) = 2 F_{35}\! \left(x \right)+F_{63}\! \left(x \right)+F_{67}\! \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_{66}\! \left(x \right)
F_{65}\! \left(x \right) = F_{17}\! \left(x \right)
F_{66}\! \left(x \right) = F_{62}\! \left(x \right)
F_{67}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)+F_{81}\! \left(x \right)
F_{69}\! \left(x \right) = 2 F_{35}\! \left(x \right)+F_{70}\! \left(x \right)+F_{79}\! \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_{43}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{78}\! \left(x \right)
F_{77}\! \left(x \right) = F_{43}\! \left(x \right)
F_{78}\! \left(x \right) = F_{74}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{57}\! \left(x \right)+F_{69}\! \left(x \right)
F_{81}\! \left(x \right) = 3 F_{35}\! \left(x \right)+F_{82}\! \left(x \right)+F_{93}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{46}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = 3 F_{35}\! \left(x \right)+F_{87}\! \left(x \right)+F_{91}\! \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_{90}\! \left(x \right)
F_{89}\! \left(x \right) = F_{46}\! \left(x \right)
F_{90}\! \left(x \right) = F_{86}\! \left(x \right)
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{74}\! \left(x \right)+F_{86}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \left(x \right) F_{68}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{109}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{20}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{108}\! \left(x \right)+F_{35}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{102}\! \left(x \right)
F_{100}\! \left(x \right) = F_{10}\! \left(x \right)+F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{18}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{97}\! \left(x \right)
F_{103}\! \left(x \right) = 2 F_{35}\! \left(x \right)+F_{104}\! \left(x \right)+F_{67}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{12}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{107}\! \left(x \right)
F_{106}\! \left(x \right) = F_{101}\! \left(x \right)
F_{107}\! \left(x \right) = F_{103}\! \left(x \right)
F_{108}\! \left(x \right) = F_{12}\! \left(x \right) F_{96}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{123}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right)+F_{121}\! \left(x \right)+F_{35}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{12}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{115}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)+F_{14}\! \left(x \right)
F_{114}\! \left(x \right) = F_{44}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{57}\! \left(x \right)
F_{116}\! \left(x \right) = F_{117}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{12}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{120}\! \left(x \right)
F_{119}\! \left(x \right) = F_{114}\! \left(x \right)
F_{120}\! \left(x \right) = F_{116}\! \left(x \right)
F_{121}\! \left(x \right) = F_{12}\! \left(x \right) F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{110}\! \left(x \right)+F_{20}\! \left(x \right)
F_{123}\! \left(x \right) = 2 F_{35}\! \left(x \right)+F_{124}\! \left(x \right)+F_{134}\! \left(x \right)
F_{124}\! \left(x \right) = F_{12}\! \left(x \right) F_{125}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{128}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{17}\! \left(x \right)
F_{127}\! \left(x \right) = F_{47}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{62}\! \left(x \right)
F_{129}\! \left(x \right) = 3 F_{35}\! \left(x \right)+F_{130}\! \left(x \right)+F_{91}\! \left(x \right)
F_{130}\! \left(x \right) = F_{12}\! \left(x \right) F_{131}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{133}\! \left(x \right)
F_{132}\! \left(x \right) = F_{127}\! \left(x \right)
F_{133}\! \left(x \right) = F_{129}\! \left(x \right)
F_{134}\! \left(x \right) = F_{109}\! \left(x \right) F_{12}\! \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_19(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_17(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_1(x) + F_14(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_12(x)*F_13(x))
Eq(F_19(x), F_20(x) + F_34(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_12(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_28(x))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_12(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_9(x))
Eq(F_27(x), F_14(x))
Eq(F_28(x), F_20(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_33(x))
Eq(F_32(x), F_24(x))
Eq(F_33(x), F_29(x))
Eq(F_34(x), F_35(x) + F_36(x) + F_94(x))
Eq(F_35(x), 0)
Eq(F_36(x), F_12(x)*F_37(x))
Eq(F_37(x), F_38(x) + F_48(x))
Eq(F_38(x), F_39(x) + F_6(x))
Eq(F_39(x), F_40(x))
Eq(F_40(x), F_12(x)*F_41(x))
Eq(F_41(x), F_13(x) + F_42(x))
Eq(F_42(x), F_43(x) + F_46(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_12(x)*F_45(x))
Eq(F_45(x), F_14(x) + F_43(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_12(x)*F_42(x))
Eq(F_48(x), F_34(x) + F_49(x))
Eq(F_49(x), 2*F_35(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_39(x))
Eq(F_53(x), F_49(x))
Eq(F_54(x), F_12(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_68(x))
Eq(F_56(x), F_57(x) + F_62(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_12(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_61(x))
Eq(F_60(x), F_14(x))
Eq(F_61(x), F_57(x))
Eq(F_62(x), 2*F_35(x) + F_63(x) + F_67(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_66(x))
Eq(F_65(x), F_17(x))
Eq(F_66(x), F_62(x))
Eq(F_67(x), F_12(x)*F_56(x))
Eq(F_68(x), F_69(x) + F_81(x))
Eq(F_69(x), 2*F_35(x) + F_70(x) + F_79(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_43(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_12(x)*F_76(x))
Eq(F_76(x), F_77(x) + F_78(x))
Eq(F_77(x), F_43(x))
Eq(F_78(x), F_74(x))
Eq(F_79(x), F_12(x)*F_80(x))
Eq(F_80(x), F_57(x) + F_69(x))
Eq(F_81(x), 3*F_35(x) + F_82(x) + F_93(x))
Eq(F_82(x), F_12(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_46(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), 3*F_35(x) + F_87(x) + F_91(x))
Eq(F_87(x), F_12(x)*F_88(x))
Eq(F_88(x), F_89(x) + F_90(x))
Eq(F_89(x), F_46(x))
Eq(F_90(x), F_86(x))
Eq(F_91(x), F_12(x)*F_92(x))
Eq(F_92(x), F_74(x) + F_86(x))
Eq(F_93(x), F_12(x)*F_68(x))
Eq(F_94(x), F_12(x)*F_95(x))
Eq(F_95(x), F_109(x) + F_96(x))
Eq(F_96(x), F_20(x) + F_97(x))
Eq(F_97(x), F_108(x) + F_35(x) + F_98(x))
Eq(F_98(x), F_12(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_102(x))
Eq(F_100(x), F_10(x) + F_101(x))
Eq(F_101(x), F_18(x))
Eq(F_102(x), F_103(x) + F_97(x))
Eq(F_103(x), F_104(x) + 2*F_35(x) + F_67(x))
Eq(F_104(x), F_105(x)*F_12(x))
Eq(F_105(x), F_106(x) + F_107(x))
Eq(F_106(x), F_101(x))
Eq(F_107(x), F_103(x))
Eq(F_108(x), F_12(x)*F_96(x))
Eq(F_109(x), F_110(x) + F_123(x))
Eq(F_110(x), F_111(x) + F_121(x) + F_35(x))
Eq(F_111(x), F_112(x)*F_12(x))
Eq(F_112(x), F_113(x) + F_115(x))
Eq(F_113(x), F_114(x) + F_14(x))
Eq(F_114(x), F_44(x))
Eq(F_115(x), F_116(x) + F_57(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_12(x))
Eq(F_118(x), F_119(x) + F_120(x))
Eq(F_119(x), F_114(x))
Eq(F_120(x), F_116(x))
Eq(F_121(x), F_12(x)*F_122(x))
Eq(F_122(x), F_110(x) + F_20(x))
Eq(F_123(x), F_124(x) + F_134(x) + 2*F_35(x))
Eq(F_124(x), F_12(x)*F_125(x))
Eq(F_125(x), F_126(x) + F_128(x))
Eq(F_126(x), F_127(x) + F_17(x))
Eq(F_127(x), F_47(x))
Eq(F_128(x), F_129(x) + F_62(x))
Eq(F_129(x), F_130(x) + 3*F_35(x) + F_91(x))
Eq(F_130(x), F_12(x)*F_131(x))
Eq(F_131(x), F_132(x) + F_133(x))
Eq(F_132(x), F_127(x))
Eq(F_133(x), F_129(x))
Eq(F_134(x), F_109(x)*F_12(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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 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": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 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": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 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, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 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": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 2, 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": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[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": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], 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