0132_0231_0312_1032_2310
Counting sequence:
1, 1, 2, 6, 19, 55, 144, 354, 836, 1922, 4336, 9646, 21228, 46314, 100328, 216038, 462820, 987106, 2097120, 4440030, 9371612, 19726298, 41418712, 86769622, 181403604, 378535890, 788529104, 1639972814, 3405774796, 7063207882, 14629732296, 30266097606, 62545461188, 129117454274, 266287972288, 548682071998, 1129576398780, 2323577307066, 4776003633080, 9809705303990, 20134806683572, 41300405518258, 84662395338672, 173447959281582, 355142255771564, 726777185959850, 1486539720753064, 3039050139172774, 6210041673678756, 12683966138023842, 25895697857380256, 52846926877425566, 107804916080181148, 219831956811022234, 448108162923364248, 913104824449367958, 1859986646104014740, 3787527286618587026, 7710162562058289040, 15690541101758807950, 31921514158802075532, 64923892228173070218, 132009512277483978632, 268342480197243633542, 545331871679038619524, 1107957565927179943810, 2250502776992565297024, 4570180844261541412734, 9278712269075904462716, 18834125699257452199802, 38221653720726190948216, 77550112085874954993526, 157313833460595056181108, 319054885498880404750194, 646964208153141394276208, 1311637290617043958103918, 2658692329855610255310700, 5388220156954265188826986, 10918111308394619734065000, 22119564605761418180951910, 44805813189467193787547492, 90744994334823102426382178, 183756724581423634555338592, 372046920986402128515825502, 753160785619913975841947484, 1524455458534047389304487770, 3085178691656533653850160984, 6242892932489945058182692694, 12630856963333645617330126676, 25551856123374802236589735762, 51683996640164626477038436176, 104528562067159296961794801486, 211378261707978681939025461068, 427398798563277539908922638154, 864082147421195431879588708168, 1746733395431671567882664279878, 3530604992041904544012302286660, 7135486386440931904518552026946, 14419525577596109442024998960960, 29136156764620710150025787735870, 58866524748098402832003155099452
Generating function in Maple syntax:
(x^7-3*x^6-x^5+x^4-5*x^3+9*x^2-5*x+1)/(2*x-1)^2/(x-1)^2
Generating function in latex syntax:
\frac{x^{7}-3 x^{6}-x^{5}+x^{4}-5 x^{3}+9 x^{2}-5 x +1}{\left(2 x -1\right)^{2} \left(x -1\right)^{2}}
Generating function in sympy syntax:
(x**7 - 3*x**6 - x**5 + x**4 - 5*x**3 + 9*x**2 - 5*x + 1)/((x - 1)**2*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
-(2*x-1)^2*(x-1)^2*F(x)+x^7-3*x^6-x^5+x^4-5*x^3+9*x^2-5*x+1 = 0
Implicit equation for the generating function in latex syntax:
-\left(2 x -1\right)^{2} \left(x -1\right)^{2} F \! \left(x \right)+x^{7}-3 x^{6}-x^{5}+x^{4}-5 x^{3}+9 x^{2}-5 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,n = 3,6,1/32*(15*n-14)*2^n-2*n+4)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ 6 & n =3 \\ \frac{\left(15 n -14\right) 2^{n}}{32}-2 n +4 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 55
a(6) = 144
a(7) = 354
a(n+2) = -4*a(n)+4*a(n+1)-2*n+8, n >= 8
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) = 55
a \! \left(6\right) = 144
a \! \left(7\right) = 354
a \! \left(n +2\right) = -4 a \! \left(n \right)+4 a \! \left(n +1\right)-2 n +8, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/18594/
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[20,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[19,x]
F[19,x] = F[10,x]+F[17,x]
F[20,x] = F[21,x]+F[41,x]
F[21,x] = F[22,x]
F[22,x] = F[12,x]*F[23,x]
F[23,x] = F[24,x]+F[5,x]
F[24,x] = F[14,x]+F[25,x]
F[25,x] = F[26,x]+F[27,x]+F[32,x]
F[26,x] = 0
F[27,x] = F[12,x]*F[28,x]
F[28,x] = F[10,x]+F[29,x]
F[29,x] = F[26,x]+F[27,x]+F[30,x]
F[30,x] = F[12,x]*F[31,x]
F[31,x] = F[14,x]+F[29,x]
F[32,x] = F[12,x]*F[33,x]
F[33,x] = F[31,x]+F[34,x]
F[34,x] = F[35,x]+F[38,x]
F[35,x] = F[36,x]
F[36,x] = F[12,x]*F[37,x]
F[37,x] = F[14,x]+F[35,x]
F[38,x] = F[39,x]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[29,x]+F[38,x]
F[41,x] = F[26,x]+F[42,x]+F[83,x]
F[42,x] = F[12,x]*F[43,x]
F[43,x] = F[44,x]+F[56,x]
F[44,x] = F[10,x]+F[45,x]
F[45,x] = F[26,x]+F[46,x]+F[55,x]
F[46,x] = F[12,x]*F[47,x]
F[47,x] = F[48,x]+F[51,x]
F[48,x] = F[10,x]+F[49,x]
F[49,x] = F[50,x]
F[50,x] = F[12,x]*F[48,x]
F[51,x] = F[17,x]+F[52,x]
F[52,x] = F[53,x]
F[53,x] = F[12,x]*F[54,x]
F[54,x] = F[49,x]+F[52,x]
F[55,x] = F[12,x]*F[13,x]
F[56,x] = F[29,x]+F[57,x]
F[57,x] = F[26,x]+F[58,x]+F[63,x]+F[69,x]
F[58,x] = F[12,x]*F[59,x]
F[59,x] = F[49,x]+F[60,x]
F[60,x] = 2*F[26,x]+F[58,x]+F[61,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[29,x]+F[60,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[62,x]+F[65,x]
F[65,x] = F[38,x]+F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[12,x]*F[68,x]
F[68,x] = F[60,x]+F[66,x]
F[69,x] = F[12,x]*F[70,x]
F[70,x] = F[71,x]+F[76,x]
F[71,x] = F[26,x]+F[36,x]+F[72,x]
F[72,x] = F[12,x]*F[73,x]
F[73,x] = F[12,x]+F[74,x]
F[74,x] = F[26,x]+F[72,x]+F[75,x]
F[75,x] = F[12,x]*F[14,x]
F[76,x] = 2*F[26,x]+F[39,x]+F[77,x]
F[77,x] = F[12,x]*F[78,x]
F[78,x] = F[79,x]+F[81,x]
F[79,x] = F[80,x]
F[80,x] = F[10,x]*F[12,x]
F[81,x] = 2*F[26,x]+F[77,x]+F[82,x]
F[82,x] = F[12,x]*F[29,x]
F[83,x] = F[12,x]*F[84,x]
F[84,x] = F[85,x]+F[88,x]
F[85,x] = F[21,x]+F[86,x]
F[86,x] = F[26,x]+F[42,x]+F[87,x]
F[87,x] = F[12,x]*F[85,x]
F[88,x] = F[123,x]+F[89,x]
F[89,x] = F[26,x]+F[36,x]+F[90,x]
F[90,x] = F[12,x]*F[91,x]
F[91,x] = F[106,x]+F[92,x]
F[92,x] = F[12,x]+F[93,x]
F[93,x] = F[26,x]+F[75,x]+F[94,x]
F[94,x] = F[12,x]*F[95,x]
F[95,x] = F[96,x]+F[99,x]
F[96,x] = F[12,x]+F[97,x]
F[97,x] = F[98,x]
F[98,x] = F[12,x]*F[96,x]
F[99,x] = F[100,x]+F[103,x]
F[100,x] = F[101,x]
F[101,x] = F[102,x]*F[12,x]
F[102,x] = F[100,x]+F[12,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[12,x]
F[105,x] = F[103,x]+F[97,x]
F[106,x] = F[107,x]+F[74,x]
F[107,x] = F[108,x]+F[113,x]+F[122,x]+F[26,x]
F[108,x] = F[109,x]*F[12,x]
F[109,x] = F[110,x]+F[97,x]
F[110,x] = 2*F[26,x]+F[108,x]+F[111,x]
F[111,x] = F[112,x]*F[12,x]
F[112,x] = F[110,x]+F[74,x]
F[113,x] = F[114,x]*F[12,x]
F[114,x] = F[112,x]+F[115,x]
F[115,x] = F[116,x]+F[119,x]
F[116,x] = F[117,x]
F[117,x] = F[118,x]*F[12,x]
F[118,x] = F[116,x]+F[74,x]
F[119,x] = F[120,x]
F[120,x] = F[12,x]*F[121,x]
F[121,x] = F[110,x]+F[119,x]
F[122,x] = F[12,x]*F[35,x]
F[123,x] = 2*F[26,x]+F[124,x]+F[39,x]
F[124,x] = F[12,x]*F[125,x]
F[125,x] = F[126,x]+F[141,x]
F[126,x] = F[127,x]+F[79,x]
F[127,x] = 2*F[26,x]+F[128,x]+F[140,x]
F[128,x] = F[12,x]*F[129,x]
F[129,x] = F[130,x]+F[133,x]
F[130,x] = F[131,x]+F[79,x]
F[131,x] = F[132,x]
F[132,x] = F[12,x]*F[130,x]
F[133,x] = F[134,x]+F[137,x]
F[134,x] = F[135,x]
F[135,x] = F[12,x]*F[136,x]
F[136,x] = F[134,x]+F[79,x]
F[137,x] = F[138,x]
F[138,x] = F[12,x]*F[139,x]
F[139,x] = F[131,x]+F[137,x]
F[140,x] = F[12,x]*F[17,x]
F[141,x] = F[142,x]+F[81,x]
F[142,x] = 2*F[26,x]+F[143,x]+F[148,x]+F[157,x]
F[143,x] = F[12,x]*F[144,x]
F[144,x] = F[131,x]+F[145,x]
F[145,x] = 3*F[26,x]+F[143,x]+F[146,x]
F[146,x] = F[12,x]*F[147,x]
F[147,x] = F[145,x]+F[81,x]
F[148,x] = F[12,x]*F[149,x]
F[149,x] = F[147,x]+F[150,x]
F[150,x] = F[151,x]+F[154,x]
F[151,x] = F[152,x]
F[152,x] = F[12,x]*F[153,x]
F[153,x] = F[151,x]+F[81,x]
F[154,x] = F[155,x]
F[155,x] = F[12,x]*F[156,x]
F[156,x] = F[145,x]+F[154,x]
F[157,x] = F[12,x]*F[38,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_{20}\! \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_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{10}\! \left(x \right)+F_{17}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{41}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{5}\! \left(x \right)
F_{24}\! \left(x \right) = F_{14}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \left(x \right)+F_{32}\! \left(x \right)
F_{26}\! \left(x \right) = 0
F_{27}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{10}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{26}\! \left(x \right)+F_{27}\! \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_{14}\! \left(x \right)+F_{29}\! \left(x \right)
F_{32}\! \left(x \right) = F_{12}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{31}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{38}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{12}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{14}\! \left(x \right)+F_{35}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{29}\! \left(x \right)+F_{38}\! \left(x \right)
F_{41}\! \left(x \right) = F_{26}\! \left(x \right)+F_{42}\! \left(x \right)+F_{83}\! \left(x \right)
F_{42}\! \left(x \right) = F_{12}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{56}\! \left(x \right)
F_{44}\! \left(x \right) = F_{10}\! \left(x \right)+F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{26}\! \left(x \right)+F_{46}\! \left(x \right)+F_{55}\! \left(x \right)
F_{46}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{51}\! \left(x \right)
F_{48}\! \left(x \right) = F_{10}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{17}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{49}\! \left(x \right)+F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{56}\! \left(x \right) = F_{29}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{26}\! \left(x \right)+F_{58}\! \left(x \right)+F_{63}\! \left(x \right)+F_{69}\! \left(x \right)
F_{58}\! \left(x \right) = F_{12}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{49}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{58}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{29}\! \left(x \right)+F_{60}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{62}\! \left(x \right)+F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{38}\! \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_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{60}\! \left(x \right)+F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{76}\! \left(x \right)
F_{71}\! \left(x \right) = F_{26}\! \left(x \right)+F_{36}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right)+F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{26}\! \left(x \right)+F_{72}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{12}\! \left(x \right) F_{14}\! \left(x \right)
F_{76}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{39}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{81}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{81}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{77}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{29}\! \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_{88}\! \left(x \right)
F_{85}\! \left(x \right) = F_{21}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{26}\! \left(x \right)+F_{42}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{85}\! \left(x \right)
F_{88}\! \left(x \right) = F_{123}\! \left(x \right)+F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{26}\! \left(x \right)+F_{36}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{106}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{12}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{26}\! \left(x \right)+F_{75}\! \left(x \right)+F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{12}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{99}\! \left(x \right)
F_{96}\! \left(x \right) = F_{12}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{12}\! \left(x \right) F_{96}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{103}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{12}\! \left(x \right)
F_{102}\! \left(x \right) = F_{100}\! \left(x \right)+F_{12}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{12}\! \left(x \right)
F_{105}\! \left(x \right) = F_{103}\! \left(x \right)+F_{97}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{74}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{113}\! \left(x \right)+F_{122}\! \left(x \right)+F_{26}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{12}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{97}\! \left(x \right)
F_{110}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{108}\! \left(x \right)+F_{111}\! \left(x \right)
F_{111}\! \left(x \right) = F_{112}\! \left(x \right) F_{12}\! \left(x \right)
F_{112}\! \left(x \right) = F_{110}\! \left(x \right)+F_{74}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{12}\! \left(x \right)
F_{114}\! \left(x \right) = F_{112}\! \left(x \right)+F_{115}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{119}\! \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_{116}\! \left(x \right)+F_{74}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{12}\! \left(x \right) F_{121}\! \left(x \right)
F_{121}\! \left(x \right) = F_{110}\! \left(x \right)+F_{119}\! \left(x \right)
F_{122}\! \left(x \right) = F_{12}\! \left(x \right) F_{35}\! \left(x \right)
F_{123}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{124}\! \left(x \right)+F_{39}\! \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_{141}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{79}\! \left(x \right)
F_{127}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{128}\! \left(x \right)+F_{140}\! \left(x \right)
F_{128}\! \left(x \right) = F_{12}\! \left(x \right) F_{129}\! \left(x \right)
F_{129}\! \left(x \right) = F_{130}\! \left(x \right)+F_{133}\! \left(x \right)
F_{130}\! \left(x \right) = F_{131}\! \left(x \right)+F_{79}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{12}\! \left(x \right) F_{130}\! \left(x \right)
F_{133}\! \left(x \right) = F_{134}\! \left(x \right)+F_{137}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right)
F_{135}\! \left(x \right) = F_{12}\! \left(x \right) F_{136}\! \left(x \right)
F_{136}\! \left(x \right) = F_{134}\! \left(x \right)+F_{79}\! \left(x \right)
F_{137}\! \left(x \right) = F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{12}\! \left(x \right) F_{139}\! \left(x \right)
F_{139}\! \left(x \right) = F_{131}\! \left(x \right)+F_{137}\! \left(x \right)
F_{140}\! \left(x \right) = F_{12}\! \left(x \right) F_{17}\! \left(x \right)
F_{141}\! \left(x \right) = F_{142}\! \left(x \right)+F_{81}\! \left(x \right)
F_{142}\! \left(x \right) = 2 F_{26}\! \left(x \right)+F_{143}\! \left(x \right)+F_{148}\! \left(x \right)+F_{157}\! \left(x \right)
F_{143}\! \left(x \right) = F_{12}\! \left(x \right) F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = F_{131}\! \left(x \right)+F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = 3 F_{26}\! \left(x \right)+F_{143}\! \left(x \right)+F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{12}\! \left(x \right) F_{147}\! \left(x \right)
F_{147}\! \left(x \right) = F_{145}\! \left(x \right)+F_{81}\! \left(x \right)
F_{148}\! \left(x \right) = F_{12}\! \left(x \right) F_{149}\! \left(x \right)
F_{149}\! \left(x \right) = F_{147}\! \left(x \right)+F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = F_{151}\! \left(x \right)+F_{154}\! \left(x \right)
F_{151}\! \left(x \right) = F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{12}\! \left(x \right) F_{153}\! \left(x \right)
F_{153}\! \left(x \right) = F_{151}\! \left(x \right)+F_{81}\! \left(x \right)
F_{154}\! \left(x \right) = F_{155}\! \left(x \right)
F_{155}\! \left(x \right) = F_{12}\! \left(x \right) F_{156}\! \left(x \right)
F_{156}\! \left(x \right) = F_{145}\! \left(x \right)+F_{154}\! \left(x \right)
F_{157}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \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_20(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_19(x))
Eq(F_19(x), F_10(x) + F_17(x))
Eq(F_20(x), F_21(x) + F_41(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_12(x)*F_23(x))
Eq(F_23(x), F_24(x) + F_5(x))
Eq(F_24(x), F_14(x) + F_25(x))
Eq(F_25(x), F_26(x) + F_27(x) + F_32(x))
Eq(F_26(x), 0)
Eq(F_27(x), F_12(x)*F_28(x))
Eq(F_28(x), F_10(x) + F_29(x))
Eq(F_29(x), F_26(x) + F_27(x) + F_30(x))
Eq(F_30(x), F_12(x)*F_31(x))
Eq(F_31(x), F_14(x) + F_29(x))
Eq(F_32(x), F_12(x)*F_33(x))
Eq(F_33(x), F_31(x) + F_34(x))
Eq(F_34(x), F_35(x) + F_38(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_12(x)*F_37(x))
Eq(F_37(x), F_14(x) + F_35(x))
Eq(F_38(x), F_39(x))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_29(x) + F_38(x))
Eq(F_41(x), F_26(x) + F_42(x) + F_83(x))
Eq(F_42(x), F_12(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_56(x))
Eq(F_44(x), F_10(x) + F_45(x))
Eq(F_45(x), F_26(x) + F_46(x) + F_55(x))
Eq(F_46(x), F_12(x)*F_47(x))
Eq(F_47(x), F_48(x) + F_51(x))
Eq(F_48(x), F_10(x) + F_49(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_12(x)*F_48(x))
Eq(F_51(x), F_17(x) + F_52(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_12(x)*F_54(x))
Eq(F_54(x), F_49(x) + F_52(x))
Eq(F_55(x), F_12(x)*F_13(x))
Eq(F_56(x), F_29(x) + F_57(x))
Eq(F_57(x), F_26(x) + F_58(x) + F_63(x) + F_69(x))
Eq(F_58(x), F_12(x)*F_59(x))
Eq(F_59(x), F_49(x) + F_60(x))
Eq(F_60(x), 2*F_26(x) + F_58(x) + F_61(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_29(x) + F_60(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_62(x) + F_65(x))
Eq(F_65(x), F_38(x) + F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_12(x)*F_68(x))
Eq(F_68(x), F_60(x) + F_66(x))
Eq(F_69(x), F_12(x)*F_70(x))
Eq(F_70(x), F_71(x) + F_76(x))
Eq(F_71(x), F_26(x) + F_36(x) + F_72(x))
Eq(F_72(x), F_12(x)*F_73(x))
Eq(F_73(x), F_12(x) + F_74(x))
Eq(F_74(x), F_26(x) + F_72(x) + F_75(x))
Eq(F_75(x), F_12(x)*F_14(x))
Eq(F_76(x), 2*F_26(x) + F_39(x) + F_77(x))
Eq(F_77(x), F_12(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_81(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_10(x)*F_12(x))
Eq(F_81(x), 2*F_26(x) + F_77(x) + F_82(x))
Eq(F_82(x), F_12(x)*F_29(x))
Eq(F_83(x), F_12(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_88(x))
Eq(F_85(x), F_21(x) + F_86(x))
Eq(F_86(x), F_26(x) + F_42(x) + F_87(x))
Eq(F_87(x), F_12(x)*F_85(x))
Eq(F_88(x), F_123(x) + F_89(x))
Eq(F_89(x), F_26(x) + F_36(x) + F_90(x))
Eq(F_90(x), F_12(x)*F_91(x))
Eq(F_91(x), F_106(x) + F_92(x))
Eq(F_92(x), F_12(x) + F_93(x))
Eq(F_93(x), F_26(x) + F_75(x) + F_94(x))
Eq(F_94(x), F_12(x)*F_95(x))
Eq(F_95(x), F_96(x) + F_99(x))
Eq(F_96(x), F_12(x) + F_97(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_12(x)*F_96(x))
Eq(F_99(x), F_100(x) + F_103(x))
Eq(F_100(x), F_101(x))
Eq(F_101(x), F_102(x)*F_12(x))
Eq(F_102(x), F_100(x) + F_12(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_12(x))
Eq(F_105(x), F_103(x) + F_97(x))
Eq(F_106(x), F_107(x) + F_74(x))
Eq(F_107(x), F_108(x) + F_113(x) + F_122(x) + F_26(x))
Eq(F_108(x), F_109(x)*F_12(x))
Eq(F_109(x), F_110(x) + F_97(x))
Eq(F_110(x), F_108(x) + F_111(x) + 2*F_26(x))
Eq(F_111(x), F_112(x)*F_12(x))
Eq(F_112(x), F_110(x) + F_74(x))
Eq(F_113(x), F_114(x)*F_12(x))
Eq(F_114(x), F_112(x) + F_115(x))
Eq(F_115(x), F_116(x) + F_119(x))
Eq(F_116(x), F_117(x))
Eq(F_117(x), F_118(x)*F_12(x))
Eq(F_118(x), F_116(x) + F_74(x))
Eq(F_119(x), F_120(x))
Eq(F_120(x), F_12(x)*F_121(x))
Eq(F_121(x), F_110(x) + F_119(x))
Eq(F_122(x), F_12(x)*F_35(x))
Eq(F_123(x), F_124(x) + 2*F_26(x) + F_39(x))
Eq(F_124(x), F_12(x)*F_125(x))
Eq(F_125(x), F_126(x) + F_141(x))
Eq(F_126(x), F_127(x) + F_79(x))
Eq(F_127(x), F_128(x) + F_140(x) + 2*F_26(x))
Eq(F_128(x), F_12(x)*F_129(x))
Eq(F_129(x), F_130(x) + F_133(x))
Eq(F_130(x), F_131(x) + F_79(x))
Eq(F_131(x), F_132(x))
Eq(F_132(x), F_12(x)*F_130(x))
Eq(F_133(x), F_134(x) + F_137(x))
Eq(F_134(x), F_135(x))
Eq(F_135(x), F_12(x)*F_136(x))
Eq(F_136(x), F_134(x) + F_79(x))
Eq(F_137(x), F_138(x))
Eq(F_138(x), F_12(x)*F_139(x))
Eq(F_139(x), F_131(x) + F_137(x))
Eq(F_140(x), F_12(x)*F_17(x))
Eq(F_141(x), F_142(x) + F_81(x))
Eq(F_142(x), F_143(x) + F_148(x) + F_157(x) + 2*F_26(x))
Eq(F_143(x), F_12(x)*F_144(x))
Eq(F_144(x), F_131(x) + F_145(x))
Eq(F_145(x), F_143(x) + F_146(x) + 3*F_26(x))
Eq(F_146(x), F_12(x)*F_147(x))
Eq(F_147(x), F_145(x) + F_81(x))
Eq(F_148(x), F_12(x)*F_149(x))
Eq(F_149(x), F_147(x) + F_150(x))
Eq(F_150(x), F_151(x) + F_154(x))
Eq(F_151(x), F_152(x))
Eq(F_152(x), F_12(x)*F_153(x))
Eq(F_153(x), F_151(x) + F_81(x))
Eq(F_154(x), F_155(x))
Eq(F_155(x), F_12(x)*F_156(x))
Eq(F_156(x), F_145(x) + F_154(x))
Eq(F_157(x), F_12(x)*F_38(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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 1, 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