0123_02143_10243_10324_10342_10423_10432_12043_20143_21043
Counting sequence:
1, 1, 2, 6, 23, 94, 391, 1633, 6827, 28548, 119384, 499255, 2087854, 8731285, 36513737, 152698377, 638575958, 2670488470, 11167831459, 46703238346, 195310296371, 816776592369, 3415713427499, 14284320005992, 59736216859096, 249813474014875, 1044705792912602, 4368900428806185, 18270494034122465, 76406170772383441, 319526276694850042, 1336240783517661142, 5588083239993111167, 23369047466795255766, 97728032323656473087, 408693093521428036945, 1709131358942573365099, 7147490496968065024252, 29890400253293405425160, 124999960151199113359791, 522742750361121793840070, 2186080561342392883294909, 9142065035579494213659913, 38231597953299247944094489, 159882376287434093106742958, 668619038067456126157406406, 2796126930603959349792274091, 11693244384195859432219759810, 48900485429319940952513906923, 204499059170871663892483113409, 855203477728610737090226600747, 3576412484655994671300875609472, 14956354357181717758401245925224, 62546626435654254967815632709619, 261566447615142742958362901154226, 1093856062539043509042865991401297, 4574444071335662524162011234049793, 19130065900266550862732548026446241, 80000851609862822466049337348433458, 334559028268382178202767886186130278, 1399106898783124984414388334066508327, 5850985771791019293394271885103730126, 24468490957678819979788707988295298551, 102325842703723174228134715504218416001, 427920876000780497598933298120065232427, 1789540855749166344644079199996184047156, 7483758456293722701947115382600583005048, 31296653804923276654833607432278450834919, 130880832820237662976637465911718202297566, 547336226629580205859436355696550677020133, 2288929085533635209759549281265642459543177, 9572171735943883381920996014847402312895273, 40030279802679588531584096984958701034104134, 167404361861128602298497834673416563989768630, 700075555511250114343654439663777554680283379, 2927676304103449471141531496343568081676798010, 12243376410063919396611282590364633317397706787, 51201106388847876943243007418138323796587341777, 214120125661351977698441780766574360422070275883, 895438232624191868340398847894071132167470738520, 3744671949769271574116794164924720565295365888184, 15660005906039926187109133726826379032926864015371, 65489257341304784454212930224336165564835351211146, 273872363321489792429844060459246320726972902971769, 1145318704721224027986480038334495069439800099082849, 4789657924865081119921551283572890432921337948092017, 20030078040860058715242841112166810480398178988479146, 83764651383584091952906435693905637285074253802925750, 350299025650331345406947032604216469187773856252090127, 1464930675944049414865451724998604703555771499822807110, 6126257078042944912915847496904729646125785601740392815, 25619659962465497721121894680013306818871140050532288241, 107139966251960886382537974491959352218054574304046738667, 448053267892266098338357945150945986044963651664978850092, 1873733377858559782014847860415729989579038040913429850792, 7835846813074544340015211412321906592143061241014651514591, 32769067362264471043737335564552410372106319353307057059062, 137038382884273868732949705810115818090989300613329449900045, 573086752086285401635520947392693776143920460565610205144649, 2396616323867151004231296159816338512294564823522463213419577, 10022513664670615549827755880847932007231190454042133608922910
Generating function in Maple syntax:
-(x^3-4*x+1)/(x-1)/(x^3-x^2-4*x+1)
Generating function in latex syntax:
-\frac{x^{3}-4 x +1}{\left(x -1\right) \left(x^{3}-x^{2}-4 x +1\right)}
Generating function in sympy syntax:
(-x**3 + 4*x - 1)/((x - 1)*(x**3 - x**2 - 4*x + 1))
Implicit equation for the generating function in Maple syntax:
(x-1)*(x^3-x^2-4*x+1)*F(x)+x^3-4*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(x -1\right) \left(x^{3}-x^{2}-4 x +1\right) F \! \left(x \right)+x^{3}-4 x +1 = 0
Explicit closed form in Maple syntax:
1/2603952*(((312*I+312*3^(1/2))*107^(1/2)+5564*I*3^(1/2)-5564)*(44+36*I*107^(1/2))^(1/3)+289328+((69*I-69*3^(1/2))*107^(1/2)-535*I*3^(1/2)-535)*(44+36*I*107^(1/2))^(2/3))*(1/8112*((-11*I-9*107^(1/2))*3^(1/2)+9*I*107^(1/2)-11)*(44+36*I*107^(1/2))^(2/3)+1/12*I*3^(1/2)*(44+36*I*107^(1/2))^(1/3)-1/12*(44+36*I*107^(1/2))^(1/3)+1/3)^(-n)+1/2603952*(((312*I-312*3^(1/2))*107^(1/2)-5564*I*3^(1/2)-5564)*(44+36*I*107^(1/2))^(1/3)+289328+((69*I+69*3^(1/2))*107^(1/2)+535*I*3^(1/2)-535)*(44+36*I*107^(1/2))^(2/3))*(1/8112*((11*I+9*107^(1/2))*3^(1/2)+9*I*107^(1/2)-11)*(44+36*I*107^(1/2))^(2/3)-1/12*I*3^(1/2)*(44+36*I*107^(1/2))^(1/3)-1/12*(44+36*I*107^(1/2))^(1/3)+1/3)^(-n)+2/3+1/2603952*((-624*I*107^(1/2)+11128)*(44+36*I*107^(1/2))^(1/3)-138*I*107^(1/2)*(44+36*I*107^(1/2))^(2/3)+1070*(44+36*I*107^(1/2))^(2/3)+289328)*(1/6*(44+36*I*107^(1/2))^(1/3)+1/3+11/4056*(44+36*I*107^(1/2))^(2/3)-3/1352*I*(44+36*I*107^(1/2))^(2/3)*107^(1/2))^(-n)
Explicit closed form in latex syntax:
\frac{\left(\left(\left(312 \,\mathrm{I}+312 \sqrt{3}\right) \sqrt{107}+5564 \,\mathrm{I} \sqrt{3}-5564\right) \left(44+36 \,\mathrm{I} \sqrt{107}\right)^{\frac{1}{3}}+289328+\left(\left(69 \,\mathrm{I}-69 \sqrt{3}\right) \sqrt{107}-535 \,\mathrm{I} \sqrt{3}-535\right) \left(44+36 \,\mathrm{I} \sqrt{107}\right)^{\frac{2}{3}}\right) \left(\frac{\left(\left(-11 \,\mathrm{I}-9 \sqrt{107}\right) \sqrt{3}+9 \,\mathrm{I} \sqrt{107}-11\right) \left(44+36 \,\mathrm{I} \sqrt{107}\right)^{\frac{2}{3}}}{8112}+\frac{\mathrm{I} \sqrt{3}\, \left(44+36 \,\mathrm{I} \sqrt{107}\right)^{\frac{1}{3}}}{12}-\frac{\left(44+36 \,\mathrm{I} \sqrt{107}\right)^{\frac{1}{3}}}{12}+\frac{1}{3}\right)^{-n}}{2603952}+\frac{\left(\left(\left(312 \,\mathrm{I}-312 \sqrt{3}\right) \sqrt{107}-5564 \,\mathrm{I} \sqrt{3}-5564\right) \left(44+36 \,\mathrm{I} \sqrt{107}\right)^{\frac{1}{3}}+289328+\left(\left(69 \,\mathrm{I}+69 \sqrt{3}\right) \sqrt{107}+535 \,\mathrm{I} \sqrt{3}-535\right) \left(44+36 \,\mathrm{I} \sqrt{107}\right)^{\frac{2}{3}}\right) \left(\frac{\left(\left(11 \,\mathrm{I}+9 \sqrt{107}\right) \sqrt{3}+9 \,\mathrm{I} \sqrt{107}-11\right) \left(44+36 \,\mathrm{I} \sqrt{107}\right)^{\frac{2}{3}}}{8112}-\frac{\mathrm{I} \sqrt{3}\, \left(44+36 \,\mathrm{I} \sqrt{107}\right)^{\frac{1}{3}}}{12}-\frac{\left(44+36 \,\mathrm{I} \sqrt{107}\right)^{\frac{1}{3}}}{12}+\frac{1}{3}\right)^{-n}}{2603952}+\frac{2}{3}+\frac{\left(\left(-624 \,\mathrm{I} \sqrt{107}+11128\right) \left(44+36 \,\mathrm{I} \sqrt{107}\right)^{\frac{1}{3}}-138 \,\mathrm{I} \sqrt{107}\, \left(44+36 \,\mathrm{I} \sqrt{107}\right)^{\frac{2}{3}}+1070 \left(44+36 \,\mathrm{I} \sqrt{107}\right)^{\frac{2}{3}}+289328\right) \left(\frac{\left(44+36 \,\mathrm{I} \sqrt{107}\right)^{\frac{1}{3}}}{6}+\frac{1}{3}+\frac{11 \left(44+36 \,\mathrm{I} \sqrt{107}\right)^{\frac{2}{3}}}{4056}-\frac{3 \,\mathrm{I} \left(44+36 \,\mathrm{I} \sqrt{107}\right)^{\frac{2}{3}} \sqrt{107}}{1352}\right)^{-n}}{2603952}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(n+3) = -a(n)+a(n+1)+4*a(n+2)-2, n >= 4
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(n +3\right) = -a \! \left(n \right)+a \! \left(n +1\right)+4 a \! \left(n +2\right)-2, \quad n \geq 4
Specification 1
Strategy pack name: point_placements_tracked_fusion
Tree: http://permpal.com/tree/24204/
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[27,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[13,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[4,x]
F[13,x] = F[14,x]+F[7,x]
F[14,x] = F[15,x]+F[16,x]+F[26,x]
F[15,x] = 0
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[21,x]
F[18,x] = F[19,x]+F[4,x]
F[19,x] = F[20,x]
F[20,x] = F[11,x]*F[4,x]
F[21,x] = F[22,x]+F[24,x]
F[22,x] = F[15,x]+F[16,x]+F[23,x]
F[23,x] = F[4,x]*F[7,x]
F[24,x] = F[25,x]
F[25,x] = F[14,x]*F[4,x]
F[26,x] = F[13,x]*F[4,x]
F[27,x] = F[2,x]+F[28,x]
F[28,x] = F[147,x]+F[15,x]+F[29,x]
F[29,x] = F[30,x]*F[4,x]
F[30,x] = F[31,x]+F[42,x]
F[31,x] = F[32,x]+F[37,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[35,x]+F[36,x]
F[35,x] = F[1,x]+F[4,x]
F[36,x] = F[4,x]
F[37,x] = F[15,x]+F[16,x]+F[38,x]
F[38,x] = F[39,x]*F[4,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[22,x]+F[7,x]
F[41,x] = F[22,x]
F[42,x] = F[144,x]+F[43,x]
F[43,x] = F[142,x]+F[15,x]+F[44,x]
F[44,x] = F[4,x]*F[45,x]
F[45,x] = F[46,x]+F[51,x]
F[46,x] = F[47,x]+F[49,x]
F[47,x] = F[48,x]
F[48,x] = F[35,x]*F[4,x]
F[49,x] = F[15,x]+F[16,x]+F[50,x]
F[50,x] = F[4,x]*F[40,x]
F[51,x] = F[116,x]+F[52,x]
F[52,x] = F[15,x]+F[44,x]+F[53,x]
F[53,x] = F[4,x]*F[54,x]
F[54,x] = F[2,x]+F[55,x]
F[55,x] = F[115,x]+F[15,x]+F[56,x]
F[56,x] = F[4,x]*F[57,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[22,x]+F[4,x]
F[59,x] = F[55,x]+F[60,x]
F[60,x] = F[100,x]+F[114,x]+F[15,x]+F[61,x]
F[61,x] = F[4,x]*F[62,x]
F[62,x] = F[63,x]+F[75,x]
F[63,x] = F[64,x]+F[69,x]
F[64,x] = F[15,x]+F[65,x]+F[68,x]
F[65,x] = F[4,x]*F[66,x]
F[66,x] = F[67,x]
F[67,x] = F[4,x]
F[68,x] = x^2
F[69,x] = F[15,x]+F[70,x]+F[71,x]+F[74,x]
F[70,x] = 0
F[71,x] = F[4,x]*F[72,x]
F[72,x] = F[73,x]
F[73,x] = F[22,x]
F[74,x] = F[22,x]*F[4,x]
F[75,x] = F[76,x]+F[94,x]
F[76,x] = F[15,x]+F[77,x]+F[91,x]+F[93,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[79,x]+F[84,x]
F[79,x] = F[80,x]+F[82,x]
F[80,x] = F[81,x]
F[81,x] = F[4,x]*F[67,x]
F[82,x] = F[83,x]
F[83,x] = F[4,x]*F[73,x]
F[84,x] = F[85,x]+F[88,x]
F[85,x] = 2*F[15,x]+F[77,x]+F[86,x]
F[86,x] = F[4,x]*F[87,x]
F[87,x] = F[55,x]
F[88,x] = F[89,x]
F[89,x] = F[4,x]*F[90,x]
F[90,x] = F[60,x]
F[91,x] = F[4,x]*F[92,x]
F[92,x] = F[87,x]
F[93,x] = F[4,x]*F[55,x]
F[94,x] = F[15,x]+F[95,x]+F[96,x]+F[97,x]+F[99,x]
F[95,x] = 0
F[96,x] = 0
F[97,x] = F[4,x]*F[98,x]
F[98,x] = F[90,x]
F[99,x] = F[4,x]*F[60,x]
F[100,x] = F[101,x]*F[4,x]
F[101,x] = F[102,x]+F[108,x]
F[102,x] = F[103,x]+F[55,x]
F[103,x] = F[104,x]
F[104,x] = F[105,x]*F[4,x]
F[105,x] = F[106,x]+F[15,x]+F[56,x]
F[106,x] = F[107,x]*F[4,x]
F[107,x] = F[105,x]+F[2,x]
F[108,x] = F[109,x]+F[60,x]
F[109,x] = F[110,x]
F[110,x] = F[111,x]*F[4,x]
F[111,x] = F[100,x]+F[112,x]+F[15,x]+F[61,x]
F[112,x] = F[113,x]*F[4,x]
F[113,x] = F[111,x]+F[28,x]
F[114,x] = F[28,x]*F[4,x]
F[115,x] = F[2,x]*F[4,x]
F[116,x] = F[100,x]+F[117,x]+F[140,x]+F[15,x]
F[117,x] = F[118,x]*F[4,x]
F[118,x] = F[119,x]+F[124,x]
F[119,x] = F[120,x]+F[122,x]
F[120,x] = F[121,x]+F[15,x]+F[65,x]
F[121,x] = F[36,x]*F[4,x]
F[122,x] = F[123,x]+F[15,x]+F[70,x]+F[71,x]
F[123,x] = F[4,x]*F[41,x]
F[124,x] = F[125,x]+F[136,x]
F[125,x] = F[126,x]+F[134,x]+F[15,x]+F[91,x]
F[126,x] = F[127,x]*F[4,x]
F[127,x] = F[128,x]+F[131,x]
F[128,x] = F[129,x]+F[130,x]
F[129,x] = F[81,x]
F[130,x] = F[83,x]
F[131,x] = F[132,x]+F[133,x]
F[132,x] = 2*F[15,x]+F[126,x]+F[86,x]
F[133,x] = F[89,x]
F[134,x] = F[135,x]*F[4,x]
F[135,x] = F[55,x]
F[136,x] = F[137,x]+F[138,x]+F[15,x]+F[96,x]+F[97,x]
F[137,x] = 0
F[138,x] = F[139,x]*F[4,x]
F[139,x] = F[60,x]
F[140,x] = F[141,x]*F[4,x]
F[141,x] = F[28,x]+F[60,x]
F[142,x] = F[143,x]*F[4,x]
F[143,x] = F[135,x]+F[54,x]
F[144,x] = F[100,x]+F[117,x]+F[145,x]+F[15,x]
F[145,x] = F[146,x]*F[4,x]
F[146,x] = F[139,x]+F[141,x]
F[147,x] = F[148,x]*F[4,x]
F[148,x] = F[107,x]+F[113,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_{27}\! \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_{13}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{26}\! \left(x \right)
F_{15}\! \left(x \right) = 0
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{4}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{4}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{11}\! \left(x \right) F_{4}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{24}\! \left(x \right)
F_{22}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{4}\! \left(x \right) F_{7}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{14}\! \left(x \right) F_{4}\! \left(x \right)
F_{26}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{27}\! \left(x \right) = F_{2}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{147}\! \left(x \right)+F_{15}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right) F_{4}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{42}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{37}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{36}\! \left(x \right)
F_{35}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{36}\! \left(x \right) = F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{22}\! \left(x \right)+F_{7}\! \left(x \right)
F_{41}\! \left(x \right) = F_{22}\! \left(x \right)
F_{42}\! \left(x \right) = F_{144}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{142}\! \left(x \right)+F_{15}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{4}\! \left(x \right) F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{51}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{49}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{35}\! \left(x \right) F_{4}\! \left(x \right)
F_{49}\! \left(x \right) = F_{15}\! \left(x \right)+F_{16}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{4}\! \left(x \right) F_{40}\! \left(x \right)
F_{51}\! \left(x \right) = F_{116}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{15}\! \left(x \right)+F_{44}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{4}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{2}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{115}\! \left(x \right)+F_{15}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{4}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{22}\! \left(x \right)+F_{4}\! \left(x \right)
F_{59}\! \left(x \right) = F_{55}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{100}\! \left(x \right)+F_{114}\! \left(x \right)+F_{15}\! \left(x \right)+F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{4}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{75}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{69}\! \left(x \right)
F_{64}\! \left(x \right) = F_{15}\! \left(x \right)+F_{65}\! \left(x \right)+F_{68}\! \left(x \right)
F_{65}\! \left(x \right) = F_{4}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{4}\! \left(x \right)
F_{68}\! \left(x \right) = x^{2}
F_{69}\! \left(x \right) = F_{15}\! \left(x \right)+F_{70}\! \left(x \right)+F_{71}\! \left(x \right)+F_{74}\! \left(x \right)
F_{70}\! \left(x \right) = 0
F_{71}\! \left(x \right) = F_{4}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{22}\! \left(x \right)
F_{74}\! \left(x \right) = F_{22}\! \left(x \right) F_{4}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{94}\! \left(x \right)
F_{76}\! \left(x \right) = F_{15}\! \left(x \right)+F_{77}\! \left(x \right)+F_{91}\! \left(x \right)+F_{93}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{84}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)+F_{82}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{4}\! \left(x \right) F_{67}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{88}\! \left(x \right)
F_{85}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{77}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{4}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{55}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{60}\! \left(x \right)
F_{91}\! \left(x \right) = F_{4}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{87}\! \left(x \right)
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{55}\! \left(x \right)
F_{94}\! \left(x \right) = F_{15}\! \left(x \right)+F_{95}\! \left(x \right)+F_{96}\! \left(x \right)+F_{97}\! \left(x \right)+F_{99}\! \left(x \right)
F_{95}\! \left(x \right) = 0
F_{96}\! \left(x \right) = 0
F_{97}\! \left(x \right) = F_{4}\! \left(x \right) F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{90}\! \left(x \right)
F_{99}\! \left(x \right) = F_{4}\! \left(x \right) F_{60}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{4}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{108}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{55}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \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_{15}\! \left(x \right)+F_{56}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{105}\! \left(x \right)+F_{2}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{60}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{4}\! \left(x \right)
F_{111}\! \left(x \right) = F_{100}\! \left(x \right)+F_{112}\! \left(x \right)+F_{15}\! \left(x \right)+F_{61}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{111}\! \left(x \right)+F_{28}\! \left(x \right)
F_{114}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{115}\! \left(x \right) = F_{2}\! \left(x \right) F_{4}\! \left(x \right)
F_{116}\! \left(x \right) = F_{100}\! \left(x \right)+F_{117}\! \left(x \right)+F_{140}\! \left(x \right)+F_{15}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right) F_{4}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{124}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right)+F_{122}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{15}\! \left(x \right)+F_{65}\! \left(x \right)
F_{121}\! \left(x \right) = F_{36}\! \left(x \right) F_{4}\! \left(x \right)
F_{122}\! \left(x \right) = F_{123}\! \left(x \right)+F_{15}\! \left(x \right)+F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{123}\! \left(x \right) = F_{4}\! \left(x \right) F_{41}\! \left(x \right)
F_{124}\! \left(x \right) = F_{125}\! \left(x \right)+F_{136}\! \left(x \right)
F_{125}\! \left(x \right) = F_{126}\! \left(x \right)+F_{134}\! \left(x \right)+F_{15}\! \left(x \right)+F_{91}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right) F_{4}\! \left(x \right)
F_{127}\! \left(x \right) = F_{128}\! \left(x \right)+F_{131}\! \left(x \right)
F_{128}\! \left(x \right) = F_{129}\! \left(x \right)+F_{130}\! \left(x \right)
F_{129}\! \left(x \right) = F_{81}\! \left(x \right)
F_{130}\! \left(x \right) = F_{83}\! \left(x \right)
F_{131}\! \left(x \right) = F_{132}\! \left(x \right)+F_{133}\! \left(x \right)
F_{132}\! \left(x \right) = 2 F_{15}\! \left(x \right)+F_{126}\! \left(x \right)+F_{86}\! \left(x \right)
F_{133}\! \left(x \right) = F_{89}\! \left(x \right)
F_{134}\! \left(x \right) = F_{135}\! \left(x \right) F_{4}\! \left(x \right)
F_{135}\! \left(x \right) = F_{55}\! \left(x \right)
F_{136}\! \left(x \right) = F_{137}\! \left(x \right)+F_{138}\! \left(x \right)+F_{15}\! \left(x \right)+F_{96}\! \left(x \right)+F_{97}\! \left(x \right)
F_{137}\! \left(x \right) = 0
F_{138}\! \left(x \right) = F_{139}\! \left(x \right) F_{4}\! \left(x \right)
F_{139}\! \left(x \right) = F_{60}\! \left(x \right)
F_{140}\! \left(x \right) = F_{141}\! \left(x \right) F_{4}\! \left(x \right)
F_{141}\! \left(x \right) = F_{28}\! \left(x \right)+F_{60}\! \left(x \right)
F_{142}\! \left(x \right) = F_{143}\! \left(x \right) F_{4}\! \left(x \right)
F_{143}\! \left(x \right) = F_{135}\! \left(x \right)+F_{54}\! \left(x \right)
F_{144}\! \left(x \right) = F_{100}\! \left(x \right)+F_{117}\! \left(x \right)+F_{145}\! \left(x \right)+F_{15}\! \left(x \right)
F_{145}\! \left(x \right) = F_{146}\! \left(x \right) F_{4}\! \left(x \right)
F_{146}\! \left(x \right) = F_{139}\! \left(x \right)+F_{141}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right) F_{4}\! \left(x \right)
F_{148}\! \left(x \right) = F_{107}\! \left(x \right)+F_{113}\! \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_27(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_13(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_4(x))
Eq(F_13(x), F_14(x) + F_7(x))
Eq(F_14(x), F_15(x) + F_16(x) + F_26(x))
Eq(F_15(x), 0)
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_21(x))
Eq(F_18(x), F_19(x) + F_4(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_11(x)*F_4(x))
Eq(F_21(x), F_22(x) + F_24(x))
Eq(F_22(x), F_15(x) + F_16(x) + F_23(x))
Eq(F_23(x), F_4(x)*F_7(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_14(x)*F_4(x))
Eq(F_26(x), F_13(x)*F_4(x))
Eq(F_27(x), F_2(x) + F_28(x))
Eq(F_28(x), F_147(x) + F_15(x) + F_29(x))
Eq(F_29(x), F_30(x)*F_4(x))
Eq(F_30(x), F_31(x) + F_42(x))
Eq(F_31(x), F_32(x) + F_37(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_35(x) + F_36(x))
Eq(F_35(x), F_1(x) + F_4(x))
Eq(F_36(x), F_4(x))
Eq(F_37(x), F_15(x) + F_16(x) + F_38(x))
Eq(F_38(x), F_39(x)*F_4(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_22(x) + F_7(x))
Eq(F_41(x), F_22(x))
Eq(F_42(x), F_144(x) + F_43(x))
Eq(F_43(x), F_142(x) + F_15(x) + F_44(x))
Eq(F_44(x), F_4(x)*F_45(x))
Eq(F_45(x), F_46(x) + F_51(x))
Eq(F_46(x), F_47(x) + F_49(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_35(x)*F_4(x))
Eq(F_49(x), F_15(x) + F_16(x) + F_50(x))
Eq(F_50(x), F_4(x)*F_40(x))
Eq(F_51(x), F_116(x) + F_52(x))
Eq(F_52(x), F_15(x) + F_44(x) + F_53(x))
Eq(F_53(x), F_4(x)*F_54(x))
Eq(F_54(x), F_2(x) + F_55(x))
Eq(F_55(x), F_115(x) + F_15(x) + F_56(x))
Eq(F_56(x), F_4(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_22(x) + F_4(x))
Eq(F_59(x), F_55(x) + F_60(x))
Eq(F_60(x), F_100(x) + F_114(x) + F_15(x) + F_61(x))
Eq(F_61(x), F_4(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_75(x))
Eq(F_63(x), F_64(x) + F_69(x))
Eq(F_64(x), F_15(x) + F_65(x) + F_68(x))
Eq(F_65(x), F_4(x)*F_66(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_4(x))
Eq(F_68(x), x**2)
Eq(F_69(x), F_15(x) + F_70(x) + F_71(x) + F_74(x))
Eq(F_70(x), 0)
Eq(F_71(x), F_4(x)*F_72(x))
Eq(F_72(x), F_73(x))
Eq(F_73(x), F_22(x))
Eq(F_74(x), F_22(x)*F_4(x))
Eq(F_75(x), F_76(x) + F_94(x))
Eq(F_76(x), F_15(x) + F_77(x) + F_91(x) + F_93(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_84(x))
Eq(F_79(x), F_80(x) + F_82(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), F_4(x)*F_67(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_4(x)*F_73(x))
Eq(F_84(x), F_85(x) + F_88(x))
Eq(F_85(x), 2*F_15(x) + F_77(x) + F_86(x))
Eq(F_86(x), F_4(x)*F_87(x))
Eq(F_87(x), F_55(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_4(x)*F_90(x))
Eq(F_90(x), F_60(x))
Eq(F_91(x), F_4(x)*F_92(x))
Eq(F_92(x), F_87(x))
Eq(F_93(x), F_4(x)*F_55(x))
Eq(F_94(x), F_15(x) + F_95(x) + F_96(x) + F_97(x) + F_99(x))
Eq(F_95(x), 0)
Eq(F_96(x), 0)
Eq(F_97(x), F_4(x)*F_98(x))
Eq(F_98(x), F_90(x))
Eq(F_99(x), F_4(x)*F_60(x))
Eq(F_100(x), F_101(x)*F_4(x))
Eq(F_101(x), F_102(x) + F_108(x))
Eq(F_102(x), F_103(x) + F_55(x))
Eq(F_103(x), F_104(x))
Eq(F_104(x), F_105(x)*F_4(x))
Eq(F_105(x), F_106(x) + F_15(x) + F_56(x))
Eq(F_106(x), F_107(x)*F_4(x))
Eq(F_107(x), F_105(x) + F_2(x))
Eq(F_108(x), F_109(x) + F_60(x))
Eq(F_109(x), F_110(x))
Eq(F_110(x), F_111(x)*F_4(x))
Eq(F_111(x), F_100(x) + F_112(x) + F_15(x) + F_61(x))
Eq(F_112(x), F_113(x)*F_4(x))
Eq(F_113(x), F_111(x) + F_28(x))
Eq(F_114(x), F_28(x)*F_4(x))
Eq(F_115(x), F_2(x)*F_4(x))
Eq(F_116(x), F_100(x) + F_117(x) + F_140(x) + F_15(x))
Eq(F_117(x), F_118(x)*F_4(x))
Eq(F_118(x), F_119(x) + F_124(x))
Eq(F_119(x), F_120(x) + F_122(x))
Eq(F_120(x), F_121(x) + F_15(x) + F_65(x))
Eq(F_121(x), F_36(x)*F_4(x))
Eq(F_122(x), F_123(x) + F_15(x) + F_70(x) + F_71(x))
Eq(F_123(x), F_4(x)*F_41(x))
Eq(F_124(x), F_125(x) + F_136(x))
Eq(F_125(x), F_126(x) + F_134(x) + F_15(x) + F_91(x))
Eq(F_126(x), F_127(x)*F_4(x))
Eq(F_127(x), F_128(x) + F_131(x))
Eq(F_128(x), F_129(x) + F_130(x))
Eq(F_129(x), F_81(x))
Eq(F_130(x), F_83(x))
Eq(F_131(x), F_132(x) + F_133(x))
Eq(F_132(x), F_126(x) + 2*F_15(x) + F_86(x))
Eq(F_133(x), F_89(x))
Eq(F_134(x), F_135(x)*F_4(x))
Eq(F_135(x), F_55(x))
Eq(F_136(x), F_137(x) + F_138(x) + F_15(x) + F_96(x) + F_97(x))
Eq(F_137(x), 0)
Eq(F_138(x), F_139(x)*F_4(x))
Eq(F_139(x), F_60(x))
Eq(F_140(x), F_141(x)*F_4(x))
Eq(F_141(x), F_28(x) + F_60(x))
Eq(F_142(x), F_143(x)*F_4(x))
Eq(F_143(x), F_135(x) + F_54(x))
Eq(F_144(x), F_100(x) + F_117(x) + F_145(x) + F_15(x))
Eq(F_145(x), F_146(x)*F_4(x))
Eq(F_146(x), F_139(x) + F_141(x))
Eq(F_147(x), F_148(x)*F_4(x))
Eq(F_148(x), F_107(x) + F_113(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.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "point_placements_tracked_fusion", "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, 2, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 2, 4], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 3, 4, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 4, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 1, 0, 4, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": 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