0132_0321_1230
Counting sequence:
1, 1, 2, 6, 21, 74, 256, 876, 2987, 10182, 34726, 118492, 404441, 1380670, 4713644, 16093028, 54944551, 187591798, 640477650, 2186726460, 7465949877, 25490345790, 87029482456, 297137237124, 1014489982275, 3463685453334, 11825761847038, 40375676479484, 137851182221585, 470653375924798, 1606911139253124, 5486337805159652, 18731528942128735, 63953440158191606, 218350702748504490, 745495930677629820, 2545282317213504877, 8690137407498753918, 29669984995567999408, 101299665167274482692, 345858690677961924219, 1180835432377298723094, 4031624348153271034838, 13764826527858486683324, 46996057415127404653001, 160454576604792645233918, 547826191588915771617372, 1870395613146077795988452, 6385930069406479640704919, 21802929051333762970827638, 74439856066522092601884546, 254153566163420844465865660, 867734552520639192659675173, 2962631077755715081706949822, 10115055205981581941508428168, 34534958668414897602619790980, 117909724261696426527462284211, 402568979709955910904609530134, 1374456470316430790563513525934, 4692687921845811340444835015804, 16021838746750383780652312982145, 54701979143309912441719581866174, 186764239079738882205573701467956, 637652998032335703938855642105316, 2177083513969865051344275165449423, 7433028059814788797499389377549302, 25377945211319425087309007179258714, 86645724725648122754237249961894652, 295827008479953640842330985489017565, 1010016584468518317860849442032235262, 3448412320914165989758735797150858080, 11773616114719627323313244304538911748, 40197639817050177313735505623853878507, 137243327038761454608315533886337635862, 468578028520945463805791124297642729350, 1599825460006258946006533429417895586108, 5462145782983144856414551469076296823609, 18648932211920061533645139017469396057470, 63671437281713956421751453131724990515212, 217387884703015702619715534491961169875684, 742208664248634897635359231704394698399239, 2534058887588508185302005857833656453769590, 8651818221856762945937304967925836418200882, 29539155112250035413145208156036032765182268, 100852984005286615760706222688292458224242069, 344333625796646392216534474441097767366515262, 1175628535176012337344725452387806153017485112, 4013846889110756564945832860669029077336814724, 13704130486091001585093880537900504003312189987, 46788828166142493210483856430263957858575028246, 159747051692387969671747664645254823427675627102, 545410550437266892266022945720491377993552342268, 1862148098364291629720596453591455865118858001393, 6357771292582632734350339922924840704488327203646, 21706788973601947677960166784516451087715592690404, 74111613309242525243139987292216122941885716228836, 253032875289766205616639615599831589592111679404863, 863908274540579771980278487814894112484675285027830, 2949567347582786676687834720059913270754477781163274, 10070452841249987162790781904609864858048560554454652, 34382676669834375297787458178319632890685286655344717
Generating function in Maple syntax:
-(5*x^5-14*x^4+22*x^3-18*x^2+7*x-1)/(2*x^2-4*x+1)/(x-1)^4
Generating function in latex syntax:
-\frac{5 x^{5}-14 x^{4}+22 x^{3}-18 x^{2}+7 x -1}{\left(2 x^{2}-4 x +1\right) \left(x -1\right)^{4}}
Generating function in sympy syntax:
(-5*x**5 + 14*x**4 - 22*x**3 + 18*x**2 - 7*x + 1)/((x - 1)**4*(2*x**2 - 4*x + 1))
Implicit equation for the generating function in Maple syntax:
(2*x^2-4*x+1)*(x-1)^4*F(x)+5*x^5-14*x^4+22*x^3-18*x^2+7*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x^{2}-4 x +1\right) \left(x -1\right)^{4} F \! \left(x \right)+5 x^{5}-14 x^{4}+22 x^{3}-18 x^{2}+7 x -1 = 0
Explicit closed form in Maple syntax:
1/12*(-75*2^(1/2)+108)*(1-1/2*2^(1/2))^(-n)+1/12*(75*2^(1/2)+108)*(1+1/2*2^(1/2))^(-n)+1/6*n^3-2*n^2+53/6*n-17
Explicit closed form in latex syntax:
\frac{\left(-75 \sqrt{2}+108\right) \left(1-\frac{\sqrt{2}}{2}\right)^{-n}}{12}+\frac{\left(75 \sqrt{2}+108\right) \left(1+\frac{\sqrt{2}}{2}\right)^{-n}}{12}+\frac{n^{3}}{6}-2 n^{2}+\frac{53 n}{6}-17
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 74
a(n+2) = -2*a(n)+4*a(n+1)-1/6*n*(n-1)*(n-5), n >= 6
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 21
a \! \left(5\right) = 74
a \! \left(n +2\right) = -2 a \! \left(n \right)+4 a \! \left(n +1\right)-\frac{n \left(n -1\right) \left(n -5\right)}{6}, \quad n \geq 6
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/14700/
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[24,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[12,x]
F[17,x] = F[18,x]+F[19,x]+F[23,x]
F[18,x] = 0
F[19,x] = F[12,x]*F[20,x]
F[20,x] = F[10,x]+F[21,x]
F[21,x] = F[22,x]
F[22,x] = F[10,x]*F[12,x]
F[23,x] = F[12,x]*F[13,x]
F[24,x] = F[25,x]+F[63,x]
F[25,x] = F[26,x]
F[26,x] = F[12,x]*F[27,x]
F[27,x] = F[28,x]+F[31,x]
F[28,x] = F[1,x]+F[29,x]
F[29,x] = F[30,x]
F[30,x] = F[12,x]*F[16,x]
F[31,x] = F[25,x]+F[32,x]
F[32,x] = F[18,x]+F[33,x]+F[61,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[35,x]+F[39,x]
F[35,x] = F[29,x]+F[36,x]
F[36,x] = F[37,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[12,x]
F[39,x] = F[32,x]+F[40,x]
F[40,x] = 2*F[18,x]+F[41,x]+F[45,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[43,x]+F[44,x]
F[43,x] = F[36,x]
F[44,x] = F[40,x]
F[45,x] = F[12,x]*F[46,x]
F[46,x] = F[47,x]
F[47,x] = F[18,x]+F[48,x]+F[60,x]
F[48,x] = F[12,x]*F[49,x]
F[49,x] = F[50,x]+F[53,x]
F[50,x] = F[12,x]+F[51,x]
F[51,x] = F[52,x]
F[52,x] = x^2
F[53,x] = F[47,x]+F[54,x]
F[54,x] = 2*F[18,x]+F[55,x]+F[59,x]
F[55,x] = F[12,x]*F[56,x]
F[56,x] = F[57,x]+F[58,x]
F[57,x] = F[51,x]
F[58,x] = F[54,x]
F[59,x] = F[12,x]*F[47,x]
F[60,x] = F[12,x]*F[25,x]
F[61,x] = F[12,x]*F[62,x]
F[62,x] = F[25,x]+F[47,x]
F[63,x] = F[156,x]+F[18,x]+F[64,x]
F[64,x] = F[12,x]*F[65,x]
F[65,x] = F[66,x]+F[81,x]
F[66,x] = F[6,x]+F[67,x]
F[67,x] = F[18,x]+F[68,x]+F[73,x]
F[68,x] = F[12,x]*F[69,x]
F[69,x] = F[10,x]+F[70,x]
F[70,x] = F[18,x]+F[22,x]+F[71,x]
F[71,x] = F[12,x]*F[72,x]
F[72,x] = F[12,x]+F[70,x]
F[73,x] = F[12,x]*F[74,x]
F[74,x] = F[72,x]+F[75,x]
F[75,x] = F[76,x]+F[78,x]
F[76,x] = F[77,x]
F[77,x] = x^2
F[78,x] = 2*F[18,x]+F[79,x]+F[80,x]
F[79,x] = F[12,x]*F[21,x]
F[80,x] = F[12,x]*F[75,x]
F[81,x] = F[63,x]+F[82,x]
F[82,x] = F[129,x]+F[136,x]+F[18,x]+F[83,x]
F[83,x] = F[12,x]*F[84,x]
F[84,x] = F[85,x]+F[89,x]
F[85,x] = F[67,x]+F[86,x]
F[86,x] = F[87,x]
F[87,x] = F[12,x]*F[88,x]
F[88,x] = F[70,x]
F[89,x] = F[82,x]+F[90,x]
F[90,x] = 2*F[18,x]+F[135,x]+F[91,x]+F[95,x]
F[91,x] = F[12,x]*F[92,x]
F[92,x] = F[93,x]+F[94,x]
F[93,x] = F[86,x]
F[94,x] = F[90,x]
F[95,x] = F[12,x]*F[96,x]
F[96,x] = F[97,x]
F[97,x] = F[111,x]+F[131,x]+F[18,x]+F[98,x]
F[98,x] = F[12,x]*F[99,x]
F[99,x] = F[100,x]+F[103,x]
F[100,x] = F[101,x]+F[70,x]
F[101,x] = F[102,x]
F[102,x] = F[12,x]*F[70,x]
F[103,x] = F[104,x]+F[97,x]
F[104,x] = 2*F[18,x]+F[105,x]+F[109,x]+F[110,x]
F[105,x] = F[106,x]*F[12,x]
F[106,x] = F[107,x]+F[108,x]
F[107,x] = F[101,x]
F[108,x] = F[104,x]
F[109,x] = F[12,x]*F[97,x]
F[110,x] = 0
F[111,x] = F[112,x]*F[12,x]
F[112,x] = F[113,x]+F[133,x]+F[18,x]
F[113,x] = F[114,x]*F[12,x]
F[114,x] = F[115,x]+F[117,x]
F[115,x] = F[10,x]+F[116,x]
F[116,x] = F[18,x]+F[68,x]+F[71,x]
F[117,x] = F[112,x]+F[118,x]
F[118,x] = F[119,x]+F[129,x]+F[131,x]+F[18,x]
F[119,x] = F[12,x]*F[120,x]
F[120,x] = F[121,x]+F[123,x]
F[121,x] = F[116,x]+F[122,x]
F[122,x] = F[87,x]
F[123,x] = F[118,x]+F[124,x]
F[124,x] = 2*F[18,x]+F[110,x]+F[125,x]+F[95,x]
F[125,x] = F[12,x]*F[126,x]
F[126,x] = F[127,x]+F[128,x]
F[127,x] = F[122,x]
F[128,x] = F[124,x]
F[129,x] = F[12,x]*F[130,x]
F[130,x] = F[112,x]+F[97,x]
F[131,x] = F[12,x]*F[132,x]
F[132,x] = F[47,x]+F[97,x]
F[133,x] = F[12,x]*F[134,x]
F[134,x] = F[112,x]+F[25,x]
F[135,x] = 0
F[136,x] = F[12,x]*F[137,x]
F[137,x] = F[132,x]+F[138,x]
F[138,x] = F[139,x]+F[141,x]
F[139,x] = F[140,x]
F[140,x] = F[12,x]*F[47,x]
F[141,x] = 2*F[18,x]+F[142,x]+F[143,x]+F[155,x]
F[142,x] = 0
F[143,x] = F[12,x]*F[144,x]
F[144,x] = 2*F[18,x]+F[111,x]+F[145,x]
F[145,x] = F[12,x]*F[146,x]
F[146,x] = F[147,x]+F[149,x]
F[147,x] = F[148,x]+F[21,x]
F[148,x] = F[102,x]
F[149,x] = F[144,x]+F[150,x]
F[150,x] = 3*F[18,x]+F[109,x]+F[151,x]
F[151,x] = F[12,x]*F[152,x]
F[152,x] = F[153,x]+F[154,x]
F[153,x] = F[148,x]
F[154,x] = F[150,x]
F[155,x] = F[12,x]*F[138,x]
F[156,x] = F[12,x]*F[157,x]
F[157,x] = F[134,x]+F[158,x]
F[158,x] = F[159,x]+F[161,x]
F[159,x] = F[160,x]+F[18,x]+F[48,x]
F[160,x] = F[12,x]*F[62,x]
F[161,x] = F[162,x]+F[164,x]+F[18,x]+F[98,x]
F[162,x] = F[12,x]*F[163,x]
F[163,x] = F[112,x]+F[144,x]
F[164,x] = F[12,x]*F[158,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_{24}\! \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_{12}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{19}\! \left(x \right)+F_{23}\! \left(x \right)
F_{18}\! \left(x \right) = 0
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{10}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{10}\! \left(x \right) F_{12}\! \left(x \right)
F_{23}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{63}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = F_{1}\! \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_{16}\! \left(x \right)
F_{31}\! \left(x \right) = F_{25}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{18}\! \left(x \right)+F_{33}\! \left(x \right)+F_{61}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)+F_{39}\! \left(x \right)
F_{35}\! \left(x \right) = F_{29}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{12}\! \left(x \right)
F_{39}\! \left(x \right) = F_{32}\! \left(x \right)+F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{41}\! \left(x \right)+F_{45}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)
F_{43}\! \left(x \right) = F_{36}\! \left(x \right)
F_{44}\! \left(x \right) = F_{40}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{18}\! \left(x \right)+F_{48}\! \left(x \right)+F_{60}\! \left(x \right)
F_{48}\! \left(x \right) = F_{12}\! \left(x \right) F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)+F_{53}\! \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_{52}\! \left(x \right) = x^{2}
F_{53}\! \left(x \right) = F_{47}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{55}\! \left(x \right)+F_{59}\! \left(x \right)
F_{55}\! \left(x \right) = F_{12}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{58}\! \left(x \right)
F_{57}\! \left(x \right) = F_{51}\! \left(x \right)
F_{58}\! \left(x \right) = F_{54}\! \left(x \right)
F_{59}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{25}\! \left(x \right)
F_{61}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{25}\! \left(x \right)+F_{47}\! \left(x \right)
F_{63}\! \left(x \right) = F_{156}\! \left(x \right)+F_{18}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{12}\! \left(x \right) F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{81}\! \left(x \right)
F_{66}\! \left(x \right) = F_{6}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{18}\! \left(x \right)+F_{68}\! \left(x \right)+F_{73}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{10}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{18}\! \left(x \right)+F_{22}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{12}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right)+F_{70}\! \left(x \right)
F_{73}\! \left(x \right) = F_{12}\! \left(x \right) F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{72}\! \left(x \right)+F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{78}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = x^{2}
F_{78}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{12}\! \left(x \right) F_{21}\! \left(x \right)
F_{80}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{81}\! \left(x \right) = F_{63}\! \left(x \right)+F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{129}\! \left(x \right)+F_{136}\! \left(x \right)+F_{18}\! \left(x \right)+F_{83}\! \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_{89}\! \left(x \right)
F_{85}\! \left(x \right) = F_{67}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{12}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{70}\! \left(x \right)
F_{89}\! \left(x \right) = F_{82}\! \left(x \right)+F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{135}\! \left(x \right)+F_{91}\! \left(x \right)+F_{95}\! \left(x \right)
F_{91}\! \left(x \right) = F_{12}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)+F_{94}\! \left(x \right)
F_{93}\! \left(x \right) = F_{86}\! \left(x \right)
F_{94}\! \left(x \right) = F_{90}\! \left(x \right)
F_{95}\! \left(x \right) = F_{12}\! \left(x \right) F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{111}\! \left(x \right)+F_{131}\! \left(x \right)+F_{18}\! \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_{103}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right)+F_{70}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)
F_{102}\! \left(x \right) = F_{12}\! \left(x \right) F_{70}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{97}\! \left(x \right)
F_{104}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{105}\! \left(x \right)+F_{109}\! \left(x \right)+F_{110}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right) F_{12}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{108}\! \left(x \right)
F_{107}\! \left(x \right) = F_{101}\! \left(x \right)
F_{108}\! \left(x \right) = F_{104}\! \left(x \right)
F_{109}\! \left(x \right) = F_{12}\! \left(x \right) F_{97}\! \left(x \right)
F_{110}\! \left(x \right) = 0
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_{133}\! \left(x \right)+F_{18}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right) F_{12}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right)+F_{117}\! \left(x \right)
F_{115}\! \left(x \right) = F_{10}\! \left(x \right)+F_{116}\! \left(x \right)
F_{116}\! \left(x \right) = F_{18}\! \left(x \right)+F_{68}\! \left(x \right)+F_{71}\! \left(x \right)
F_{117}\! \left(x \right) = F_{112}\! \left(x \right)+F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)+F_{129}\! \left(x \right)+F_{131}\! \left(x \right)+F_{18}\! \left(x \right)
F_{119}\! \left(x \right) = F_{12}\! \left(x \right) F_{120}\! \left(x \right)
F_{120}\! \left(x \right) = F_{121}\! \left(x \right)+F_{123}\! \left(x \right)
F_{121}\! \left(x \right) = F_{116}\! \left(x \right)+F_{122}\! \left(x \right)
F_{122}\! \left(x \right) = F_{87}\! \left(x \right)
F_{123}\! \left(x \right) = F_{118}\! \left(x \right)+F_{124}\! \left(x \right)
F_{124}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{110}\! \left(x \right)+F_{125}\! \left(x \right)+F_{95}\! \left(x \right)
F_{125}\! \left(x \right) = F_{12}\! \left(x \right) F_{126}\! \left(x \right)
F_{126}\! \left(x \right) = F_{127}\! \left(x \right)+F_{128}\! \left(x \right)
F_{127}\! \left(x \right) = F_{122}\! \left(x \right)
F_{128}\! \left(x \right) = F_{124}\! \left(x \right)
F_{129}\! \left(x \right) = F_{12}\! \left(x \right) F_{130}\! \left(x \right)
F_{130}\! \left(x \right) = F_{112}\! \left(x \right)+F_{97}\! \left(x \right)
F_{131}\! \left(x \right) = F_{12}\! \left(x \right) F_{132}\! \left(x \right)
F_{132}\! \left(x \right) = F_{47}\! \left(x \right)+F_{97}\! \left(x \right)
F_{133}\! \left(x \right) = F_{12}\! \left(x \right) F_{134}\! \left(x \right)
F_{134}\! \left(x \right) = F_{112}\! \left(x \right)+F_{25}\! \left(x \right)
F_{135}\! \left(x \right) = 0
F_{136}\! \left(x \right) = F_{12}\! \left(x \right) F_{137}\! \left(x \right)
F_{137}\! \left(x \right) = F_{132}\! \left(x \right)+F_{138}\! \left(x \right)
F_{138}\! \left(x \right) = F_{139}\! \left(x \right)+F_{141}\! \left(x \right)
F_{139}\! \left(x \right) = F_{140}\! \left(x \right)
F_{140}\! \left(x \right) = F_{12}\! \left(x \right) F_{47}\! \left(x \right)
F_{141}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{142}\! \left(x \right)+F_{143}\! \left(x \right)+F_{155}\! \left(x \right)
F_{142}\! \left(x \right) = 0
F_{143}\! \left(x \right) = F_{12}\! \left(x \right) F_{144}\! \left(x \right)
F_{144}\! \left(x \right) = 2 F_{18}\! \left(x \right)+F_{111}\! \left(x \right)+F_{145}\! \left(x \right)
F_{145}\! \left(x \right) = F_{12}\! \left(x \right) F_{146}\! \left(x \right)
F_{146}\! \left(x \right) = F_{147}\! \left(x \right)+F_{149}\! \left(x \right)
F_{147}\! \left(x \right) = F_{148}\! \left(x \right)+F_{21}\! \left(x \right)
F_{148}\! \left(x \right) = F_{102}\! \left(x \right)
F_{149}\! \left(x \right) = F_{144}\! \left(x \right)+F_{150}\! \left(x \right)
F_{150}\! \left(x \right) = 3 F_{18}\! \left(x \right)+F_{109}\! \left(x \right)+F_{151}\! \left(x \right)
F_{151}\! \left(x \right) = F_{12}\! \left(x \right) F_{152}\! \left(x \right)
F_{152}\! \left(x \right) = F_{153}\! \left(x \right)+F_{154}\! \left(x \right)
F_{153}\! \left(x \right) = F_{148}\! \left(x \right)
F_{154}\! \left(x \right) = F_{150}\! \left(x \right)
F_{155}\! \left(x \right) = F_{12}\! \left(x \right) F_{138}\! \left(x \right)
F_{156}\! \left(x \right) = F_{12}\! \left(x \right) F_{157}\! \left(x \right)
F_{157}\! \left(x \right) = F_{134}\! \left(x \right)+F_{158}\! \left(x \right)
F_{158}\! \left(x \right) = F_{159}\! \left(x \right)+F_{161}\! \left(x \right)
F_{159}\! \left(x \right) = F_{160}\! \left(x \right)+F_{18}\! \left(x \right)+F_{48}\! \left(x \right)
F_{160}\! \left(x \right) = F_{12}\! \left(x \right) F_{62}\! \left(x \right)
F_{161}\! \left(x \right) = F_{162}\! \left(x \right)+F_{164}\! \left(x \right)+F_{18}\! \left(x \right)+F_{98}\! \left(x \right)
F_{162}\! \left(x \right) = F_{12}\! \left(x \right) F_{163}\! \left(x \right)
F_{163}\! \left(x \right) = F_{112}\! \left(x \right)+F_{144}\! \left(x \right)
F_{164}\! \left(x \right) = F_{12}\! \left(x \right) F_{158}\! \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_24(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_12(x))
Eq(F_17(x), F_18(x) + F_19(x) + F_23(x))
Eq(F_18(x), 0)
Eq(F_19(x), F_12(x)*F_20(x))
Eq(F_20(x), F_10(x) + F_21(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_10(x)*F_12(x))
Eq(F_23(x), F_12(x)*F_13(x))
Eq(F_24(x), F_25(x) + F_63(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_12(x)*F_27(x))
Eq(F_27(x), F_28(x) + F_31(x))
Eq(F_28(x), F_1(x) + F_29(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_12(x)*F_16(x))
Eq(F_31(x), F_25(x) + F_32(x))
Eq(F_32(x), F_18(x) + F_33(x) + F_61(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_39(x))
Eq(F_35(x), F_29(x) + F_36(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_12(x))
Eq(F_39(x), F_32(x) + F_40(x))
Eq(F_40(x), 2*F_18(x) + F_41(x) + F_45(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_43(x) + F_44(x))
Eq(F_43(x), F_36(x))
Eq(F_44(x), F_40(x))
Eq(F_45(x), F_12(x)*F_46(x))
Eq(F_46(x), F_47(x))
Eq(F_47(x), F_18(x) + F_48(x) + F_60(x))
Eq(F_48(x), F_12(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_53(x))
Eq(F_50(x), F_12(x) + F_51(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), x**2)
Eq(F_53(x), F_47(x) + F_54(x))
Eq(F_54(x), 2*F_18(x) + F_55(x) + F_59(x))
Eq(F_55(x), F_12(x)*F_56(x))
Eq(F_56(x), F_57(x) + F_58(x))
Eq(F_57(x), F_51(x))
Eq(F_58(x), F_54(x))
Eq(F_59(x), F_12(x)*F_47(x))
Eq(F_60(x), F_12(x)*F_25(x))
Eq(F_61(x), F_12(x)*F_62(x))
Eq(F_62(x), F_25(x) + F_47(x))
Eq(F_63(x), F_156(x) + F_18(x) + F_64(x))
Eq(F_64(x), F_12(x)*F_65(x))
Eq(F_65(x), F_66(x) + F_81(x))
Eq(F_66(x), F_6(x) + F_67(x))
Eq(F_67(x), F_18(x) + F_68(x) + F_73(x))
Eq(F_68(x), F_12(x)*F_69(x))
Eq(F_69(x), F_10(x) + F_70(x))
Eq(F_70(x), F_18(x) + F_22(x) + F_71(x))
Eq(F_71(x), F_12(x)*F_72(x))
Eq(F_72(x), F_12(x) + F_70(x))
Eq(F_73(x), F_12(x)*F_74(x))
Eq(F_74(x), F_72(x) + F_75(x))
Eq(F_75(x), F_76(x) + F_78(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), x**2)
Eq(F_78(x), 2*F_18(x) + F_79(x) + F_80(x))
Eq(F_79(x), F_12(x)*F_21(x))
Eq(F_80(x), F_12(x)*F_75(x))
Eq(F_81(x), F_63(x) + F_82(x))
Eq(F_82(x), F_129(x) + F_136(x) + F_18(x) + F_83(x))
Eq(F_83(x), F_12(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_89(x))
Eq(F_85(x), F_67(x) + F_86(x))
Eq(F_86(x), F_87(x))
Eq(F_87(x), F_12(x)*F_88(x))
Eq(F_88(x), F_70(x))
Eq(F_89(x), F_82(x) + F_90(x))
Eq(F_90(x), F_135(x) + 2*F_18(x) + F_91(x) + F_95(x))
Eq(F_91(x), F_12(x)*F_92(x))
Eq(F_92(x), F_93(x) + F_94(x))
Eq(F_93(x), F_86(x))
Eq(F_94(x), F_90(x))
Eq(F_95(x), F_12(x)*F_96(x))
Eq(F_96(x), F_97(x))
Eq(F_97(x), F_111(x) + F_131(x) + F_18(x) + F_98(x))
Eq(F_98(x), F_12(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_103(x))
Eq(F_100(x), F_101(x) + F_70(x))
Eq(F_101(x), F_102(x))
Eq(F_102(x), F_12(x)*F_70(x))
Eq(F_103(x), F_104(x) + F_97(x))
Eq(F_104(x), F_105(x) + F_109(x) + F_110(x) + 2*F_18(x))
Eq(F_105(x), F_106(x)*F_12(x))
Eq(F_106(x), F_107(x) + F_108(x))
Eq(F_107(x), F_101(x))
Eq(F_108(x), F_104(x))
Eq(F_109(x), F_12(x)*F_97(x))
Eq(F_110(x), 0)
Eq(F_111(x), F_112(x)*F_12(x))
Eq(F_112(x), F_113(x) + F_133(x) + F_18(x))
Eq(F_113(x), F_114(x)*F_12(x))
Eq(F_114(x), F_115(x) + F_117(x))
Eq(F_115(x), F_10(x) + F_116(x))
Eq(F_116(x), F_18(x) + F_68(x) + F_71(x))
Eq(F_117(x), F_112(x) + F_118(x))
Eq(F_118(x), F_119(x) + F_129(x) + F_131(x) + F_18(x))
Eq(F_119(x), F_12(x)*F_120(x))
Eq(F_120(x), F_121(x) + F_123(x))
Eq(F_121(x), F_116(x) + F_122(x))
Eq(F_122(x), F_87(x))
Eq(F_123(x), F_118(x) + F_124(x))
Eq(F_124(x), F_110(x) + F_125(x) + 2*F_18(x) + F_95(x))
Eq(F_125(x), F_12(x)*F_126(x))
Eq(F_126(x), F_127(x) + F_128(x))
Eq(F_127(x), F_122(x))
Eq(F_128(x), F_124(x))
Eq(F_129(x), F_12(x)*F_130(x))
Eq(F_130(x), F_112(x) + F_97(x))
Eq(F_131(x), F_12(x)*F_132(x))
Eq(F_132(x), F_47(x) + F_97(x))
Eq(F_133(x), F_12(x)*F_134(x))
Eq(F_134(x), F_112(x) + F_25(x))
Eq(F_135(x), 0)
Eq(F_136(x), F_12(x)*F_137(x))
Eq(F_137(x), F_132(x) + F_138(x))
Eq(F_138(x), F_139(x) + F_141(x))
Eq(F_139(x), F_140(x))
Eq(F_140(x), F_12(x)*F_47(x))
Eq(F_141(x), F_142(x) + F_143(x) + F_155(x) + 2*F_18(x))
Eq(F_142(x), 0)
Eq(F_143(x), F_12(x)*F_144(x))
Eq(F_144(x), F_111(x) + F_145(x) + 2*F_18(x))
Eq(F_145(x), F_12(x)*F_146(x))
Eq(F_146(x), F_147(x) + F_149(x))
Eq(F_147(x), F_148(x) + F_21(x))
Eq(F_148(x), F_102(x))
Eq(F_149(x), F_144(x) + F_150(x))
Eq(F_150(x), F_109(x) + F_151(x) + 3*F_18(x))
Eq(F_151(x), F_12(x)*F_152(x))
Eq(F_152(x), F_153(x) + F_154(x))
Eq(F_153(x), F_148(x))
Eq(F_154(x), F_150(x))
Eq(F_155(x), F_12(x)*F_138(x))
Eq(F_156(x), F_12(x)*F_157(x))
Eq(F_157(x), F_134(x) + F_158(x))
Eq(F_158(x), F_159(x) + F_161(x))
Eq(F_159(x), F_160(x) + F_18(x) + F_48(x))
Eq(F_160(x), F_12(x)*F_62(x))
Eq(F_161(x), F_162(x) + F_164(x) + F_18(x) + F_98(x))
Eq(F_162(x), F_12(x)*F_163(x))
Eq(F_163(x), F_112(x) + F_144(x))
Eq(F_164(x), F_12(x)*F_158(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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 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, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 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": 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