0132_0213_2301
Counting sequence:
1, 1, 2, 6, 21, 73, 237, 711, 1988, 5253, 13301, 32673, 78669, 187230, 443398, 1050209, 2497187, 5976456, 14419577, 35101838, 86229874, 213707024, 534022585, 1344450284, 3407215499, 8684458421, 22243751970, 57208235104, 147636483121, 382077767531, 991081141309, 2575597009441, 6703498350192, 17468326889263, 45564044345061, 118940339443027, 310672859747785, 811875650472304, 2122480192243670, 5550479686964811, 14518513510446447, 37983620370197122, 99388367137934793, 260091321093401712, 680700878192484302, 1781633081488224594, 4663424310090854153, 12207056552045495622, 31954508383819200279, 83649853937465781759, 218981542629703102642, 573267189403933702034, 1500763730586764505965, 3928909160565871381821, 10285729563930236837549, 26927802149664349346795, 70496704107543311767708, 184560328589129556716777, 483180246434579249471413, 1264972196148887884333109, 3311719624650267622131845, 8670152666617529099529170, 22698669199912043286765126, 59425714276695038748352165, 155578187705639930485066555, 407308267767786430882830092, 1066345435006098644781143161, 2791725639173779921250213890, 7308826612574805659681641962, 19134744311095813549511411812, 50095386250655082792899554425, 131151373710458520078539319952, 343358652239307027223972291363, 898924415363452419721020861529, 2353414253840663465324686755362, 6161317656693031477284893702388, 16130537318417952037115070447081, 42230291465140934912273252833375, 110560331334607209530216175893181, 289450690902769679887569540504357, 757791717799648347647223615802568, 1983924414743605488276248987957043, 5193981429717102548011189458772709, 13598019678561719378187393178675143, 35600077209440386752952620872133633, 93202211147032696656556697537409540, 244006554606861401654655861045953494, 638817449385273278955619530517292783, 1672445786895030724053283753047772295, 4378519897837220965975721239230017190, 11463113879381951309595513917001185033, 30010821685220301214611398278910170820, 78569351064864348798554456178964194886, 205697231284067658031112760226506616262, 538522342331776690837763883337851903625, 1409869794790235025253855965262284191306, 3691087040177066565838592079000911327279, 9663391321977626952834364236047316038723, 25299086918149910691295124220161032287474, 66233869417101841593283726931288480487430, 173402521302098174382964436237035418440741
Generating function in Maple syntax:
-(10*x^9-64*x^8+192*x^7-367*x^6+447*x^5-358*x^4+189*x^3-63*x^2+12*x-1)/(x^2-3*x+1)/(2*x-1)^2/(x-1)^6
Generating function in latex syntax:
-\frac{10 x^{9}-64 x^{8}+192 x^{7}-367 x^{6}+447 x^{5}-358 x^{4}+189 x^{3}-63 x^{2}+12 x -1}{\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{6}}
Generating function in sympy syntax:
(-10*x**9 + 64*x**8 - 192*x**7 + 367*x**6 - 447*x**5 + 358*x**4 - 189*x**3 + 63*x**2 - 12*x + 1)/((x - 1)**6*(2*x - 1)**2*(x**2 - 3*x + 1))
Implicit equation for the generating function in Maple syntax:
(x^2-3*x+1)*(2*x-1)^2*(x-1)^6*F(x)+10*x^9-64*x^8+192*x^7-367*x^6+447*x^5-358*x^4+189*x^3-63*x^2+12*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{6} F \! \left(x \right)+10 x^{9}-64 x^{8}+192 x^{7}-367 x^{6}+447 x^{5}-358 x^{4}+189 x^{3}-63 x^{2}+12 x -1 = 0
Explicit closed form in Maple syntax:
1/120*(-12*5^(1/2)+60)*(3/2-1/2*5^(1/2))^(-n)+1/120*(12*5^(1/2)+60)*(3/2+1/2*5^(1/2))^(-n)-1/40*n^5-13/24*n^3-n^2+2^n*n-73/30*n+2^(n+1)-2
Explicit closed form in latex syntax:
\frac{\left(-12 \sqrt{5}+60\right) \left(\frac{3}{2}-\frac{\sqrt{5}}{2}\right)^{-n}}{120}+\frac{\left(12 \sqrt{5}+60\right) \left(\frac{3}{2}+\frac{\sqrt{5}}{2}\right)^{-n}}{120}-\frac{n^{5}}{40}-\frac{13 n^{3}}{24}-n^{2}+2^{n} n -\frac{73 n}{30}+2^{n +1}-2
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 73
a(6) = 237
a(7) = 711
a(8) = 1988
a(9) = 5253
a(n+4) = -4*a(n)+16*a(n+1)-17*a(n+2)+7*a(n+3)+1/120*(n-1)*(3*n^4-12*n^3-97*n^2-22*n-120), n >= 10
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) = 73
a \! \left(6\right) = 237
a \! \left(7\right) = 711
a \! \left(8\right) = 1988
a \! \left(9\right) = 5253
a \! \left(n +4\right) = -4 a \! \left(n \right)+16 a \! \left(n +1\right)-17 a \! \left(n +2\right)+7 a \! \left(n +3\right)+\frac{\left(n -1\right) \left(3 n^{4}-12 n^{3}-97 n^{2}-22 n -120\right)}{120}, \quad n \geq 10
Specification 1
Strategy pack name: insertion_point_row_placements
Tree: http://permpal.com/tree/259/
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[13,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[16,x]+F[6,x]
F[6,x] = F[7,x]
F[7,x] = F[13,x]*F[8,x]
F[8,x] = F[14,x]+F[9,x]
F[9,x] = F[10,x]*F[11,x]
F[10,x] = F[1,x]+F[6,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[11,x]*F[13,x]
F[13,x] = x
F[14,x] = F[15,x]
F[15,x] = F[11,x]^2*F[13,x]*F[6,x]
F[16,x] = F[17,x]
F[17,x] = F[13,x]*F[18,x]
F[18,x] = F[19,x]+F[62,x]
F[19,x] = F[20,x]+F[55,x]
F[20,x] = F[21,x]+F[33,x]
F[21,x] = F[22,x]
F[22,x] = F[13,x]*F[23,x]
F[23,x] = F[24,x]+F[27,x]
F[24,x] = F[1,x]+F[25,x]
F[25,x] = F[26,x]
F[26,x] = F[13,x]*F[24,x]
F[27,x] = F[21,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[13,x]*F[30,x]
F[30,x] = F[31,x]+F[32,x]
F[31,x] = F[12,x]
F[32,x] = F[29,x]
F[33,x] = F[31,x]+F[34,x]
F[34,x] = F[35,x]+F[36,x]+F[38,x]
F[35,x] = 0
F[36,x] = F[13,x]*F[37,x]
F[37,x] = F[21,x]+F[34,x]
F[38,x] = F[13,x]*F[39,x]
F[39,x] = F[40,x]+F[45,x]
F[40,x] = F[31,x]+F[41,x]
F[41,x] = F[35,x]+F[42,x]+F[44,x]
F[42,x] = F[13,x]*F[43,x]
F[43,x] = F[25,x]+F[41,x]
F[44,x] = F[13,x]*F[40,x]
F[45,x] = F[34,x]+F[46,x]
F[46,x] = 2*F[35,x]+F[47,x]+F[49,x]
F[47,x] = F[13,x]*F[48,x]
F[48,x] = F[28,x]+F[46,x]
F[49,x] = F[13,x]*F[50,x]
F[50,x] = F[51,x]+F[54,x]
F[51,x] = F[52,x]
F[52,x] = F[13,x]*F[53,x]
F[53,x] = F[31,x]+F[51,x]
F[54,x] = F[49,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[21,x]*F[31,x]
F[57,x] = F[58,x]+F[85,x]
F[58,x] = F[35,x]+F[59,x]+F[79,x]
F[59,x] = F[13,x]*F[60,x]
F[60,x] = F[61,x]+F[62,x]
F[61,x] = F[31,x]+F[58,x]
F[62,x] = F[58,x]+F[63,x]
F[63,x] = 2*F[35,x]+F[64,x]+F[66,x]
F[64,x] = F[65,x]
F[65,x] = F[31,x]^2*F[13,x]*F[8,x]
F[66,x] = F[13,x]*F[67,x]
F[67,x] = F[68,x]+F[71,x]
F[68,x] = F[69,x]
F[69,x] = F[13,x]*F[70,x]
F[70,x] = F[31,x]+F[68,x]
F[71,x] = 2*F[35,x]+F[72,x]+F[78,x]
F[72,x] = F[13,x]*F[73,x]
F[73,x] = F[74,x]+F[77,x]
F[74,x] = F[75,x]
F[75,x] = F[13,x]*F[76,x]
F[76,x] = F[31,x]+F[74,x]
F[77,x] = F[72,x]
F[78,x] = F[13,x]*F[67,x]
F[79,x] = F[13,x]*F[80,x]
F[80,x] = F[31,x]+F[81,x]
F[81,x] = F[35,x]+F[82,x]+F[84,x]
F[82,x] = F[13,x]*F[83,x]
F[83,x] = F[31,x]+F[81,x]
F[84,x] = F[13,x]*F[80,x]
F[85,x] = F[35,x]+F[86,x]+F[88,x]
F[86,x] = F[13,x]*F[87,x]
F[87,x] = F[34,x]+F[85,x]
F[88,x] = F[89,x]
F[89,x] = F[13,x]*F[90,x]
F[90,x] = F[91,x]+F[99,x]
F[91,x] = F[92,x]+F[93,x]
F[92,x] = F[25,x]*F[31,x]
F[93,x] = F[94,x]
F[94,x] = F[13,x]*F[95,x]
F[95,x] = F[96,x]+F[97,x]
F[96,x] = F[24,x]*F[81,x]
F[97,x] = F[98,x]
F[98,x] = F[11,x]*F[31,x]*F[40,x]
F[99,x] = F[100,x]+F[103,x]
F[100,x] = F[101,x]*F[31,x]
F[101,x] = F[102,x]+F[21,x]
F[102,x] = F[25,x]*F[31,x]
F[103,x] = F[104,x]+F[105,x]
F[104,x] = F[21,x]*F[81,x]
F[105,x] = F[31,x]*F[93,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_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{0}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{16}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{14}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{11}\! \left(x \right) F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{11} \left(x \right)^{2} F_{13}\! \left(x \right) F_{6}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{13}\! \left(x \right) F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{62}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{55}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{33}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{13}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{27}\! \left(x \right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{13}\! \left(x \right) F_{24}\! \left(x \right)
F_{27}\! \left(x \right) = F_{21}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{13}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{32}\! \left(x \right)
F_{31}\! \left(x \right) = F_{12}\! \left(x \right)
F_{32}\! \left(x \right) = F_{29}\! \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_{36}\! \left(x \right)+F_{38}\! \left(x \right)
F_{35}\! \left(x \right) = 0
F_{36}\! \left(x \right) = F_{13}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{21}\! \left(x \right)+F_{34}\! \left(x \right)
F_{38}\! \left(x \right) = F_{13}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{45}\! \left(x \right)
F_{40}\! \left(x \right) = F_{31}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{35}\! \left(x \right)+F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{13}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{25}\! \left(x \right)+F_{41}\! \left(x \right)
F_{44}\! \left(x \right) = F_{13}\! \left(x \right) F_{40}\! \left(x \right)
F_{45}\! \left(x \right) = F_{34}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = 2 F_{35}\! \left(x \right)+F_{47}\! \left(x \right)+F_{49}\! \left(x \right)
F_{47}\! \left(x \right) = F_{13}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{28}\! \left(x \right)+F_{46}\! \left(x \right)
F_{49}\! \left(x \right) = F_{13}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{54}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{13}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{31}\! \left(x \right)+F_{51}\! \left(x \right)
F_{54}\! \left(x \right) = F_{49}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{21}\! \left(x \right) F_{31}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{85}\! \left(x \right)
F_{58}\! \left(x \right) = F_{35}\! \left(x \right)+F_{59}\! \left(x \right)+F_{79}\! \left(x \right)
F_{59}\! \left(x \right) = F_{13}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{62}\! \left(x \right)
F_{61}\! \left(x \right) = F_{31}\! \left(x \right)+F_{58}\! \left(x \right)
F_{62}\! \left(x \right) = F_{58}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = 2 F_{35}\! \left(x \right)+F_{64}\! \left(x \right)+F_{66}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{31} \left(x \right)^{2} F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{66}\! \left(x \right) = F_{13}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)+F_{71}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{13}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{31}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = 2 F_{35}\! \left(x \right)+F_{72}\! \left(x \right)+F_{78}\! \left(x \right)
F_{72}\! \left(x \right) = F_{13}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{77}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{13}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{31}\! \left(x \right)+F_{74}\! \left(x \right)
F_{77}\! \left(x \right) = F_{72}\! \left(x \right)
F_{78}\! \left(x \right) = F_{13}\! \left(x \right) F_{67}\! \left(x \right)
F_{79}\! \left(x \right) = F_{13}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{31}\! \left(x \right)+F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{35}\! \left(x \right)+F_{82}\! \left(x \right)+F_{84}\! \left(x \right)
F_{82}\! \left(x \right) = F_{13}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{31}\! \left(x \right)+F_{81}\! \left(x \right)
F_{84}\! \left(x \right) = F_{13}\! \left(x \right) F_{80}\! \left(x \right)
F_{85}\! \left(x \right) = F_{35}\! \left(x \right)+F_{86}\! \left(x \right)+F_{88}\! \left(x \right)
F_{86}\! \left(x \right) = F_{13}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{34}\! \left(x \right)+F_{85}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{13}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{99}\! \left(x \right)
F_{91}\! \left(x \right) = F_{92}\! \left(x \right)+F_{93}\! \left(x \right)
F_{92}\! \left(x \right) = F_{25}\! \left(x \right) F_{31}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{13}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)+F_{97}\! \left(x \right)
F_{96}\! \left(x \right) = F_{24}\! \left(x \right) F_{81}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{11}\! \left(x \right) F_{31}\! \left(x \right) F_{40}\! \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_{31}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{21}\! \left(x \right)
F_{102}\! \left(x \right) = F_{25}\! \left(x \right) F_{31}\! \left(x \right)
F_{103}\! \left(x \right) = F_{104}\! \left(x \right)+F_{105}\! \left(x \right)
F_{104}\! \left(x \right) = F_{21}\! \left(x \right) F_{81}\! \left(x \right)
F_{105}\! \left(x \right) = F_{31}\! \left(x \right) F_{93}\! \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_13(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_16(x) + F_6(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_13(x)*F_8(x))
Eq(F_8(x), F_14(x) + F_9(x))
Eq(F_9(x), F_10(x)*F_11(x))
Eq(F_10(x), F_1(x) + F_6(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_11(x)*F_13(x))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_11(x)**2*F_13(x)*F_6(x))
Eq(F_16(x), F_17(x))
Eq(F_17(x), F_13(x)*F_18(x))
Eq(F_18(x), F_19(x) + F_62(x))
Eq(F_19(x), F_20(x) + F_55(x))
Eq(F_20(x), F_21(x) + F_33(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_13(x)*F_23(x))
Eq(F_23(x), F_24(x) + F_27(x))
Eq(F_24(x), F_1(x) + F_25(x))
Eq(F_25(x), F_26(x))
Eq(F_26(x), F_13(x)*F_24(x))
Eq(F_27(x), F_21(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_13(x)*F_30(x))
Eq(F_30(x), F_31(x) + F_32(x))
Eq(F_31(x), F_12(x))
Eq(F_32(x), F_29(x))
Eq(F_33(x), F_31(x) + F_34(x))
Eq(F_34(x), F_35(x) + F_36(x) + F_38(x))
Eq(F_35(x), 0)
Eq(F_36(x), F_13(x)*F_37(x))
Eq(F_37(x), F_21(x) + F_34(x))
Eq(F_38(x), F_13(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_45(x))
Eq(F_40(x), F_31(x) + F_41(x))
Eq(F_41(x), F_35(x) + F_42(x) + F_44(x))
Eq(F_42(x), F_13(x)*F_43(x))
Eq(F_43(x), F_25(x) + F_41(x))
Eq(F_44(x), F_13(x)*F_40(x))
Eq(F_45(x), F_34(x) + F_46(x))
Eq(F_46(x), 2*F_35(x) + F_47(x) + F_49(x))
Eq(F_47(x), F_13(x)*F_48(x))
Eq(F_48(x), F_28(x) + F_46(x))
Eq(F_49(x), F_13(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_54(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_13(x)*F_53(x))
Eq(F_53(x), F_31(x) + F_51(x))
Eq(F_54(x), F_49(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_21(x)*F_31(x))
Eq(F_57(x), F_58(x) + F_85(x))
Eq(F_58(x), F_35(x) + F_59(x) + F_79(x))
Eq(F_59(x), F_13(x)*F_60(x))
Eq(F_60(x), F_61(x) + F_62(x))
Eq(F_61(x), F_31(x) + F_58(x))
Eq(F_62(x), F_58(x) + F_63(x))
Eq(F_63(x), 2*F_35(x) + F_64(x) + F_66(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_13(x)*F_31(x)**2*F_8(x))
Eq(F_66(x), F_13(x)*F_67(x))
Eq(F_67(x), F_68(x) + F_71(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_13(x)*F_70(x))
Eq(F_70(x), F_31(x) + F_68(x))
Eq(F_71(x), 2*F_35(x) + F_72(x) + F_78(x))
Eq(F_72(x), F_13(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_77(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_13(x)*F_76(x))
Eq(F_76(x), F_31(x) + F_74(x))
Eq(F_77(x), F_72(x))
Eq(F_78(x), F_13(x)*F_67(x))
Eq(F_79(x), F_13(x)*F_80(x))
Eq(F_80(x), F_31(x) + F_81(x))
Eq(F_81(x), F_35(x) + F_82(x) + F_84(x))
Eq(F_82(x), F_13(x)*F_83(x))
Eq(F_83(x), F_31(x) + F_81(x))
Eq(F_84(x), F_13(x)*F_80(x))
Eq(F_85(x), F_35(x) + F_86(x) + F_88(x))
Eq(F_86(x), F_13(x)*F_87(x))
Eq(F_87(x), F_34(x) + F_85(x))
Eq(F_88(x), F_89(x))
Eq(F_89(x), F_13(x)*F_90(x))
Eq(F_90(x), F_91(x) + F_99(x))
Eq(F_91(x), F_92(x) + F_93(x))
Eq(F_92(x), F_25(x)*F_31(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_13(x)*F_95(x))
Eq(F_95(x), F_96(x) + F_97(x))
Eq(F_96(x), F_24(x)*F_81(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_11(x)*F_31(x)*F_40(x))
Eq(F_99(x), F_100(x) + F_103(x))
Eq(F_100(x), F_101(x)*F_31(x))
Eq(F_101(x), F_102(x) + F_21(x))
Eq(F_102(x), F_25(x)*F_31(x))
Eq(F_103(x), F_104(x) + F_105(x))
Eq(F_104(x), F_21(x)*F_81(x))
Eq(F_105(x), F_31(x)*F_93(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": false, "place_row": true, "strategy_class": "RowAndColumnPlacementFactory"}], [{"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}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_point_row_placements", "symmetries": [], "ver_strats": [{"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}, {"class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "InsertionEncodingVerificationStrategy"}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "strategy_class": "OneByOneVerificationStrategy", "symmetry": false}, {"basis": [], "class_module": "tilings.strategies.verification", "ignore_parent": true, "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": [2, 3, 0, 1], "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": [2, 3, 0, 1], "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": [2, 3, 0, 1], "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": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [2, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[2, 0], [2, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [2, 0]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"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": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[1, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": 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