0132_1302_3120
Counting sequence:
1, 1, 2, 6, 21, 73, 241, 754, 2252, 6471, 18003, 48736, 128878, 333949, 850061, 2130078, 5263536, 12845251, 30998743, 74055916, 175309058, 411566361, 958923057, 2218787146, 5101322596, 11660165503, 26508001691, 59961770424, 135006257622, 302660977141, 675786261013, 1503238554166, 3332089315928, 7361573945979, 16213501543071, 35605278884548, 77975131259626, 170321223090961, 371119534113593, 806766656881506, 1749941475083148, 3787817557689271, 8182565533909987, 17642763579294736, 37971634065245246, 81583762780980333, 174998270676829341, 374783931490239694, 801447219625460992, 1711367858400789811, 3649323073053656423, 7771524106981213596, 16529055057379853778, 35112314494794073609, 74500796835776431681, 157896202935609591418, 334279682341575067316, 706957055106110981871, 1493609809218170259243, 3152519739159347201896, 6647673337969041737638, 14005113977211673642981, 29479626412044773754917, 61999506831737802983526, 130285894628096742525096, 273565214613112650467563, 573970441853472698534191, 1203354902904368890120564, 2521061172321663290706362, 5277982414369776908372481, 11042221002522537597340233, 23086469143128978038459026, 48236907587177170388126428, 100723354713126662762924839, 210192532152527908461611891, 438377280604789165187402688, 913754302602862000624110606, 1903567039778822507060005981, 3963425520674698792112491693, 8247896404320807544432889086, 17155035169650217560697736528, 35663311678631560653832195491, 74103525964917924521964473847, 153903510391859981715144445516, 319488870978656125145474666146, 662926562443878054241878675193, 1374935513164110052976828092241, 2850434311707043419222414725034, 5906850240263305815747966537732, 12235489863286877292034219053151, 25334442903975307325810577248443, 52436045214030494994039654322456, 108487803797803764425990925717878, 224371680360318033304366669107669, 463868512120624842807450837979701, 958660766422598484881881799070358, 1980530751251108486600112881013496, 4090233117961410692604299980051291, 8444375245257835893732694858666943, 17427818908262726340451862755415076, 35956513134661155651766018700743818
Generating function in Maple syntax:
(3*x^7-31*x^6+86*x^5-120*x^4+94*x^3-42*x^2+10*x-1)/(2*x-1)^4/(x-1)^3
Generating function in latex syntax:
\frac{3 x^{7}-31 x^{6}+86 x^{5}-120 x^{4}+94 x^{3}-42 x^{2}+10 x -1}{\left(2 x -1\right)^{4} \left(x -1\right)^{3}}
Generating function in sympy syntax:
(3*x**7 - 31*x**6 + 86*x**5 - 120*x**4 + 94*x**3 - 42*x**2 + 10*x - 1)/((x - 1)**3*(2*x - 1)**4)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^4*(x-1)^3*F(x)-3*x^7+31*x^6-86*x^5+120*x^4-94*x^3+42*x^2-10*x+1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{4} \left(x -1\right)^{3} F \! \left(x \right)-3 x^{7}+31 x^{6}-86 x^{5}+120 x^{4}-94 x^{3}+42 x^{2}-10 x +1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,1/32*(n^3-10*n^2+79*n-230)*2^n+1/2*n^2+5/2*n+8)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ \frac{\left(n^{3}-10 n^{2}+79 n -230\right) 2^{n}}{32}+\frac{n^{2}}{2}+\frac{5 n}{2}+8 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 21
a(5) = 73
a(6) = 241
a(7) = 754
a(n+4) = 1/2*n^2-16*a(n)+32*a(n+1)-24*a(n+2)+8*a(n+3)-3/2*n+2, 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) = 21
a \! \left(5\right) = 73
a \! \left(6\right) = 241
a \! \left(7\right) = 754
a \! \left(n +4\right) = \frac{n^{2}}{2}-16 a \! \left(n \right)+32 a \! \left(n +1\right)-24 a \! \left(n +2\right)+8 a \! \left(n +3\right)-\frac{3 n}{2}+2, \quad n \geq 8
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/299/
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[14,x]*F[4,x]
F[4,x] = F[0,x]+F[5,x]
F[5,x] = F[6,x]
F[6,x] = F[14,x]*F[7,x]
F[7,x] = F[46,x]+F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[32,x]
F[10,x] = F[11,x]+F[15,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = F[13,x]
F[13,x] = F[10,x]*F[14,x]
F[14,x] = x
F[15,x] = F[12,x]+F[16,x]
F[16,x] = F[17,x]*F[20,x]
F[17,x] = F[18,x]
F[18,x] = F[14,x]*F[19,x]
F[19,x] = F[1,x]+F[17,x]
F[20,x] = F[21,x]
F[21,x] = F[14,x]*F[22,x]
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[1,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = F[14,x]*F[23,x]
F[26,x] = F[17,x]+F[27,x]
F[27,x] = F[28,x]+F[29,x]+F[31,x]
F[28,x] = 0
F[29,x] = F[14,x]*F[30,x]
F[30,x] = F[24,x]+F[27,x]
F[31,x] = F[14,x]*F[26,x]
F[32,x] = F[1,x]+F[33,x]
F[33,x] = F[14,x]*F[34,x]
F[34,x] = F[19,x]+F[35,x]
F[35,x] = F[36,x]
F[36,x] = F[14,x]*F[19,x]*F[37,x]*F[43,x]
F[37,x] = F[23,x]+F[38,x]
F[38,x] = F[17,x]+F[39,x]
F[39,x] = F[28,x]+F[40,x]+F[42,x]
F[40,x] = F[14,x]*F[41,x]
F[41,x] = F[24,x]+F[39,x]
F[42,x] = F[14,x]*F[38,x]
F[43,x] = F[1,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[14,x]*F[37,x]
F[46,x] = F[43,x]*F[47,x]
F[47,x] = F[112,x]+F[48,x]
F[48,x] = F[17,x]+F[49,x]
F[49,x] = F[28,x]+F[50,x]+F[53,x]
F[50,x] = F[14,x]*F[51,x]
F[51,x] = F[20,x]+F[52,x]
F[52,x] = F[50,x]
F[53,x] = F[14,x]*F[54,x]
F[54,x] = F[55,x]+F[73,x]
F[55,x] = F[17,x]+F[56,x]
F[56,x] = F[28,x]+F[50,x]+F[57,x]
F[57,x] = F[14,x]*F[58,x]
F[58,x] = F[59,x]+F[65,x]
F[59,x] = F[17,x]+F[60,x]
F[60,x] = F[28,x]+F[61,x]+F[64,x]
F[61,x] = F[14,x]*F[62,x]
F[62,x] = F[24,x]+F[63,x]
F[63,x] = F[61,x]
F[64,x] = F[14,x]*F[59,x]
F[65,x] = F[66,x]+F[69,x]
F[66,x] = F[67,x]
F[67,x] = F[14,x]*F[68,x]
F[68,x] = F[17,x]+F[66,x]
F[69,x] = 2*F[28,x]+F[70,x]+F[72,x]
F[70,x] = F[14,x]*F[71,x]
F[71,x] = F[60,x]+F[69,x]
F[72,x] = F[14,x]*F[65,x]
F[73,x] = F[74,x]+F[80,x]
F[74,x] = F[28,x]+F[75,x]+F[78,x]
F[75,x] = F[14,x]*F[76,x]
F[76,x] = F[17,x]+F[77,x]
F[77,x] = F[75,x]
F[78,x] = F[14,x]*F[79,x]
F[79,x] = F[17,x]+F[74,x]
F[80,x] = F[28,x]+F[81,x]+F[92,x]+F[94,x]
F[81,x] = F[14,x]*F[82,x]
F[82,x] = F[83,x]+F[91,x]
F[83,x] = F[28,x]+F[29,x]+F[84,x]
F[84,x] = F[14,x]*F[85,x]
F[85,x] = F[26,x]+F[86,x]
F[86,x] = F[66,x]+F[87,x]
F[87,x] = 2*F[28,x]+F[88,x]+F[90,x]
F[88,x] = F[14,x]*F[89,x]
F[89,x] = F[27,x]+F[87,x]
F[90,x] = F[14,x]*F[86,x]
F[91,x] = F[81,x]
F[92,x] = F[14,x]*F[93,x]
F[93,x] = F[56,x]+F[80,x]
F[94,x] = F[14,x]*F[95,x]
F[95,x] = F[104,x]+F[96,x]
F[96,x] = F[74,x]+F[97,x]
F[97,x] = F[101,x]+F[103,x]+F[28,x]+F[98,x]
F[98,x] = F[14,x]*F[99,x]
F[99,x] = F[100,x]+F[27,x]
F[100,x] = F[98,x]
F[101,x] = F[102,x]*F[14,x]
F[102,x] = F[60,x]+F[97,x]
F[103,x] = F[14,x]*F[96,x]
F[104,x] = F[105,x]+F[108,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[14,x]
F[107,x] = F[105,x]+F[74,x]
F[108,x] = 3*F[28,x]+F[109,x]+F[111,x]
F[109,x] = F[110,x]*F[14,x]
F[110,x] = F[108,x]+F[97,x]
F[111,x] = F[104,x]*F[14,x]
F[112,x] = F[113,x]+F[49,x]
F[113,x] = F[114,x]
F[114,x] = F[115,x]*F[14,x]
F[115,x] = F[116,x]+F[117,x]
F[116,x] = F[52,x]
F[117,x] = F[118,x]
F[118,x] = F[119,x]
F[119,x] = F[120,x]*F[14,x]
F[120,x] = F[118,x]+F[52,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_{14}\! \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_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{14}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{46}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right) F_{32}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{15}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = F_{10}\! \left(x \right) F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = x
F_{15}\! \left(x \right) = F_{12}\! \left(x \right)+F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right) F_{20}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{14}\! \left(x \right) F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{14}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{1}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{14}\! \left(x \right) F_{23}\! \left(x \right)
F_{26}\! \left(x \right) = F_{17}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)+F_{31}\! \left(x \right)
F_{28}\! \left(x \right) = 0
F_{29}\! \left(x \right) = F_{14}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{24}\! \left(x \right)+F_{27}\! \left(x \right)
F_{31}\! \left(x \right) = F_{14}\! \left(x \right) F_{26}\! \left(x \right)
F_{32}\! \left(x \right) = F_{1}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{14}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{19}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{14}\! \left(x \right) F_{19}\! \left(x \right) F_{37}\! \left(x \right) F_{43}\! \left(x \right)
F_{37}\! \left(x \right) = F_{23}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{17}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{28}\! \left(x \right)+F_{40}\! \left(x \right)+F_{42}\! \left(x \right)
F_{40}\! \left(x \right) = F_{14}\! \left(x \right) F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{24}\! \left(x \right)+F_{39}\! \left(x \right)
F_{42}\! \left(x \right) = F_{14}\! \left(x \right) F_{38}\! \left(x \right)
F_{43}\! \left(x \right) = F_{1}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{14}\! \left(x \right) F_{37}\! \left(x \right)
F_{46}\! \left(x \right) = F_{43}\! \left(x \right) F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{112}\! \left(x \right)+F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{17}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{28}\! \left(x \right)+F_{50}\! \left(x \right)+F_{53}\! \left(x \right)
F_{50}\! \left(x \right) = F_{14}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{20}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = F_{14}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{73}\! \left(x \right)
F_{55}\! \left(x \right) = F_{17}\! \left(x \right)+F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{28}\! \left(x \right)+F_{50}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{14}\! \left(x \right) F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{65}\! \left(x \right)
F_{59}\! \left(x \right) = F_{17}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{28}\! \left(x \right)+F_{61}\! \left(x \right)+F_{64}\! \left(x \right)
F_{61}\! \left(x \right) = F_{14}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{24}\! \left(x \right)+F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{61}\! \left(x \right)
F_{64}\! \left(x \right) = F_{14}\! \left(x \right) F_{59}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)+F_{69}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{14}\! \left(x \right) F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{17}\! \left(x \right)+F_{66}\! \left(x \right)
F_{69}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{70}\! \left(x \right)+F_{72}\! \left(x \right)
F_{70}\! \left(x \right) = F_{14}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{60}\! \left(x \right)+F_{69}\! \left(x \right)
F_{72}\! \left(x \right) = F_{14}\! \left(x \right) F_{65}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{80}\! \left(x \right)
F_{74}\! \left(x \right) = F_{28}\! \left(x \right)+F_{75}\! \left(x \right)+F_{78}\! \left(x \right)
F_{75}\! \left(x \right) = F_{14}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{17}\! \left(x \right)+F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{75}\! \left(x \right)
F_{78}\! \left(x \right) = F_{14}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{17}\! \left(x \right)+F_{74}\! \left(x \right)
F_{80}\! \left(x \right) = F_{28}\! \left(x \right)+F_{81}\! \left(x \right)+F_{92}\! \left(x \right)+F_{94}\! \left(x \right)
F_{81}\! \left(x \right) = F_{14}\! \left(x \right) F_{82}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)+F_{91}\! \left(x \right)
F_{83}\! \left(x \right) = F_{28}\! \left(x \right)+F_{29}\! \left(x \right)+F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{14}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{26}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{66}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = 2 F_{28}\! \left(x \right)+F_{88}\! \left(x \right)+F_{90}\! \left(x \right)
F_{88}\! \left(x \right) = F_{14}\! \left(x \right) F_{89}\! \left(x \right)
F_{89}\! \left(x \right) = F_{27}\! \left(x \right)+F_{87}\! \left(x \right)
F_{90}\! \left(x \right) = F_{14}\! \left(x \right) F_{86}\! \left(x \right)
F_{91}\! \left(x \right) = F_{81}\! \left(x \right)
F_{92}\! \left(x \right) = F_{14}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{56}\! \left(x \right)+F_{80}\! \left(x \right)
F_{94}\! \left(x \right) = F_{14}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{104}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{74}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{101}\! \left(x \right)+F_{103}\! \left(x \right)+F_{28}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{14}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{27}\! \left(x \right)
F_{100}\! \left(x \right) = F_{98}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right) F_{14}\! \left(x \right)
F_{102}\! \left(x \right) = F_{60}\! \left(x \right)+F_{97}\! \left(x \right)
F_{103}\! \left(x \right) = F_{14}\! \left(x \right) F_{96}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{108}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{14}\! \left(x \right)
F_{107}\! \left(x \right) = F_{105}\! \left(x \right)+F_{74}\! \left(x \right)
F_{108}\! \left(x \right) = 3 F_{28}\! \left(x \right)+F_{109}\! \left(x \right)+F_{111}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right) F_{14}\! \left(x \right)
F_{110}\! \left(x \right) = F_{108}\! \left(x \right)+F_{97}\! \left(x \right)
F_{111}\! \left(x \right) = F_{104}\! \left(x \right) F_{14}\! \left(x \right)
F_{112}\! \left(x \right) = F_{113}\! \left(x \right)+F_{49}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{14}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{117}\! \left(x \right)
F_{116}\! \left(x \right) = F_{52}\! \left(x \right)
F_{117}\! \left(x \right) = F_{118}\! \left(x \right)
F_{118}\! \left(x \right) = F_{119}\! \left(x \right)
F_{119}\! \left(x \right) = F_{120}\! \left(x \right) F_{14}\! \left(x \right)
F_{120}\! \left(x \right) = F_{118}\! \left(x \right)+F_{52}\! \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_14(x)*F_4(x))
Eq(F_4(x), F_0(x) + F_5(x))
Eq(F_5(x), F_6(x))
Eq(F_6(x), F_14(x)*F_7(x))
Eq(F_7(x), F_46(x) + F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_32(x))
Eq(F_10(x), F_11(x) + F_15(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), F_13(x))
Eq(F_13(x), F_10(x)*F_14(x))
Eq(F_14(x), x)
Eq(F_15(x), F_12(x) + F_16(x))
Eq(F_16(x), F_17(x)*F_20(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_14(x)*F_19(x))
Eq(F_19(x), F_1(x) + F_17(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_14(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_26(x))
Eq(F_23(x), F_1(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_14(x)*F_23(x))
Eq(F_26(x), F_17(x) + F_27(x))
Eq(F_27(x), F_28(x) + F_29(x) + F_31(x))
Eq(F_28(x), 0)
Eq(F_29(x), F_14(x)*F_30(x))
Eq(F_30(x), F_24(x) + F_27(x))
Eq(F_31(x), F_14(x)*F_26(x))
Eq(F_32(x), F_1(x) + F_33(x))
Eq(F_33(x), F_14(x)*F_34(x))
Eq(F_34(x), F_19(x) + F_35(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_14(x)*F_19(x)*F_37(x)*F_43(x))
Eq(F_37(x), F_23(x) + F_38(x))
Eq(F_38(x), F_17(x) + F_39(x))
Eq(F_39(x), F_28(x) + F_40(x) + F_42(x))
Eq(F_40(x), F_14(x)*F_41(x))
Eq(F_41(x), F_24(x) + F_39(x))
Eq(F_42(x), F_14(x)*F_38(x))
Eq(F_43(x), F_1(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_14(x)*F_37(x))
Eq(F_46(x), F_43(x)*F_47(x))
Eq(F_47(x), F_112(x) + F_48(x))
Eq(F_48(x), F_17(x) + F_49(x))
Eq(F_49(x), F_28(x) + F_50(x) + F_53(x))
Eq(F_50(x), F_14(x)*F_51(x))
Eq(F_51(x), F_20(x) + F_52(x))
Eq(F_52(x), F_50(x))
Eq(F_53(x), F_14(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_73(x))
Eq(F_55(x), F_17(x) + F_56(x))
Eq(F_56(x), F_28(x) + F_50(x) + F_57(x))
Eq(F_57(x), F_14(x)*F_58(x))
Eq(F_58(x), F_59(x) + F_65(x))
Eq(F_59(x), F_17(x) + F_60(x))
Eq(F_60(x), F_28(x) + F_61(x) + F_64(x))
Eq(F_61(x), F_14(x)*F_62(x))
Eq(F_62(x), F_24(x) + F_63(x))
Eq(F_63(x), F_61(x))
Eq(F_64(x), F_14(x)*F_59(x))
Eq(F_65(x), F_66(x) + F_69(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_14(x)*F_68(x))
Eq(F_68(x), F_17(x) + F_66(x))
Eq(F_69(x), 2*F_28(x) + F_70(x) + F_72(x))
Eq(F_70(x), F_14(x)*F_71(x))
Eq(F_71(x), F_60(x) + F_69(x))
Eq(F_72(x), F_14(x)*F_65(x))
Eq(F_73(x), F_74(x) + F_80(x))
Eq(F_74(x), F_28(x) + F_75(x) + F_78(x))
Eq(F_75(x), F_14(x)*F_76(x))
Eq(F_76(x), F_17(x) + F_77(x))
Eq(F_77(x), F_75(x))
Eq(F_78(x), F_14(x)*F_79(x))
Eq(F_79(x), F_17(x) + F_74(x))
Eq(F_80(x), F_28(x) + F_81(x) + F_92(x) + F_94(x))
Eq(F_81(x), F_14(x)*F_82(x))
Eq(F_82(x), F_83(x) + F_91(x))
Eq(F_83(x), F_28(x) + F_29(x) + F_84(x))
Eq(F_84(x), F_14(x)*F_85(x))
Eq(F_85(x), F_26(x) + F_86(x))
Eq(F_86(x), F_66(x) + F_87(x))
Eq(F_87(x), 2*F_28(x) + F_88(x) + F_90(x))
Eq(F_88(x), F_14(x)*F_89(x))
Eq(F_89(x), F_27(x) + F_87(x))
Eq(F_90(x), F_14(x)*F_86(x))
Eq(F_91(x), F_81(x))
Eq(F_92(x), F_14(x)*F_93(x))
Eq(F_93(x), F_56(x) + F_80(x))
Eq(F_94(x), F_14(x)*F_95(x))
Eq(F_95(x), F_104(x) + F_96(x))
Eq(F_96(x), F_74(x) + F_97(x))
Eq(F_97(x), F_101(x) + F_103(x) + F_28(x) + F_98(x))
Eq(F_98(x), F_14(x)*F_99(x))
Eq(F_99(x), F_100(x) + F_27(x))
Eq(F_100(x), F_98(x))
Eq(F_101(x), F_102(x)*F_14(x))
Eq(F_102(x), F_60(x) + F_97(x))
Eq(F_103(x), F_14(x)*F_96(x))
Eq(F_104(x), F_105(x) + F_108(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_14(x))
Eq(F_107(x), F_105(x) + F_74(x))
Eq(F_108(x), F_109(x) + F_111(x) + 3*F_28(x))
Eq(F_109(x), F_110(x)*F_14(x))
Eq(F_110(x), F_108(x) + F_97(x))
Eq(F_111(x), F_104(x)*F_14(x))
Eq(F_112(x), F_113(x) + F_49(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_115(x)*F_14(x))
Eq(F_115(x), F_116(x) + F_117(x))
Eq(F_116(x), F_52(x))
Eq(F_117(x), F_118(x))
Eq(F_118(x), F_119(x))
Eq(F_119(x), F_120(x)*F_14(x))
Eq(F_120(x), F_118(x) + F_52(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": 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": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rules": [{"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 0], [0, 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": [[1, 2]]}, {"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], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 2], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], [0, 2], [0, 0], [0, 2]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 2], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[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": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "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], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}], "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], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 1], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 1], [0, 1], [0, 0], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 3], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 3]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 3]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 3], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 3], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 2], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 3], [0, 3], [0, 3], [0, 3]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": [1, 3, 0, 2], "pos": [[0, 2], 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