0132_0213_0231_2301
Counting sequence:
1, 1, 2, 6, 20, 64, 190, 527, 1388, 3526, 8751, 21429, 52154, 126817, 309181, 757489, 1867361, 4634661, 11581745, 29132378, 73724221, 187591151, 479620902, 1231359236, 3172526415, 8198154574, 21237405480, 55128206372, 143341931018, 373219892486, 972828116976, 2538016737089, 6626189749674, 17309414045412, 45237627929481, 118270325815759, 309298471676896, 809058153605671, 2116707758117855, 5538659939153523, 14494324257118991, 37934142349758451, 99287212071352027, 259884612910950116, 680278665731425235, 1780771064376533509, 4661665091491420920, 12203467746098013942, 31947190034430924173, 83634935763706993996, 218951143332225962626, 573205264909065763774, 1500637629797207398544, 3928652455387121459532, 10285207146373473058706, 26926739300152302188579, 70494542379722187370456, 184555933075893257801906, 483171311292918562436115, 1264954037635190343957593, 3311682731162120222029686, 8670077726719729675119901, 22698517014273435205363377, 59425405293731804137634021, 155577560516341424386578605, 407306994942445344952160369, 1066342852461928325474568885, 2791720400298462987770608862, 7308815987250219203015515353, 19134722765298735456793433931, 50095342568765116248722504826, 131151285166086966272735776984, 343358472789380678177501598139, 898924051741233238758390231802, 2353413517151492137660087833356, 6161316164425222890477064378824, 16130534296103403000542195884166, 42230285344953973113213122300866, 110560318943117558480267206012900, 289450665817558922884014240884213, 757791667024763923832798358594806, 1983924311984910821032769223555376, 5193981221781861574294971500368077, 13598019257855534152296440477690451, 35600076358356609744253681981739900, 93202209425522329525324752864851779, 244006551125155041164523838007789875, 638817442344489305520019217151048007, 1672445772658720272271410591837594683, 4378519869055115052590629847962693791, 11463113821198769463182640996887573951, 30010821567615997482500272163646870344, 78569350827179861255761443398494490959, 205697230803746922788385213565817596097, 538522341361231700038025747817119120556, 1409869792829338003025813609822261869994, 3691087036215658440125375199323914525401, 9663391313975582538893666139099588473176, 25299086901987365538385199351078288992710, 66233869384459838637406819842748607144258, 173402521236180343171096507359207098058476
Generating function in Maple syntax:
-(7*x^8-48*x^7+140*x^6-223*x^5+220*x^4-137*x^3+52*x^2-11*x+1)/(x^2-3*x+1)/(2*x-1)^2/(x-1)^5
Generating function in latex syntax:
-\frac{7 x^{8}-48 x^{7}+140 x^{6}-223 x^{5}+220 x^{4}-137 x^{3}+52 x^{2}-11 x +1}{\left(x^{2}-3 x +1\right) \left(2 x -1\right)^{2} \left(x -1\right)^{5}}
Generating function in sympy syntax:
(-7*x**8 + 48*x**7 - 140*x**6 + 223*x**5 - 220*x**4 + 137*x**3 - 52*x**2 + 11*x - 1)/((x - 1)**5*(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)^5*F(x)+7*x^8-48*x^7+140*x^6-223*x^5+220*x^4-137*x^3+52*x^2-11*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)^{5} F \! \left(x \right)+7 x^{8}-48 x^{7}+140 x^{6}-223 x^{5}+220 x^{4}-137 x^{3}+52 x^{2}-11 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)-1/24*n*(n^3+2*n^2+11*n-24*2^(-1+n)+10)
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 \left(n^{3}+2 n^{2}+11 n -24 \,2^{-1+n}+10\right)}{24}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 64
a(6) = 190
a(7) = 527
a(8) = 1388
a(n+4) = -4*a(n)+16*a(n+1)-17*a(n+2)+7*a(n+3)+1/24*n*(n+1)*(n^2-3*n-22), n >= 9
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) = 20
a \! \left(5\right) = 64
a \! \left(6\right) = 190
a \! \left(7\right) = 527
a \! \left(8\right) = 1388
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{n \left(n +1\right) \left(n^{2}-3 n -22\right)}{24}, \quad n \geq 9
Specification 1
Strategy pack name: insertion_point_placements
Tree: http://permpal.com/tree/21171/
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[14,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[7,x]
F[14,x] = F[15,x]+F[2,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[4,x]
F[17,x] = F[18,x]+F[97,x]
F[18,x] = F[19,x]+F[45,x]
F[19,x] = F[20,x]+F[7,x]
F[20,x] = F[21,x]+F[7,x]
F[21,x] = F[22,x]+F[23,x]+F[37,x]
F[22,x] = 0
F[23,x] = F[24,x]*F[4,x]
F[24,x] = F[25,x]+F[28,x]
F[25,x] = F[11,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[25,x]*F[4,x]
F[28,x] = F[29,x]+F[35,x]
F[29,x] = F[30,x]
F[30,x] = F[31,x]*F[4,x]
F[31,x] = F[29,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[34,x]*F[4,x]
F[34,x] = F[1,x]+F[32,x]
F[35,x] = F[36,x]
F[36,x] = F[28,x]*F[4,x]
F[37,x] = F[38,x]*F[4,x]
F[38,x] = F[31,x]+F[39,x]
F[39,x] = F[40,x]+F[43,x]
F[40,x] = F[41,x]
F[41,x] = F[4,x]*F[42,x]
F[42,x] = F[32,x]+F[40,x]
F[43,x] = F[44,x]
F[44,x] = F[39,x]*F[4,x]
F[45,x] = F[46,x]+F[56,x]
F[46,x] = F[47,x]+F[54,x]
F[47,x] = F[11,x]*F[48,x]
F[48,x] = F[49,x]
F[49,x] = F[4,x]*F[50,x]
F[50,x] = F[51,x]+F[53,x]
F[51,x] = F[1,x]+F[52,x]
F[52,x] = F[48,x]
F[53,x] = F[34,x]*F[48,x]
F[54,x] = F[32,x]*F[55,x]
F[55,x] = F[30,x]
F[56,x] = F[15,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[10,x]*F[4,x]*F[59,x]
F[59,x] = F[60,x]+F[81,x]
F[60,x] = F[61,x]+F[75,x]
F[61,x] = F[62,x]
F[62,x] = F[4,x]*F[63,x]
F[63,x] = F[64,x]+F[68,x]
F[64,x] = F[65,x]+F[67,x]
F[65,x] = F[32,x]*F[66,x]
F[66,x] = F[1,x]+F[4,x]
F[67,x] = F[32,x]*F[34,x]
F[68,x] = F[60,x]+F[69,x]
F[69,x] = F[32,x]*F[70,x]
F[70,x] = F[32,x]+F[71,x]
F[71,x] = F[22,x]+F[72,x]+F[74,x]
F[72,x] = F[4,x]*F[73,x]
F[73,x] = F[4,x]+F[71,x]
F[74,x] = F[32,x]*F[4,x]
F[75,x] = F[32,x]*F[76,x]
F[76,x] = F[22,x]+F[77,x]+F[79,x]
F[77,x] = F[4,x]*F[78,x]
F[78,x] = F[32,x]+F[76,x]
F[79,x] = F[4,x]*F[80,x]
F[80,x] = F[32,x]+F[76,x]
F[81,x] = F[82,x]+F[92,x]
F[82,x] = F[83,x]
F[83,x] = F[4,x]*F[84,x]
F[84,x] = F[85,x]+F[90,x]
F[85,x] = F[32,x]+F[86,x]
F[86,x] = F[22,x]+F[87,x]+F[89,x]
F[87,x] = F[4,x]*F[88,x]
F[88,x] = F[11,x]+F[86,x]
F[89,x] = F[4,x]*F[85,x]
F[90,x] = F[48,x]*F[91,x]
F[91,x] = F[10,x]+F[85,x]
F[92,x] = F[93,x]
F[93,x] = F[4,x]*F[94,x]
F[94,x] = F[95,x]+F[96,x]
F[95,x] = F[32,x]*F[85,x]
F[96,x] = F[61,x]*F[91,x]
F[97,x] = F[101,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]+F[47,x]
F[100,x] = F[32,x]^2*F[10,x]
F[101,x] = F[102,x]+F[104,x]
F[102,x] = F[103,x]
F[103,x] = F[11,x]*F[32,x]*F[48,x]
F[104,x] = F[105,x]+F[113,x]
F[105,x] = F[106,x]
F[106,x] = F[107,x]*F[32,x]*F[34,x]*F[4,x]
F[107,x] = F[108,x]+F[32,x]
F[108,x] = F[109,x]+F[32,x]
F[109,x] = F[110,x]+F[112,x]+F[22,x]
F[110,x] = F[111,x]*F[4,x]
F[111,x] = F[109,x]+F[32,x]
F[112,x] = F[108,x]*F[4,x]
F[113,x] = F[114,x]
F[114,x] = F[32,x]^3*F[11,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_{14}\! \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_{7}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{2}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
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_{97}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{45}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{7}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{7}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)+F_{23}\! \left(x \right)+F_{37}\! \left(x \right)
F_{22}\! \left(x \right) = 0
F_{23}\! \left(x \right) = F_{24}\! \left(x \right) F_{4}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{25}\! \left(x \right) = F_{11}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{25}\! \left(x \right) F_{4}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{35}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right) F_{4}\! \left(x \right)
F_{31}\! \left(x \right) = F_{29}\! \left(x \right)+F_{32}\! \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_{1}\! \left(x \right)+F_{32}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{28}\! \left(x \right) F_{4}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{4}\! \left(x \right)
F_{38}\! \left(x \right) = F_{31}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{43}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{4}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{32}\! \left(x \right)+F_{40}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{39}\! \left(x \right) F_{4}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{56}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{54}\! \left(x \right)
F_{47}\! \left(x \right) = F_{11}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{4}\! \left(x \right) F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right)+F_{53}\! \left(x \right)
F_{51}\! \left(x \right) = F_{1}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{48}\! \left(x \right)
F_{53}\! \left(x \right) = F_{34}\! \left(x \right) F_{48}\! \left(x \right)
F_{54}\! \left(x \right) = F_{32}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{30}\! \left(x \right)
F_{56}\! \left(x \right) = F_{15}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{10}\! \left(x \right) F_{4}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{81}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right)+F_{75}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{4}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right)+F_{68}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{65}\! \left(x \right) = F_{32}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)
F_{67}\! \left(x \right) = F_{32}\! \left(x \right) F_{34}\! \left(x \right)
F_{68}\! \left(x \right) = F_{60}\! \left(x \right)+F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{32}\! \left(x \right) F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{32}\! \left(x \right)+F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{22}\! \left(x \right)+F_{72}\! \left(x \right)+F_{74}\! \left(x \right)
F_{72}\! \left(x \right) = F_{4}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{4}\! \left(x \right)+F_{71}\! \left(x \right)
F_{74}\! \left(x \right) = F_{32}\! \left(x \right) F_{4}\! \left(x \right)
F_{75}\! \left(x \right) = F_{32}\! \left(x \right) F_{76}\! \left(x \right)
F_{76}\! \left(x \right) = F_{22}\! \left(x \right)+F_{77}\! \left(x \right)+F_{79}\! \left(x \right)
F_{77}\! \left(x \right) = F_{4}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{32}\! \left(x \right)+F_{76}\! \left(x \right)
F_{79}\! \left(x \right) = F_{4}\! \left(x \right) F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{32}\! \left(x \right)+F_{76}\! \left(x \right)
F_{81}\! \left(x \right) = F_{82}\! \left(x \right)+F_{92}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{4}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{90}\! \left(x \right)
F_{85}\! \left(x \right) = F_{32}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{22}\! \left(x \right)+F_{87}\! \left(x \right)+F_{89}\! \left(x \right)
F_{87}\! \left(x \right) = F_{4}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{11}\! \left(x \right)+F_{86}\! \left(x \right)
F_{89}\! \left(x \right) = F_{4}\! \left(x \right) F_{85}\! \left(x \right)
F_{90}\! \left(x \right) = F_{48}\! \left(x \right) F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = F_{10}\! \left(x \right)+F_{85}\! \left(x \right)
F_{92}\! \left(x \right) = F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{4}\! \left(x \right) F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{95}\! \left(x \right)+F_{96}\! \left(x \right)
F_{95}\! \left(x \right) = F_{32}\! \left(x \right) F_{85}\! \left(x \right)
F_{96}\! \left(x \right) = F_{61}\! \left(x \right) F_{91}\! \left(x \right)
F_{97}\! \left(x \right) = F_{101}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{47}\! \left(x \right)
F_{100}\! \left(x \right) = F_{32} \left(x \right)^{2} F_{10}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{104}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{11}\! \left(x \right) F_{32}\! \left(x \right) F_{48}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{113}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{32}\! \left(x \right) F_{34}\! \left(x \right) F_{4}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)+F_{32}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right)+F_{32}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{112}\! \left(x \right)+F_{22}\! \left(x \right)
F_{110}\! \left(x \right) = F_{111}\! \left(x \right) F_{4}\! \left(x \right)
F_{111}\! \left(x \right) = F_{109}\! \left(x \right)+F_{32}\! \left(x \right)
F_{112}\! \left(x \right) = F_{108}\! \left(x \right) F_{4}\! \left(x \right)
F_{113}\! \left(x \right) = F_{114}\! \left(x \right)
F_{114}\! \left(x \right) = F_{32} \left(x \right)^{3} F_{11}\! \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_14(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_7(x))
Eq(F_14(x), F_15(x) + F_2(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_4(x))
Eq(F_17(x), F_18(x) + F_97(x))
Eq(F_18(x), F_19(x) + F_45(x))
Eq(F_19(x), F_20(x) + F_7(x))
Eq(F_20(x), F_21(x) + F_7(x))
Eq(F_21(x), F_22(x) + F_23(x) + F_37(x))
Eq(F_22(x), 0)
Eq(F_23(x), F_24(x)*F_4(x))
Eq(F_24(x), F_25(x) + F_28(x))
Eq(F_25(x), F_11(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_25(x)*F_4(x))
Eq(F_28(x), F_29(x) + F_35(x))
Eq(F_29(x), F_30(x))
Eq(F_30(x), F_31(x)*F_4(x))
Eq(F_31(x), F_29(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_34(x)*F_4(x))
Eq(F_34(x), F_1(x) + F_32(x))
Eq(F_35(x), F_36(x))
Eq(F_36(x), F_28(x)*F_4(x))
Eq(F_37(x), F_38(x)*F_4(x))
Eq(F_38(x), F_31(x) + F_39(x))
Eq(F_39(x), F_40(x) + F_43(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_4(x)*F_42(x))
Eq(F_42(x), F_32(x) + F_40(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_39(x)*F_4(x))
Eq(F_45(x), F_46(x) + F_56(x))
Eq(F_46(x), F_47(x) + F_54(x))
Eq(F_47(x), F_11(x)*F_48(x))
Eq(F_48(x), F_49(x))
Eq(F_49(x), F_4(x)*F_50(x))
Eq(F_50(x), F_51(x) + F_53(x))
Eq(F_51(x), F_1(x) + F_52(x))
Eq(F_52(x), F_48(x))
Eq(F_53(x), F_34(x)*F_48(x))
Eq(F_54(x), F_32(x)*F_55(x))
Eq(F_55(x), F_30(x))
Eq(F_56(x), F_15(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_10(x)*F_4(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_81(x))
Eq(F_60(x), F_61(x) + F_75(x))
Eq(F_61(x), F_62(x))
Eq(F_62(x), F_4(x)*F_63(x))
Eq(F_63(x), F_64(x) + F_68(x))
Eq(F_64(x), F_65(x) + F_67(x))
Eq(F_65(x), F_32(x)*F_66(x))
Eq(F_66(x), F_1(x) + F_4(x))
Eq(F_67(x), F_32(x)*F_34(x))
Eq(F_68(x), F_60(x) + F_69(x))
Eq(F_69(x), F_32(x)*F_70(x))
Eq(F_70(x), F_32(x) + F_71(x))
Eq(F_71(x), F_22(x) + F_72(x) + F_74(x))
Eq(F_72(x), F_4(x)*F_73(x))
Eq(F_73(x), F_4(x) + F_71(x))
Eq(F_74(x), F_32(x)*F_4(x))
Eq(F_75(x), F_32(x)*F_76(x))
Eq(F_76(x), F_22(x) + F_77(x) + F_79(x))
Eq(F_77(x), F_4(x)*F_78(x))
Eq(F_78(x), F_32(x) + F_76(x))
Eq(F_79(x), F_4(x)*F_80(x))
Eq(F_80(x), F_32(x) + F_76(x))
Eq(F_81(x), F_82(x) + F_92(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_4(x)*F_84(x))
Eq(F_84(x), F_85(x) + F_90(x))
Eq(F_85(x), F_32(x) + F_86(x))
Eq(F_86(x), F_22(x) + F_87(x) + F_89(x))
Eq(F_87(x), F_4(x)*F_88(x))
Eq(F_88(x), F_11(x) + F_86(x))
Eq(F_89(x), F_4(x)*F_85(x))
Eq(F_90(x), F_48(x)*F_91(x))
Eq(F_91(x), F_10(x) + F_85(x))
Eq(F_92(x), F_93(x))
Eq(F_93(x), F_4(x)*F_94(x))
Eq(F_94(x), F_95(x) + F_96(x))
Eq(F_95(x), F_32(x)*F_85(x))
Eq(F_96(x), F_61(x)*F_91(x))
Eq(F_97(x), F_101(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x) + F_47(x))
Eq(F_100(x), F_10(x)*F_32(x)**2)
Eq(F_101(x), F_102(x) + F_104(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_11(x)*F_32(x)*F_48(x))
Eq(F_104(x), F_105(x) + F_113(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_107(x)*F_32(x)*F_34(x)*F_4(x))
Eq(F_107(x), F_108(x) + F_32(x))
Eq(F_108(x), F_109(x) + F_32(x))
Eq(F_109(x), F_110(x) + F_112(x) + F_22(x))
Eq(F_110(x), F_111(x)*F_4(x))
Eq(F_111(x), F_109(x) + F_32(x))
Eq(F_112(x), F_108(x)*F_4(x))
Eq(F_113(x), F_114(x))
Eq(F_114(x), F_11(x)*F_32(x)**3)
Pack JSON:
{"expansion_strats": [[{"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_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": [0, 2, 3, 1], "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": [0, 2, 3, 1], "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": [0, 2, 3, 1], "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], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 2, 1], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 0, 2], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 2], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[1, 0], [1, 0], [1, 2], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 0], [1, 0], [1, 2]]}, {"patt": [0, 2, 1, 3], "pos": [[1, 0], [1, 2], [1, 0], [1, 2]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 2], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 2], [1, 2], [1, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[1, 0], [1, 0], [1, 0], [1, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1]], [[1, 0], [1, 2]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"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]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 1], [0, 1], [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, 2, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 1], [0, 0], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 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