0132_0213_1203_3120
Counting sequence:
1, 1, 2, 6, 20, 64, 190, 521, 1329, 3191, 7304, 16128, 34710, 73426, 153678, 319747, 663459, 1375489, 2851976, 5915842, 12275696, 25476276, 52864718, 109653997, 227311765, 470862107, 974537400, 2015178932, 4163232170, 8593125606, 17720805342, 36512358343, 75168367431, 154626838597, 317837490648, 652847204950, 1340044666244, 2748797127400, 5635018905662, 11544898309137, 23639531358329, 48378548966911, 98956090779304, 202310191798568, 413416433548350, 844425002209850, 1724034316522670, 3518437306841163, 7177612019757291, 14636698920367561, 29836347682850280, 60798595143707818, 123848989952427672, 252201579361158748, 513410357780773358, 1044835113846411253, 2125699024455408989, 4323455642656842531, 8791026473057981528, 17870283321891937372, 36317027395662439762, 73786976295452352206, 149879795599578629310, 304371277216978085519, 617965926470130642575, 1254378597013209246093, 2545650682172986543800, 5165088340639861934014, 10477750633868343048492, 21250649172914863491856, 43091594156187127869918, 87363779933090220947353, 177088743107613664167233, 358899852698095205100679, 727244438361927749169608, 1473378342655331928741456, 2984535617173618652619494, 6044629098073149027627682, 12240373923598123846991374, 24782979302099901857523347, 50170421514007114874847795, 101549768847628855175554961, 205517389334486964604926536, 415870481947432441439221650, 841412370451781911403922240, 1702167554017397884297573636, 3443020734262463896414168590, 6963412720980264053737324285, 14081567946871200635027457573, 28472620903563746331393781291, 57564211826770182792233592056, 116366363692825745850701439748, 235208607464222252241828657914, 475368975085586025573124811190, 960641470485455093334505367198, 1941089981599476271055596598359, 3921794044456084710895244505559, 7922816251426433759370330909653, 16004088827881396193913002127000, 32325090305819849738184319309862, 65284005911753814177099945110228
Generating function in Maple syntax:
(2*x^10-16*x^9+62*x^8-159*x^7+286*x^6-346*x^5+282*x^4-154*x^3+54*x^2-11*x+1)/(2*x-1)^2/(x-1)^8
Generating function in latex syntax:
\frac{2 x^{10}-16 x^{9}+62 x^{8}-159 x^{7}+286 x^{6}-346 x^{5}+282 x^{4}-154 x^{3}+54 x^{2}-11 x +1}{\left(2 x -1\right)^{2} \left(x -1\right)^{8}}
Generating function in sympy syntax:
(2*x**10 - 16*x**9 + 62*x**8 - 159*x**7 + 286*x**6 - 346*x**5 + 282*x**4 - 154*x**3 + 54*x**2 - 11*x + 1)/((x - 1)**8*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^2*(x-1)^8*F(x)-2*x^10+16*x^9-62*x^8+159*x^7-286*x^6+346*x^5-282*x^4+154*x^3-54*x^2+11*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{2} \left(x -1\right)^{8} F \! \left(x \right)-2 x^{10}+16 x^{9}-62 x^{8}+159 x^{7}-286 x^{6}+346 x^{5}-282 x^{4}+154 x^{3}-54 x^{2}+11 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(n = 0,1,-1-367/420*n+3*2^(-1+n)-83/720*n^3+1/5040*n^7-1/90*n^5-n^2+2^(-1+n)*n)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0 \\ -1-\frac{367 n}{420}+3 \,2^{-1+n}-\frac{83 n^{3}}{720}+\frac{n^{7}}{5040}-\frac{n^{5}}{90}-n^{2}+2^{-1+n} n & \mathit{\text{otherwise}} \end{array}\right.
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) = 521
a(8) = 1329
a(9) = 3191
a(10) = 7304
a(n+2) = -4*a(n)+4*a(n+1)+1/5040*n*(n^6-14*n^5-56*n^4+700*n^3-161*n^2-3206*n+12816), n >= 11
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) = 521
a \! \left(8\right) = 1329
a \! \left(9\right) = 3191
a \! \left(10\right) = 7304
a \! \left(n +2\right) = -4 a \! \left(n \right)+4 a \! \left(n +1\right)+\frac{n \left(n^{6}-14 n^{5}-56 n^{4}+700 n^{3}-161 n^{2}-3206 n +12816\right)}{5040}, \quad n \geq 11
Specification 1
Strategy pack name: point_placements
Tree: http://permpal.com/tree/15274/
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[20,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[18,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[16,x]
F[16,x] = F[17,x]+F[9,x]
F[17,x] = F[14,x]
F[18,x] = F[19,x]
F[19,x] = F[12,x]*F[13,x]
F[20,x] = F[21,x]+F[31,x]
F[21,x] = F[22,x]
F[22,x] = F[12,x]*F[23,x]
F[23,x] = F[24,x]+F[25,x]
F[24,x] = F[1,x]+F[14,x]
F[25,x] = F[21,x]+F[26,x]
F[26,x] = F[27,x]
F[27,x] = F[12,x]*F[28,x]
F[28,x] = F[29,x]+F[30,x]
F[29,x] = F[14,x]
F[30,x] = F[26,x]
F[31,x] = F[32,x]+F[33,x]+F[89,x]
F[32,x] = 0
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[35,x]+F[46,x]
F[35,x] = F[36,x]+F[6,x]
F[36,x] = F[37,x]
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[13,x]+F[39,x]
F[39,x] = F[40,x]+F[44,x]
F[40,x] = F[41,x]
F[41,x] = F[12,x]*F[42,x]
F[42,x] = F[17,x]+F[43,x]
F[43,x] = F[40,x]
F[44,x] = F[45,x]
F[45,x] = F[12,x]*F[39,x]
F[46,x] = F[31,x]+F[47,x]
F[47,x] = 2*F[32,x]+F[48,x]+F[52,x]
F[48,x] = F[12,x]*F[49,x]
F[49,x] = F[50,x]+F[51,x]
F[50,x] = F[36,x]
F[51,x] = F[47,x]
F[52,x] = F[12,x]*F[53,x]
F[53,x] = F[54,x]+F[61,x]
F[54,x] = F[26,x]+F[55,x]
F[55,x] = 2*F[32,x]+F[56,x]+F[60,x]
F[56,x] = F[12,x]*F[57,x]
F[57,x] = F[58,x]+F[59,x]
F[58,x] = F[18,x]
F[59,x] = F[55,x]
F[60,x] = F[12,x]*F[54,x]
F[61,x] = F[62,x]+F[76,x]
F[62,x] = 2*F[32,x]+F[63,x]+F[72,x]
F[63,x] = F[12,x]*F[64,x]
F[64,x] = F[65,x]+F[66,x]
F[65,x] = F[40,x]
F[66,x] = F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[12,x]*F[69,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[40,x]
F[71,x] = F[67,x]
F[72,x] = F[12,x]*F[73,x]
F[73,x] = F[74,x]+F[75,x]
F[74,x] = F[26,x]
F[75,x] = F[62,x]
F[76,x] = 3*F[32,x]+F[77,x]+F[88,x]
F[77,x] = F[12,x]*F[78,x]
F[78,x] = F[79,x]+F[80,x]
F[79,x] = F[44,x]
F[80,x] = F[81,x]
F[81,x] = 3*F[32,x]+F[82,x]+F[86,x]
F[82,x] = F[12,x]*F[83,x]
F[83,x] = F[84,x]+F[85,x]
F[84,x] = F[44,x]
F[85,x] = F[81,x]
F[86,x] = F[12,x]*F[87,x]
F[87,x] = F[67,x]+F[81,x]
F[88,x] = F[12,x]*F[61,x]
F[89,x] = F[12,x]*F[90,x]
F[90,x] = F[91,x]+F[98,x]
F[91,x] = F[21,x]+F[92,x]
F[92,x] = F[32,x]+F[93,x]+F[97,x]
F[93,x] = F[12,x]*F[94,x]
F[94,x] = F[95,x]+F[96,x]
F[95,x] = F[10,x]+F[18,x]
F[96,x] = F[55,x]+F[92,x]
F[97,x] = F[12,x]*F[91,x]
F[98,x] = F[113,x]+F[99,x]
F[99,x] = F[100,x]+F[104,x]+F[32,x]
F[100,x] = F[101,x]*F[12,x]
F[101,x] = F[102,x]+F[103,x]
F[102,x] = F[14,x]+F[40,x]
F[103,x] = F[26,x]+F[67,x]
F[104,x] = F[105,x]*F[12,x]
F[105,x] = F[106,x]+F[112,x]
F[106,x] = F[107,x]+F[21,x]
F[107,x] = F[108,x]
F[108,x] = F[109,x]*F[12,x]
F[109,x] = F[110,x]+F[111,x]
F[110,x] = F[10,x]
F[111,x] = F[107,x]
F[112,x] = F[99,x]
F[113,x] = 2*F[32,x]+F[114,x]+F[118,x]
F[114,x] = F[115,x]*F[12,x]
F[115,x] = F[116,x]+F[117,x]
F[116,x] = F[18,x]+F[44,x]
F[117,x] = F[55,x]+F[81,x]
F[118,x] = F[12,x]*F[98,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_{20}\! \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_{18}\! \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_{17}\! \left(x \right)+F_{9}\! \left(x \right)
F_{17}\! \left(x \right) = F_{14}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{31}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{12}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)
F_{24}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{25}\! \left(x \right) = F_{21}\! \left(x \right)+F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{12}\! \left(x \right) F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)+F_{30}\! \left(x \right)
F_{29}\! \left(x \right) = F_{14}\! \left(x \right)
F_{30}\! \left(x \right) = F_{26}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{33}\! \left(x \right)+F_{89}\! \left(x \right)
F_{32}\! \left(x \right) = 0
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_{46}\! \left(x \right)
F_{35}\! \left(x \right) = F_{36}\! \left(x \right)+F_{6}\! \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_{13}\! \left(x \right)+F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{44}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{12}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{17}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{40}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{12}\! \left(x \right) F_{39}\! \left(x \right)
F_{46}\! \left(x \right) = F_{31}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{48}\! \left(x \right)+F_{52}\! \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_{51}\! \left(x \right)
F_{50}\! \left(x \right) = F_{36}\! \left(x \right)
F_{51}\! \left(x \right) = F_{47}\! \left(x \right)
F_{52}\! \left(x \right) = F_{12}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{61}\! \left(x \right)
F_{54}\! \left(x \right) = F_{26}\! \left(x \right)+F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{56}\! \left(x \right)+F_{60}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)+F_{59}\! \left(x \right)
F_{58}\! \left(x \right) = F_{18}\! \left(x \right)
F_{59}\! \left(x \right) = F_{55}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{76}\! \left(x \right)
F_{62}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{63}\! \left(x \right)+F_{72}\! \left(x \right)
F_{63}\! \left(x \right) = F_{12}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{66}\! \left(x \right)
F_{65}\! \left(x \right) = F_{40}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{40}\! \left(x \right)
F_{71}\! \left(x \right) = F_{67}\! \left(x \right)
F_{72}\! \left(x \right) = F_{12}\! \left(x \right) F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{75}\! \left(x \right)
F_{74}\! \left(x \right) = F_{26}\! \left(x \right)
F_{75}\! \left(x \right) = F_{62}\! \left(x \right)
F_{76}\! \left(x \right) = 3 F_{32}\! \left(x \right)+F_{77}\! \left(x \right)+F_{88}\! \left(x \right)
F_{77}\! \left(x \right) = F_{12}\! \left(x \right) F_{78}\! \left(x \right)
F_{78}\! \left(x \right) = F_{79}\! \left(x \right)+F_{80}\! \left(x \right)
F_{79}\! \left(x \right) = F_{44}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = 3 F_{32}\! \left(x \right)+F_{82}\! \left(x \right)+F_{86}\! \left(x \right)
F_{82}\! \left(x \right) = F_{12}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{85}\! \left(x \right)
F_{84}\! \left(x \right) = F_{44}\! \left(x \right)
F_{85}\! \left(x \right) = F_{81}\! \left(x \right)
F_{86}\! \left(x \right) = F_{12}\! \left(x \right) F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{67}\! \left(x \right)+F_{81}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{89}\! \left(x \right) = F_{12}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{91}\! \left(x \right)+F_{98}\! \left(x \right)
F_{91}\! \left(x \right) = F_{21}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{32}\! \left(x \right)+F_{93}\! \left(x \right)+F_{97}\! \left(x \right)
F_{93}\! \left(x \right) = F_{12}\! \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_{10}\! \left(x \right)+F_{18}\! \left(x \right)
F_{96}\! \left(x \right) = F_{55}\! \left(x \right)+F_{92}\! \left(x \right)
F_{97}\! \left(x \right) = F_{12}\! \left(x \right) F_{91}\! \left(x \right)
F_{98}\! \left(x \right) = F_{113}\! \left(x \right)+F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)+F_{104}\! \left(x \right)+F_{32}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{12}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{103}\! \left(x \right)
F_{102}\! \left(x \right) = F_{14}\! \left(x \right)+F_{40}\! \left(x \right)
F_{103}\! \left(x \right) = F_{26}\! \left(x \right)+F_{67}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{12}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)+F_{112}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right)+F_{21}\! \left(x \right)
F_{107}\! \left(x \right) = F_{108}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{12}\! \left(x \right)
F_{109}\! \left(x \right) = F_{110}\! \left(x \right)+F_{111}\! \left(x \right)
F_{110}\! \left(x \right) = F_{10}\! \left(x \right)
F_{111}\! \left(x \right) = F_{107}\! \left(x \right)
F_{112}\! \left(x \right) = F_{99}\! \left(x \right)
F_{113}\! \left(x \right) = 2 F_{32}\! \left(x \right)+F_{114}\! \left(x \right)+F_{118}\! \left(x \right)
F_{114}\! \left(x \right) = F_{115}\! \left(x \right) F_{12}\! \left(x \right)
F_{115}\! \left(x \right) = F_{116}\! \left(x \right)+F_{117}\! \left(x \right)
F_{116}\! \left(x \right) = F_{18}\! \left(x \right)+F_{44}\! \left(x \right)
F_{117}\! \left(x \right) = F_{55}\! \left(x \right)+F_{81}\! \left(x \right)
F_{118}\! \left(x \right) = F_{12}\! \left(x \right) F_{98}\! \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_20(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_18(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_9(x))
Eq(F_17(x), F_14(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_12(x)*F_13(x))
Eq(F_20(x), F_21(x) + F_31(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_12(x)*F_23(x))
Eq(F_23(x), F_24(x) + F_25(x))
Eq(F_24(x), F_1(x) + F_14(x))
Eq(F_25(x), F_21(x) + F_26(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_12(x)*F_28(x))
Eq(F_28(x), F_29(x) + F_30(x))
Eq(F_29(x), F_14(x))
Eq(F_30(x), F_26(x))
Eq(F_31(x), F_32(x) + F_33(x) + F_89(x))
Eq(F_32(x), 0)
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_35(x) + F_46(x))
Eq(F_35(x), F_36(x) + F_6(x))
Eq(F_36(x), F_37(x))
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_13(x) + F_39(x))
Eq(F_39(x), F_40(x) + F_44(x))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_12(x)*F_42(x))
Eq(F_42(x), F_17(x) + F_43(x))
Eq(F_43(x), F_40(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_12(x)*F_39(x))
Eq(F_46(x), F_31(x) + F_47(x))
Eq(F_47(x), 2*F_32(x) + F_48(x) + F_52(x))
Eq(F_48(x), F_12(x)*F_49(x))
Eq(F_49(x), F_50(x) + F_51(x))
Eq(F_50(x), F_36(x))
Eq(F_51(x), F_47(x))
Eq(F_52(x), F_12(x)*F_53(x))
Eq(F_53(x), F_54(x) + F_61(x))
Eq(F_54(x), F_26(x) + F_55(x))
Eq(F_55(x), 2*F_32(x) + F_56(x) + F_60(x))
Eq(F_56(x), F_12(x)*F_57(x))
Eq(F_57(x), F_58(x) + F_59(x))
Eq(F_58(x), F_18(x))
Eq(F_59(x), F_55(x))
Eq(F_60(x), F_12(x)*F_54(x))
Eq(F_61(x), F_62(x) + F_76(x))
Eq(F_62(x), 2*F_32(x) + F_63(x) + F_72(x))
Eq(F_63(x), F_12(x)*F_64(x))
Eq(F_64(x), F_65(x) + F_66(x))
Eq(F_65(x), F_40(x))
Eq(F_66(x), F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_12(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_40(x))
Eq(F_71(x), F_67(x))
Eq(F_72(x), F_12(x)*F_73(x))
Eq(F_73(x), F_74(x) + F_75(x))
Eq(F_74(x), F_26(x))
Eq(F_75(x), F_62(x))
Eq(F_76(x), 3*F_32(x) + F_77(x) + F_88(x))
Eq(F_77(x), F_12(x)*F_78(x))
Eq(F_78(x), F_79(x) + F_80(x))
Eq(F_79(x), F_44(x))
Eq(F_80(x), F_81(x))
Eq(F_81(x), 3*F_32(x) + F_82(x) + F_86(x))
Eq(F_82(x), F_12(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_85(x))
Eq(F_84(x), F_44(x))
Eq(F_85(x), F_81(x))
Eq(F_86(x), F_12(x)*F_87(x))
Eq(F_87(x), F_67(x) + F_81(x))
Eq(F_88(x), F_12(x)*F_61(x))
Eq(F_89(x), F_12(x)*F_90(x))
Eq(F_90(x), F_91(x) + F_98(x))
Eq(F_91(x), F_21(x) + F_92(x))
Eq(F_92(x), F_32(x) + F_93(x) + F_97(x))
Eq(F_93(x), F_12(x)*F_94(x))
Eq(F_94(x), F_95(x) + F_96(x))
Eq(F_95(x), F_10(x) + F_18(x))
Eq(F_96(x), F_55(x) + F_92(x))
Eq(F_97(x), F_12(x)*F_91(x))
Eq(F_98(x), F_113(x) + F_99(x))
Eq(F_99(x), F_100(x) + F_104(x) + F_32(x))
Eq(F_100(x), F_101(x)*F_12(x))
Eq(F_101(x), F_102(x) + F_103(x))
Eq(F_102(x), F_14(x) + F_40(x))
Eq(F_103(x), F_26(x) + F_67(x))
Eq(F_104(x), F_105(x)*F_12(x))
Eq(F_105(x), F_106(x) + F_112(x))
Eq(F_106(x), F_107(x) + F_21(x))
Eq(F_107(x), F_108(x))
Eq(F_108(x), F_109(x)*F_12(x))
Eq(F_109(x), F_110(x) + F_111(x))
Eq(F_110(x), F_10(x))
Eq(F_111(x), F_107(x))
Eq(F_112(x), F_99(x))
Eq(F_113(x), F_114(x) + F_118(x) + 2*F_32(x))
Eq(F_114(x), F_115(x)*F_12(x))
Eq(F_115(x), F_116(x) + F_117(x))
Eq(F_116(x), F_18(x) + F_44(x))
Eq(F_117(x), F_55(x) + F_81(x))
Eq(F_118(x), F_12(x)*F_98(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, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "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": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0, 3], "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": 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": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"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": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 1], [2, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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": [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], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"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": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "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": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"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": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "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], "pos": [[0, 0]]}], "requirements": []}, {"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": [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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2], "pos": [[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": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"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": [1, 2, 0, 3], "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": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"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": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [1, 0], [1, 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