0132_0213_1203_1230_3012
Counting sequence:
1, 1, 2, 6, 19, 56, 162, 485, 1526, 5018, 17041, 59163, 208586, 743771, 2675764, 9696868, 35360783, 129649618, 477646246, 1767275068, 6564139232, 24466296966, 91482611505, 343059690401, 1289904270694, 4861946600121, 18367353392512, 69533551433105, 263747952585621, 1002242218001234, 3814986504274614, 14544636042755921, 55534064882755982, 212336130421475966, 812944042164667033, 3116285494931465555, 11959798385899548730, 45950804324684996047, 176733862787109043916, 680425371730141389593, 2622127042276760032917, 10113918591638331639036, 39044429911905145379370, 150853479205086486576126, 583300119592998529413100, 2257117854077251044482894, 8740328711533178197588385, 33868773757191054665187661, 131327898242169378064278126, 509552245179617158419637973, 1978261657756160686575074056, 7684785670514316438547128053, 29869166945772626036410010781, 116157871455782434390137731646, 451959718027953471673460967838, 1759414616608818871357915198260, 6852456927844873498140945221800, 26700952856774851905201942967852, 104088460289122304035046327598741, 405944995127576985733148174181465, 1583850964596120042690825518610878, 6182127958584855650493638317572047, 24139737743045626825722068756168732, 94295850558771979787952552626597276, 368479169875816659479036820603623775, 1440418573150919668872534839814121754, 5632681584560312734993988429309438870, 22033725021956517463358670283087458716, 86218923998960285726185831056191867616, 337485502510215975556784101516579847086, 1321422108420282270489942675644241478465, 5175569924646105559418941000510598822757, 20276890389709399862928999873224186013854, 79463489365077377841208239743834346924601, 311496878311103321137536294935263756998624, 1221395654430378811828760727535901831743153, 4790408930363303911328386217339258784886133, 18793142726809884575211361293559879217999258, 73745243611532458459690151878064057587879206, 289450081175264899454283846067379829637615058, 1136359577947336271931632877065973247389307532, 4462290049988320482463241297605328036594495396, 17526585015616776834735140518076156280212689765, 68854441132780194707888052034928342639896420401, 270557451039395118028642463289588762561398865230, 1063353702922273835973036658044156350360742115379, 4180080073556524734514695828172007546207117518420, 16435314834665426797069144960764666122783595214951, 64633260585762914370496637486149061529875906186681, 254224158304000796523953440778846307133157747670296, 1000134600800354781929399250536549404476265836414530, 3935312233584004685417853572763361709934446802021842, 15487357822491889407128326963778362972288150996184164, 60960876535340415751462563580829680832404363897667486, 239993345518077005168915776623476774686989682346686529, 944973797977428207852605870454939680458374248083465253, 3721443204405954385563870541379246795011359042085583038, 14657929356129575437016877846657032980635950785455071373, 57743358069601357782187700608042856688245579804018677976, 227508830794229349661819540395688854529189526615358288093, 896519947090131496687170070074100633348210213731825069997
Generating function in Maple syntax:
1/2*(-(x^2+x-1)*(x-1)^4*(1-4*x)^(1/2)-2*x^8+2*x^7+5*x^6-3*x^5-x^4+6*x^3-9*x^2+5*x-1)/x/(x^2+x-1)/(x-1)^4
Generating function in latex syntax:
\frac{-\left(x^{2}+x -1\right) \left(x -1\right)^{4} \sqrt{1-4 x}-2 x^{8}+2 x^{7}+5 x^{6}-3 x^{5}-x^{4}+6 x^{3}-9 x^{2}+5 x -1}{2 x \left(x^{2}+x -1\right) \left(x -1\right)^{4}}
Generating function in sympy syntax:
(-x**8 + x**7 + 5*x**6/2 - 3*x**5/2 - x**4/2 + 3*x**3 - 9*x**2/2 + 5*x/2 + sqrt(1 - 4*x)*(x - 1)**4*(-x**2 - x + 1)/2 - 1/2)/(x*(x - 1)**4*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
x*(x^2+x-1)^2*(x-1)^8*F(x)^2+(x^2+x-1)*(2*x^8-2*x^7-5*x^6+3*x^5+x^4-6*x^3+9*x^2-5*x+1)*(x-1)^4*F(x)+x^15-2*x^14-4*x^13+9*x^12-2*x^11-2*x^10+18*x^9-52*x^8+64*x^7-11*x^6-85*x^5+134*x^4-101*x^3+43*x^2-10*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(x^{2}+x -1\right)^{2} \left(x -1\right)^{8} F \! \left(x \right)^{2}+\left(x^{2}+x -1\right) \left(2 x^{8}-2 x^{7}-5 x^{6}+3 x^{5}+x^{4}-6 x^{3}+9 x^{2}-5 x +1\right) \left(x -1\right)^{4} F \! \left(x \right)+x^{15}-2 x^{14}-4 x^{13}+9 x^{12}-2 x^{11}-2 x^{10}+18 x^{9}-52 x^{8}+64 x^{7}-11 x^{6}-85 x^{5}+134 x^{4}-101 x^{3}+43 x^{2}-10 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(5) = 56
a(6) = 162
a(7) = 485
a(8) = 1526
a(9) = 5018
a(10) = 17041
a(11) = 59163
a(n+5) = 2*(2*n+1)/(6+n)*a(n)+(7*n+10)/(6+n)*a(1+n)-2*(3*n+8)/(6+n)*a(n+2)-(24+7*n)/(6+n)*a(n+3)+2*(3*n+14)/(6+n)*a(n+4)-1/2*(n^4-12*n^3-11*n^2+120*n+92)/(6+n), n >= 12
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) = 19
a \! \left(5\right) = 56
a \! \left(6\right) = 162
a \! \left(7\right) = 485
a \! \left(8\right) = 1526
a \! \left(9\right) = 5018
a \! \left(10\right) = 17041
a \! \left(11\right) = 59163
a \! \left(n +5\right) = \frac{2 \left(2 n +1\right) a \! \left(n \right)}{6+n}+\frac{\left(7 n +10\right) a \! \left(1+n \right)}{6+n}-\frac{2 \left(3 n +8\right) a \! \left(n +2\right)}{6+n}-\frac{\left(24+7 n \right) a \! \left(n +3\right)}{6+n}+\frac{2 \left(3 n +14\right) a \! \left(n +4\right)}{6+n}-\frac{n^{4}-12 n^{3}-11 n^{2}+120 n +92}{2 \left(6+n \right)}, \quad n \geq 12
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21623/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[12,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[74,x]
F[4,x] = F[12,x]*F[5,x]
F[5,x] = F[30,x]+F[6,x]
F[6,x] = F[16,x]+F[7,x]
F[7,x] = F[1,x]+F[8,x]
F[8,x] = F[9,x]
F[9,x] = F[10,x]*F[12,x]
F[10,x] = F[11,x]+F[13,x]
F[11,x] = F[1,x]+F[12,x]
F[12,x] = x
F[13,x] = F[14,x]+F[8,x]
F[14,x] = F[15,x]
F[15,x] = F[12,x]*F[8,x]
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[18,x]
F[18,x] = F[12,x]*F[19,x]
F[19,x] = F[1,x]+F[17,x]
F[20,x] = F[21,x]
F[21,x] = F[12,x]*F[22,x]
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[12,x]+F[24,x]
F[24,x] = F[25,x]
F[25,x] = x^2
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[21,x]
F[28,x] = F[29,x]
F[29,x] = F[12,x]*F[27,x]
F[30,x] = F[31,x]+F[58,x]
F[31,x] = F[32,x]+F[35,x]
F[32,x] = F[33,x]
F[33,x] = F[12,x]*F[34,x]
F[34,x] = F[1,x]+F[32,x]
F[35,x] = F[36,x]+F[37,x]+F[39,x]
F[36,x] = 0
F[37,x] = F[12,x]*F[38,x]
F[38,x] = F[35,x]+F[8,x]
F[39,x] = F[12,x]*F[40,x]
F[40,x] = F[41,x]+F[45,x]
F[41,x] = F[32,x]+F[42,x]
F[42,x] = F[43,x]
F[43,x] = F[12,x]*F[44,x]
F[44,x] = F[12,x]+F[42,x]
F[45,x] = F[46,x]+F[52,x]
F[46,x] = F[36,x]+F[39,x]+F[47,x]
F[47,x] = F[12,x]*F[48,x]
F[48,x] = F[32,x]+F[49,x]
F[49,x] = F[36,x]+F[47,x]+F[50,x]
F[50,x] = F[12,x]*F[51,x]
F[51,x] = F[32,x]+F[49,x]
F[52,x] = F[53,x]
F[53,x] = F[12,x]*F[54,x]
F[54,x] = F[55,x]+F[57,x]
F[55,x] = F[56,x]
F[56,x] = F[12,x]*F[32,x]
F[57,x] = F[53,x]
F[58,x] = F[59,x]+F[67,x]
F[59,x] = F[36,x]+F[60,x]+F[62,x]
F[60,x] = F[12,x]*F[61,x]
F[61,x] = F[17,x]+F[59,x]
F[62,x] = F[12,x]*F[63,x]
F[63,x] = F[32,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[12,x]*F[66,x]
F[66,x] = F[17,x]+F[64,x]
F[67,x] = 2*F[36,x]+F[68,x]+F[70,x]
F[68,x] = F[12,x]*F[69,x]
F[69,x] = F[20,x]+F[67,x]
F[70,x] = F[12,x]*F[71,x]
F[71,x] = F[72,x]+F[73,x]
F[72,x] = F[55,x]
F[73,x] = F[70,x]
F[74,x] = F[12,x]*F[75,x]
F[75,x] = F[76,x,1]
F[76,x,k[0]] = F[1,x]+F[100,x,k[0]]+F[77,x,k[0]]+F[98,x,k[0]]
F[77,x,k[0]] = F[12,x]*F[78,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]+F[87,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]+F[84,x,k[0]]
F[80,x,k[0]] = F[1,x]+F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]
F[82,x,k[0]] = F[80,x,k[0]]*F[83,x,k[0]]
F[83,x,k[0]] = k[0]*x
F[84,x,k[0]] = F[32,x]+F[85,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[83,x,k[0]]*F[84,x,k[0]]
F[87,x,k[0]] = F[88,x,k[0]]+F[93,x,k[0]]
F[88,x,k[0]] = F[32,x]+F[89,x,k[0]]
F[89,x,k[0]] = F[36,x]+F[90,x,k[0]]+F[92,x,k[0]]
F[90,x,k[0]] = F[12,x]*F[91,x,k[0]]
F[91,x,k[0]] = F[81,x,k[0]]+F[89,x,k[0]]
F[92,x,k[0]] = F[83,x,k[0]]*F[88,x,k[0]]
F[93,x,k[0]] = F[49,x]+F[94,x,k[0]]
F[94,x,k[0]] = 2*F[36,x]+F[95,x,k[0]]+F[97,x,k[0]]
F[95,x,k[0]] = F[12,x]*F[96,x,k[0]]
F[96,x,k[0]] = F[85,x,k[0]]+F[94,x,k[0]]
F[97,x,k[0]] = F[83,x,k[0]]*F[93,x,k[0]]
F[98,x,k[0]] = F[12,x]*F[99,x,k[0]]
F[99,x,k[0]] = 1/(-1+k[0])*(F[76,x,k[0]]*k[0]-F[76,x,1])
F[100,x,k[0]] = F[76,x,k[0]]*F[83,x,k[0]]
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_{12}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{74}\! \left(x \right)
F_{4}\! \left(x \right) = F_{12}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{30}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{16}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{1}\! \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_{12}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{13}\! \left(x \right)
F_{11}\! \left(x \right) = F_{1}\! \left(x \right)+F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = x
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{8}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{12}\! \left(x \right) F_{8}\! \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_{12}\! \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_{12}\! \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_{12}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = x^{2}
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{21}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{12}\! \left(x \right) F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)+F_{58}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{35}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{12}\! \left(x \right) F_{34}\! \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_{37}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = 0
F_{37}\! \left(x \right) = F_{12}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{35}\! \left(x \right)+F_{8}\! \left(x \right)
F_{39}\! \left(x \right) = F_{12}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)+F_{45}\! \left(x \right)
F_{41}\! \left(x \right) = F_{32}\! \left(x \right)+F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{12}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{12}\! \left(x \right)+F_{42}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{52}\! \left(x \right)
F_{46}\! \left(x \right) = F_{36}\! \left(x \right)+F_{39}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = F_{12}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{32}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{36}\! \left(x \right)+F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{12}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{32}\! \left(x \right)+F_{49}\! \left(x \right)
F_{52}\! \left(x \right) = F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{12}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{12}\! \left(x \right) F_{32}\! \left(x \right)
F_{57}\! \left(x \right) = F_{53}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)+F_{67}\! \left(x \right)
F_{59}\! \left(x \right) = F_{36}\! \left(x \right)+F_{60}\! \left(x \right)+F_{62}\! \left(x \right)
F_{60}\! \left(x \right) = F_{12}\! \left(x \right) F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{17}\! \left(x \right)+F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = F_{12}\! \left(x \right) F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{32}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{12}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{17}\! \left(x \right)+F_{64}\! \left(x \right)
F_{67}\! \left(x \right) = 2 F_{36}\! \left(x \right)+F_{68}\! \left(x \right)+F_{70}\! \left(x \right)
F_{68}\! \left(x \right) = F_{12}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{20}\! \left(x \right)+F_{67}\! \left(x \right)
F_{70}\! \left(x \right) = F_{12}\! \left(x \right) F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)+F_{73}\! \left(x \right)
F_{72}\! \left(x \right) = F_{55}\! \left(x \right)
F_{73}\! \left(x \right) = F_{70}\! \left(x \right)
F_{74}\! \left(x \right) = F_{12}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x , 1\right)
F_{76}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{100}\! \left(x , y\right)+F_{77}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)+F_{87}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)+F_{84}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{80}\! \left(x , y\right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = y x
F_{84}\! \left(x , y\right) = F_{32}\! \left(x \right)+F_{85}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{83}\! \left(x , y\right) F_{84}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{88}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{32}\! \left(x \right)+F_{89}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{36}\! \left(x \right)+F_{90}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{81}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{83}\! \left(x , y\right) F_{88}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{49}\! \left(x \right)+F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = 2 F_{36}\! \left(x \right)+F_{95}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{85}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{83}\! \left(x , y\right) F_{93}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{12}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = \frac{F_{76}\! \left(x , y\right) y -F_{76}\! \left(x , 1\right)}{-1+y}
F_{100}\! \left(x , y\right) = F_{76}\! \left(x , y\right) F_{83}\! \left(x , y\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_12(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_74(x))
Eq(F_4(x), F_12(x)*F_5(x))
Eq(F_5(x), F_30(x) + F_6(x))
Eq(F_6(x), F_16(x) + F_7(x))
Eq(F_7(x), F_1(x) + F_8(x))
Eq(F_8(x), F_9(x))
Eq(F_9(x), F_10(x)*F_12(x))
Eq(F_10(x), F_11(x) + F_13(x))
Eq(F_11(x), F_1(x) + F_12(x))
Eq(F_12(x), x)
Eq(F_13(x), F_14(x) + F_8(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_12(x)*F_8(x))
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_12(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_12(x)*F_22(x))
Eq(F_22(x), F_23(x) + F_26(x))
Eq(F_23(x), F_12(x) + F_24(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), x**2)
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_21(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_12(x)*F_27(x))
Eq(F_30(x), F_31(x) + F_58(x))
Eq(F_31(x), F_32(x) + F_35(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_12(x)*F_34(x))
Eq(F_34(x), F_1(x) + F_32(x))
Eq(F_35(x), F_36(x) + F_37(x) + F_39(x))
Eq(F_36(x), 0)
Eq(F_37(x), F_12(x)*F_38(x))
Eq(F_38(x), F_35(x) + F_8(x))
Eq(F_39(x), F_12(x)*F_40(x))
Eq(F_40(x), F_41(x) + F_45(x))
Eq(F_41(x), F_32(x) + F_42(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_12(x)*F_44(x))
Eq(F_44(x), F_12(x) + F_42(x))
Eq(F_45(x), F_46(x) + F_52(x))
Eq(F_46(x), F_36(x) + F_39(x) + F_47(x))
Eq(F_47(x), F_12(x)*F_48(x))
Eq(F_48(x), F_32(x) + F_49(x))
Eq(F_49(x), F_36(x) + F_47(x) + F_50(x))
Eq(F_50(x), F_12(x)*F_51(x))
Eq(F_51(x), F_32(x) + F_49(x))
Eq(F_52(x), F_53(x))
Eq(F_53(x), F_12(x)*F_54(x))
Eq(F_54(x), F_55(x) + F_57(x))
Eq(F_55(x), F_56(x))
Eq(F_56(x), F_12(x)*F_32(x))
Eq(F_57(x), F_53(x))
Eq(F_58(x), F_59(x) + F_67(x))
Eq(F_59(x), F_36(x) + F_60(x) + F_62(x))
Eq(F_60(x), F_12(x)*F_61(x))
Eq(F_61(x), F_17(x) + F_59(x))
Eq(F_62(x), F_12(x)*F_63(x))
Eq(F_63(x), F_32(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_12(x)*F_66(x))
Eq(F_66(x), F_17(x) + F_64(x))
Eq(F_67(x), 2*F_36(x) + F_68(x) + F_70(x))
Eq(F_68(x), F_12(x)*F_69(x))
Eq(F_69(x), F_20(x) + F_67(x))
Eq(F_70(x), F_12(x)*F_71(x))
Eq(F_71(x), F_72(x) + F_73(x))
Eq(F_72(x), F_55(x))
Eq(F_73(x), F_70(x))
Eq(F_74(x), F_12(x)*F_75(x))
Eq(F_75(x), F_76(x, 1))
Eq(F_76(x, k_0), F_1(x) + F_100(x, k_0) + F_77(x, k_0) + F_98(x, k_0))
Eq(F_77(x, k_0), F_12(x)*F_78(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0) + F_87(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0) + F_84(x, k_0))
Eq(F_80(x, k_0), F_1(x) + F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0))
Eq(F_82(x, k_0), F_80(x, k_0)*F_83(x, k_0))
Eq(F_83(x, k_0), k_0*x)
Eq(F_84(x, k_0), F_32(x) + F_85(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_83(x, k_0)*F_84(x, k_0))
Eq(F_87(x, k_0), F_88(x, k_0) + F_93(x, k_0))
Eq(F_88(x, k_0), F_32(x) + F_89(x, k_0))
Eq(F_89(x, k_0), F_36(x) + F_90(x, k_0) + F_92(x, k_0))
Eq(F_90(x, k_0), F_12(x)*F_91(x, k_0))
Eq(F_91(x, k_0), F_81(x, k_0) + F_89(x, k_0))
Eq(F_92(x, k_0), F_83(x, k_0)*F_88(x, k_0))
Eq(F_93(x, k_0), F_49(x) + F_94(x, k_0))
Eq(F_94(x, k_0), 2*F_36(x) + F_95(x, k_0) + F_97(x, k_0))
Eq(F_95(x, k_0), F_12(x)*F_96(x, k_0))
Eq(F_96(x, k_0), F_85(x, k_0) + F_94(x, k_0))
Eq(F_97(x, k_0), F_83(x, k_0)*F_93(x, k_0))
Eq(F_98(x, k_0), F_12(x)*F_99(x, k_0))
Eq(F_99(x, k_0), (k_0*F_76(x, k_0) - F_76(x, 1))/(k_0 - 1))
Eq(F_100(x, k_0), F_76(x, k_0)*F_83(x, k_0))
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"}]], "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.rearrange_assumption", "strategy_class": "RearrangeAssumptionFactory"}, {"class_module": "tilings.strategies.assumption_insertion", "strategy_class": "AddAssumptionFactory"}, {"class_module": "tilings.strategies.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "row_placements_tracked_fusion", "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": [1, 2, 0, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "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], "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, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}], "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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 1, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 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, 1, 2], "pos": [[2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 0], [0, 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], "pos": [[0, 0]]}], "requirements": []}, {"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], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1], "pos": [[2, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [2, 1], [3, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [3, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [3, 1], [3, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [3, 1], [3, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[3, 1], [3, 1]]}, {"patt": [1, 0], "pos": [[2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [1, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 1], [1, 1], [3, 1]]}], "requirements": [[{"patt": [0], "pos": [[2, 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, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 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