0231_1230_2013_3012
Counting sequence:
1, 1, 2, 6, 20, 64, 196, 592, 1812, 5710, 18612, 62583, 215826, 758814, 2706632, 9759684, 35487908, 129905946, 478161828, 1768310415, 6566216010, 24470459530, 91490950200, 343076388541, 1289937699130, 4862013507364, 18367487286576, 69533819347777, 263748488617182, 1002243290388666, 3814988649570960, 14544640334188716, 55534073466976772, 212336147592105714, 812944076509461956, 3116285563626770191, 11959798523299398490, 45950804599499640130, 176733863336762505368, 680425372829487417465, 2622127044475515352850, 10113918596035944632740, 39044429920700536968160, 150853479222677537690881, 583300119628181065161646, 2257117854147616817415122, 8740328711673910878384304, 33868773757472521863121673, 131327898242732315431393562, 509552245180743037961430320, 1978261657758412453437437552, 7684785670518819984858163173, 29869166945781633149397133646, 116157871455800448649063301574, 451959718027989500244628445616, 1759414616608890928586517774591, 6852456927845017612737734289270, 26700952856775140134621372591840, 104088460289122880494250622201288, 405944995127578138652148050178037, 1583850964596122348529781992694966, 6182127958584860262173099274564466, 24139737743045636049083495401007392, 94295850558771998234679458655887996, 368479169875816696372497190132604356, 1440418573150919742659466189082023842, 5632681584560312882567868295525507844, 22033725021956517758506457793409723343, 86218923998960286316481451022406705402, 337485502510215976737375414172469870898, 1321422108420282272851125418625052091736, 5175569924646105564141306676864710867777, 20276890389709399872373731533993931388194, 79463489365077377860097703563827849671684, 311496878311103321175315223381766295666432, 1221395654430378811904318585733876454136929, 4790408930363303911479501935846693107786638, 18793142726809884575513592733991202486847426, 73745243611532458460294614764454643826606448, 289450081175264899455492771849105396439013005, 1136359577947336271934050728643896715016937650, 4462290049988320482468077000784591700198387480, 17526585015616776834744811924472572669793788320, 68854441132780194707907394847782481209780406061, 270557451039395118028681148915396234554261775646, 1063353702922273835973114029295931794990284493702, 4180080073556524734514850570675818130963113595024, 16435314834665426797069454445772707488436315062343, 64633260585762914370497256456165824152818984705542, 254224158304000796523954678718880932466822271029248, 1000134600800354781929401726416620435123010888073576, 3935312233584004685417858524523506651295131276390837, 15487357822491889407128336867298657515056130320695254, 60960876535340415751462583387870277458054127293287074, 239993345518077005168915816237557980138449624260061792, 944973797977428207852605949683102111101568351778706849, 3721443204405954385563870699835571688238181884466442778, 14657929356129575437016878163569682818770305325075399496, 57743358069601357782187701241868156448135432373108051888, 227508830794229349661819541663339454184271084098244085965, 896519947090131496687170072609401832877296324532152148270
Generating function in Maple syntax:
1/2*(-2*(-1+x)^4*(x-1/2)*(1-4*x)^(1/2)+2*x^5-11*x^4+16*x^3-14*x^2+6*x-1)/x/(2*x-1)/(-1+x)^4
Generating function in latex syntax:
\frac{-2 \left(-1+x \right)^{4} \left(x -\frac{1}{2}\right) \sqrt{1-4 x}+2 x^{5}-11 x^{4}+16 x^{3}-14 x^{2}+6 x -1}{2 x \left(2 x -1\right) \left(-1+x \right)^{4}}
Generating function in sympy syntax:
(x**5 - 11*x**4/2 + 8*x**3 - 7*x**2 + 3*x - sqrt(1 - 4*x)*(x - 1)**4*(x - 1/2) - 1/2)/(x*(x - 1)**4*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*(-1+x)^8*F(x)^2-(2*x-1)*(2*x^5-11*x^4+16*x^3-14*x^2+6*x-1)*(-1+x)^4*F(x)+4*x^10-36*x^9+143*x^8-334*x^7+516*x^6-546*x^5+400*x^4-199*x^3+64*x^2-12*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} \left(-1+x \right)^{8} F \! \left(x \right)^{2}-\left(2 x -1\right) \left(2 x^{5}-11 x^{4}+16 x^{3}-14 x^{2}+6 x -1\right) \left(-1+x \right)^{4} F \! \left(x \right)+4 x^{10}-36 x^{9}+143 x^{8}-334 x^{7}+516 x^{6}-546 x^{5}+400 x^{4}-199 x^{3}+64 x^{2}-12 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 64
a(6) = 196
a(7) = 592
a(n+3) = 8*(2*n+1)/(n+4)*a(n)-4*(5*n+8)/(n+4)*a(1+n)+2*(4*n+11)/(n+4)*a(n+2)+1/2*(n-1)*(1+n)*(n^2-6*n-8)/(n+4), 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) = 20
a \! \left(5\right) = 64
a \! \left(6\right) = 196
a \! \left(7\right) = 592
a \! \left(n +3\right) = \frac{8 \left(2 n +1\right) a \! \left(n \right)}{n +4}-\frac{4 \left(5 n +8\right) a \! \left(1+n \right)}{n +4}+\frac{2 \left(4 n +11\right) a \! \left(n +2\right)}{n +4}+\frac{\left(n -1\right) \left(1+n \right) \left(n^{2}-6 n -8\right)}{2 n +8}, \quad n \geq 8
Specification 1
Strategy pack name: requirement_placements_tracked_fusion
Tree: http://permpal.com/tree/21463/
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[9,x]
F[4,x] = F[5,x]+F[74,x]
F[5,x] = F[10,x]+F[6,x]
F[6,x] = F[1,x]+F[7,x]
F[7,x] = F[8,x]
F[8,x] = F[6,x]*F[9,x]
F[9,x] = x
F[10,x] = F[11,x]+F[36,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[9,x]
F[13,x] = F[14,x]+F[22,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[17,x]*F[9,x]
F[17,x] = F[14,x]+F[18,x]
F[18,x] = F[19,x]+F[7,x]
F[19,x] = F[20,x]
F[20,x] = F[21,x]*F[9,x]
F[21,x] = F[15,x]+F[19,x]
F[22,x] = F[23,x]+F[7,x]
F[23,x] = F[24,x]+F[25,x]+F[27,x]
F[24,x] = 0
F[25,x] = F[26,x]*F[9,x]
F[26,x] = F[15,x]+F[23,x]
F[27,x] = F[28,x]*F[9,x]
F[28,x] = F[18,x]+F[29,x]
F[29,x] = F[30,x]+F[33,x]
F[30,x] = F[31,x]
F[31,x] = F[32,x]*F[9,x]
F[32,x] = F[30,x]+F[7,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[9,x]
F[35,x] = F[19,x]+F[33,x]
F[36,x] = F[24,x]+F[37,x]+F[57,x]
F[37,x] = F[38,x]*F[9,x]
F[38,x] = F[39,x]+F[53,x]
F[39,x] = F[40,x]+F[7,x]
F[40,x] = F[24,x]+F[41,x]+F[50,x]
F[41,x] = F[42,x]*F[9,x]
F[42,x] = F[39,x]+F[43,x]
F[43,x] = F[44,x]+F[47,x]
F[44,x] = F[45,x]
F[45,x] = F[46,x]*F[9,x]
F[46,x] = F[44,x]+F[7,x]
F[47,x] = F[48,x]
F[48,x] = F[49,x]*F[9,x]
F[49,x] = F[40,x]+F[47,x]
F[50,x] = F[51,x]*F[9,x]
F[51,x] = F[52,x]+F[7,x]
F[52,x] = F[24,x]+F[45,x]+F[50,x]
F[53,x] = F[54,x]+F[59,x]
F[54,x] = F[24,x]+F[55,x]+F[57,x]
F[55,x] = F[56,x]*F[9,x]
F[56,x] = F[54,x]+F[7,x]
F[57,x] = F[58,x]*F[9,x]
F[58,x] = F[54,x]+F[7,x]
F[59,x] = F[24,x]+F[60,x]+F[62,x]+F[71,x]
F[60,x] = F[61,x]*F[9,x]
F[61,x] = F[40,x]+F[59,x]
F[62,x] = F[63,x]*F[9,x]
F[63,x] = F[43,x]+F[64,x]
F[64,x] = F[65,x]+F[68,x]
F[65,x] = F[66,x]
F[66,x] = F[67,x]*F[9,x]
F[67,x] = F[44,x]+F[65,x]
F[68,x] = F[69,x]
F[69,x] = F[70,x]*F[9,x]
F[70,x] = F[47,x]+F[68,x]
F[71,x] = F[72,x]*F[9,x]
F[72,x] = F[30,x]+F[73,x]
F[73,x] = 2*F[24,x]+F[66,x]+F[71,x]
F[74,x] = F[75,x]
F[75,x] = F[76,x,1]
F[76,x,k[0]] = F[77,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]*F[88,x,k[0]]*F[9,x]
F[79,x,k[0]] = F[80,x,k[0]]+F[98,x,k[0]]
F[80,x,k[0]] = F[58,x]+F[81,x,k[0]]
F[81,x,k[0]] = F[82,x,k[0]]+F[89,x,k[0]]
F[82,x,k[0]] = F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]*F[9,x]
F[84,x,k[0]] = F[82,x,k[0]]+F[85,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[87,x,k[0]]*F[88,x,k[0]]
F[87,x,k[0]] = k[0]*x
F[88,x,k[0]] = F[1,x]+F[85,x,k[0]]
F[89,x,k[0]] = 2*F[24,x]+F[90,x,k[0]]+F[97,x,k[0]]
F[90,x,k[0]] = F[9,x]*F[91,x,k[0]]
F[91,x,k[0]] = F[89,x,k[0]]+F[92,x,k[0]]
F[92,x,k[0]] = F[24,x]+F[93,x,k[0]]+F[95,x,k[0]]
F[93,x,k[0]] = F[87,x,k[0]]*F[94,x,k[0]]
F[94,x,k[0]] = F[7,x]+F[92,x,k[0]]
F[95,x,k[0]] = F[9,x]*F[96,x,k[0]]
F[96,x,k[0]] = F[85,x,k[0]]+F[92,x,k[0]]
F[97,x,k[0]] = F[81,x,k[0]]*F[9,x]
F[98,x,k[0]] = (F[77,x,k[0]]*k[0]-F[77,x,1])/(-1+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_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{4}\! \left(x \right) F_{9}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)+F_{74}\! \left(x \right)
F_{5}\! \left(x \right) = F_{10}\! \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_{6}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = x
F_{10}\! \left(x \right) = F_{11}\! \left(x \right)+F_{36}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{13}\! \left(x \right) F_{9}\! \left(x \right)
F_{13}\! \left(x \right) = F_{14}\! \left(x \right)+F_{22}\! \left(x \right)
F_{14}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{15}\! \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_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{7}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right) F_{9}\! \left(x \right)
F_{21}\! \left(x \right) = F_{15}\! \left(x \right)+F_{19}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{7}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)+F_{27}\! \left(x \right)
F_{24}\! \left(x \right) = 0
F_{25}\! \left(x \right) = F_{26}\! \left(x \right) F_{9}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right)+F_{23}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right) F_{9}\! \left(x \right)
F_{28}\! \left(x \right) = F_{18}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{33}\! \left(x \right)
F_{30}\! \left(x \right) = F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{9}\! \left(x \right)
F_{32}\! \left(x \right) = F_{30}\! \left(x \right)+F_{7}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right) F_{9}\! \left(x \right)
F_{35}\! \left(x \right) = F_{19}\! \left(x \right)+F_{33}\! \left(x \right)
F_{36}\! \left(x \right) = F_{24}\! \left(x \right)+F_{37}\! \left(x \right)+F_{57}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right) F_{9}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{53}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{7}\! \left(x \right)
F_{40}\! \left(x \right) = F_{24}\! \left(x \right)+F_{41}\! \left(x \right)+F_{50}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right) F_{9}\! \left(x \right)
F_{42}\! \left(x \right) = F_{39}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{47}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right) F_{9}\! \left(x \right)
F_{46}\! \left(x \right) = F_{44}\! \left(x \right)+F_{7}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right) F_{9}\! \left(x \right)
F_{49}\! \left(x \right) = F_{40}\! \left(x \right)+F_{47}\! \left(x \right)
F_{50}\! \left(x \right) = F_{51}\! \left(x \right) F_{9}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{7}\! \left(x \right)
F_{52}\! \left(x \right) = F_{24}\! \left(x \right)+F_{45}\! \left(x \right)+F_{50}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right)+F_{59}\! \left(x \right)
F_{54}\! \left(x \right) = F_{24}\! \left(x \right)+F_{55}\! \left(x \right)+F_{57}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right) F_{9}\! \left(x \right)
F_{56}\! \left(x \right) = F_{54}\! \left(x \right)+F_{7}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right) F_{9}\! \left(x \right)
F_{58}\! \left(x \right) = F_{54}\! \left(x \right)+F_{7}\! \left(x \right)
F_{59}\! \left(x \right) = F_{24}\! \left(x \right)+F_{60}\! \left(x \right)+F_{62}\! \left(x \right)+F_{71}\! \left(x \right)
F_{60}\! \left(x \right) = F_{61}\! \left(x \right) F_{9}\! \left(x \right)
F_{61}\! \left(x \right) = F_{40}\! \left(x \right)+F_{59}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right) F_{9}\! \left(x \right)
F_{63}\! \left(x \right) = F_{43}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{68}\! \left(x \right)
F_{65}\! \left(x \right) = F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right) F_{9}\! \left(x \right)
F_{67}\! \left(x \right) = F_{44}\! \left(x \right)+F_{65}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right) F_{9}\! \left(x \right)
F_{70}\! \left(x \right) = F_{47}\! \left(x \right)+F_{68}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right) F_{9}\! \left(x \right)
F_{72}\! \left(x \right) = F_{30}\! \left(x \right)+F_{73}\! \left(x \right)
F_{73}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{66}\! \left(x \right)+F_{71}\! \left(x \right)
F_{74}\! \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_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right) F_{88}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{58}\! \left(x \right)+F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{82}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{84}\! \left(x , y\right) = F_{82}\! \left(x , y\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_{87}\! \left(x , y\right) F_{88}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = y x
F_{88}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{85}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = 2 F_{24}\! \left(x \right)+F_{90}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{9}\! \left(x \right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{89}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{93}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{87}\! \left(x , y\right) F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{7}\! \left(x \right)+F_{92}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{9}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{85}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{81}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{98}\! \left(x , y\right) = \frac{F_{77}\! \left(x , y\right) y -F_{77}\! \left(x , 1\right)}{-1+y}
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_9(x))
Eq(F_4(x), F_5(x) + F_74(x))
Eq(F_5(x), F_10(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_6(x)*F_9(x))
Eq(F_9(x), x)
Eq(F_10(x), F_11(x) + F_36(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_13(x)*F_9(x))
Eq(F_13(x), F_14(x) + F_22(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_17(x)*F_9(x))
Eq(F_17(x), F_14(x) + F_18(x))
Eq(F_18(x), F_19(x) + F_7(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_21(x)*F_9(x))
Eq(F_21(x), F_15(x) + F_19(x))
Eq(F_22(x), F_23(x) + F_7(x))
Eq(F_23(x), F_24(x) + F_25(x) + F_27(x))
Eq(F_24(x), 0)
Eq(F_25(x), F_26(x)*F_9(x))
Eq(F_26(x), F_15(x) + F_23(x))
Eq(F_27(x), F_28(x)*F_9(x))
Eq(F_28(x), F_18(x) + F_29(x))
Eq(F_29(x), F_30(x) + F_33(x))
Eq(F_30(x), F_31(x))
Eq(F_31(x), F_32(x)*F_9(x))
Eq(F_32(x), F_30(x) + F_7(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_9(x))
Eq(F_35(x), F_19(x) + F_33(x))
Eq(F_36(x), F_24(x) + F_37(x) + F_57(x))
Eq(F_37(x), F_38(x)*F_9(x))
Eq(F_38(x), F_39(x) + F_53(x))
Eq(F_39(x), F_40(x) + F_7(x))
Eq(F_40(x), F_24(x) + F_41(x) + F_50(x))
Eq(F_41(x), F_42(x)*F_9(x))
Eq(F_42(x), F_39(x) + F_43(x))
Eq(F_43(x), F_44(x) + F_47(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_46(x)*F_9(x))
Eq(F_46(x), F_44(x) + F_7(x))
Eq(F_47(x), F_48(x))
Eq(F_48(x), F_49(x)*F_9(x))
Eq(F_49(x), F_40(x) + F_47(x))
Eq(F_50(x), F_51(x)*F_9(x))
Eq(F_51(x), F_52(x) + F_7(x))
Eq(F_52(x), F_24(x) + F_45(x) + F_50(x))
Eq(F_53(x), F_54(x) + F_59(x))
Eq(F_54(x), F_24(x) + F_55(x) + F_57(x))
Eq(F_55(x), F_56(x)*F_9(x))
Eq(F_56(x), F_54(x) + F_7(x))
Eq(F_57(x), F_58(x)*F_9(x))
Eq(F_58(x), F_54(x) + F_7(x))
Eq(F_59(x), F_24(x) + F_60(x) + F_62(x) + F_71(x))
Eq(F_60(x), F_61(x)*F_9(x))
Eq(F_61(x), F_40(x) + F_59(x))
Eq(F_62(x), F_63(x)*F_9(x))
Eq(F_63(x), F_43(x) + F_64(x))
Eq(F_64(x), F_65(x) + F_68(x))
Eq(F_65(x), F_66(x))
Eq(F_66(x), F_67(x)*F_9(x))
Eq(F_67(x), F_44(x) + F_65(x))
Eq(F_68(x), F_69(x))
Eq(F_69(x), F_70(x)*F_9(x))
Eq(F_70(x), F_47(x) + F_68(x))
Eq(F_71(x), F_72(x)*F_9(x))
Eq(F_72(x), F_30(x) + F_73(x))
Eq(F_73(x), 2*F_24(x) + F_66(x) + F_71(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_76(x, 1))
Eq(F_76(x, k_0), F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0)*F_88(x, k_0)*F_9(x))
Eq(F_79(x, k_0), F_80(x, k_0) + F_98(x, k_0))
Eq(F_80(x, k_0), F_58(x) + F_81(x, k_0))
Eq(F_81(x, k_0), F_82(x, k_0) + F_89(x, k_0))
Eq(F_82(x, k_0), F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0)*F_9(x))
Eq(F_84(x, k_0), F_82(x, k_0) + F_85(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_87(x, k_0)*F_88(x, k_0))
Eq(F_87(x, k_0), k_0*x)
Eq(F_88(x, k_0), F_1(x) + F_85(x, k_0))
Eq(F_89(x, k_0), 2*F_24(x) + F_90(x, k_0) + F_97(x, k_0))
Eq(F_90(x, k_0), F_9(x)*F_91(x, k_0))
Eq(F_91(x, k_0), F_89(x, k_0) + F_92(x, k_0))
Eq(F_92(x, k_0), F_24(x) + F_93(x, k_0) + F_95(x, k_0))
Eq(F_93(x, k_0), F_87(x, k_0)*F_94(x, k_0))
Eq(F_94(x, k_0), F_7(x) + F_92(x, k_0))
Eq(F_95(x, k_0), F_9(x)*F_96(x, k_0))
Eq(F_96(x, k_0), F_85(x, k_0) + F_92(x, k_0))
Eq(F_97(x, k_0), F_81(x, k_0)*F_9(x))
Eq(F_98(x, k_0), (-k_0*F_77(x, k_0) + F_77(x, 1))/(1 - k_0))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": false, "limited_insertion": true, "maxreqlen": 2, "strategy_class": "RequirementInsertionFactory"}, {"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.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.requirement_insertion", "ignore_parent": true, "strategy_class": "RequirementCorroborationFactory"}, {"class_module": "tilings.strategies.fusion.fusion", "strategy_class": "FusionFactory", "tracked": true}], "iterative": false, "name": "requirement_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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "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, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 0, 1, 2], "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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1, 3], "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_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [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, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 0], [0, 0]]}, {"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, 2], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 2], [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], "pos": [[0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}], "requirements": [[{"patt": [0, 1], "pos": [[0, 1], [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, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [0, 0], [0, 0]]}, {"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": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0, 1], "pos": [[0, 1], [0, 1]]}], "ignore_parent": false, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [{"assumption": "TrackingAssumption", "class_module": "tilings.assumptions", "gps": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[2, 0]]}]}], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 1]]}], [{"patt": [0], "pos": [[1, 2]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[1, 3]]}, {"patt": [0], "pos": [[2, 2]]}, {"patt": [0], "pos": [[2, 3]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [2, 0]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 3]]}, {"patt": [0, 1], "pos": [[0, 3], [0, 3]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": 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