0132_0231_1023_1230_3012
Counting sequence:
1, 1, 2, 6, 19, 55, 159, 482, 1530, 5047, 17137, 59419, 209202, 745169, 2678823, 9703402, 35374510, 129678119, 477704917, 1767395079, 6564383534, 24466792449, 91483613547, 343061712343, 1289908343400, 4861954792085, 18367369851669, 69533584473037, 263748018862150, 1002242350872373, 3814986770531415, 14544636576101882, 55534065950794518, 212336132559731719, 812944046444703517, 3116285503497241839, 11959798403040329222, 45950804358981487873, 176733862855726185907, 680425371867414762299, 2622127042551370024904, 10113918592187653957789, 39044429913003955597677, 150853479207284374927733, 583300119597394739611486, 2257117854086044166289173, 8740328711550765576104927, 33868773757226231258533503, 131327898242239734222185780, 509552245179757875542981197, 1978261657756442128600503537, 7684785670514879335184257069, 29869166945773751850049280962, 116157871455784686050367553229, 451959718027957975047236903347, 1759414616608827878191734641769, 6852456927844891511948167972532, 26700952856774887933042239904353, 104088460289122376091092356769277, 405944995127577129845831519253841, 1583850964596120330917148930783150, 6182127958584856226947833150674045, 24139737743045627978632963153156279, 94295850558771982093778394160111898, 368479169875816664090695061140974566, 1440418573150919678095861931098682823, 5632681584560312753440659779558740397, 22033725021956517500252040761476098943, 86218923998960285799972616958539362870, 337485502510215975704357746044735087745, 1321422108420282270785090082369582422851, 5175569924646105560009236004353771422803, 20276890389709399864109590188972052386280, 79463489365077377843569420873784091550989, 311496878311103321142258658001678779303133, 1221395654430378811838205454973701421283237, 4790408930363303911347275674326343041946830, 18793142726809884575249140210950502355029909, 73745243611532458459765709718373243562827887, 289450081175264899454434961756942595911306579, 1136359577947336271931935108459571113961369564, 4462290049988320482463845760415940498087089989, 17526585015616776834736349443735270265571025777, 68854441132780194707890469886307876401334707013, 270557451039395118028647298992447024937370197026, 1063353702922273835973046329450033375756501149213, 4180080073556524734514715170984021292495546711907, 16435314834665426797069183646389113811501181094913, 64633260585762914370496714857398636798948716562260, 254224158304000796523953595521346557759081734526865, 1000134600800354781929399560021551685707529814845421, 3935312233584004685417854191733369152464169129703393, 15487357822491889407128328201718382517394206027081310, 60960876535340415751462566056709727462730278705812029, 239993345518077005168915781575236880147801927084856263, 944973797977428207852605880358459911120272957428031887, 3721443204405954385563870561186287288275591095764820300, 14657929356129575437016877886271114018845123747671873149, 57743358069601357782187700687271018848285069218300708777, 227508830794229349661819540554145178984570357788629100109, 896519947090131496687170070391013282477894871912921867514
Generating function in Maple syntax:
1/2*(-2*(x-1/2)*(x-1)^4*(1-4*x)^(1/2)-4*x^10+10*x^9-4*x^8-6*x^7+6*x^6+4*x^5-11*x^4+16*x^3-14*x^2+6*x-1)/x/(2*x-1)/(x-1)^4
Generating function in latex syntax:
\frac{-2 \left(x -\frac{1}{2}\right) \left(x -1\right)^{4} \sqrt{1-4 x}-4 x^{10}+10 x^{9}-4 x^{8}-6 x^{7}+6 x^{6}+4 x^{5}-11 x^{4}+16 x^{3}-14 x^{2}+6 x -1}{2 x \left(2 x -1\right) \left(x -1\right)^{4}}
Generating function in sympy syntax:
(-2*x**10 + 5*x**9 - 2*x**8 - 3*x**7 + 3*x**6 + 2*x**5 - 11*x**4/2 + 8*x**3 - 7*x**2 + 3*x + sqrt(1 - 4*x)*(1 - 2*x)*(x - 1)**4/2 - 1/2)/(x*(x - 1)**4*(2*x - 1))
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*(x-1)^8*F(x)^2+(2*x-1)*(4*x^10-10*x^9+4*x^8+6*x^7-6*x^6-4*x^5+11*x^4-16*x^3+14*x^2-6*x+1)*(x-1)^4*F(x)+4*x^19-20*x^18+33*x^17-8*x^16-38*x^15+34*x^14+39*x^13-113*x^12+127*x^11-65*x^10-54*x^9+205*x^8-376*x^7+523*x^6-543*x^5+399*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(x -1\right)^{8} F \! \left(x \right)^{2}+\left(2 x -1\right) \left(4 x^{10}-10 x^{9}+4 x^{8}+6 x^{7}-6 x^{6}-4 x^{5}+11 x^{4}-16 x^{3}+14 x^{2}-6 x +1\right) \left(x -1\right)^{4} F \! \left(x \right)+4 x^{19}-20 x^{18}+33 x^{17}-8 x^{16}-38 x^{15}+34 x^{14}+39 x^{13}-113 x^{12}+127 x^{11}-65 x^{10}-54 x^{9}+205 x^{8}-376 x^{7}+523 x^{6}-543 x^{5}+399 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) = 19
a(5) = 55
a(6) = 159
a(7) = 482
a(8) = 1530
a(9) = 5047
a(10) = 17137
a(11) = 59419
a(12) = 209202
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^4-15*n^3+54*n^2-28*n-28)/(n+4), n >= 13
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) = 55
a \! \left(6\right) = 159
a \! \left(7\right) = 482
a \! \left(8\right) = 1530
a \! \left(9\right) = 5047
a \! \left(10\right) = 17137
a \! \left(11\right) = 59419
a \! \left(12\right) = 209202
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{n^{4}-15 n^{3}+54 n^{2}-28 n -28}{2 \left(n +4\right)}, \quad n \geq 13
Specification 1
Strategy pack name: requirement_placements_tracked_fusion
Tree: http://permpal.com/tree/21693/
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[67,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[42,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[9,x]
F[13,x] = F[14,x]+F[26,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[18,x]+F[21,x]
F[18,x] = F[1,x]+F[19,x]
F[19,x] = F[20,x]
F[20,x] = F[18,x]*F[9,x]
F[21,x] = F[22,x]
F[22,x] = F[23,x]*F[9,x]
F[23,x] = F[24,x]+F[25,x]
F[24,x] = F[1,x]+F[9,x]
F[25,x] = F[22,x]
F[26,x] = F[27,x]+F[33,x]
F[27,x] = F[28,x]
F[28,x] = F[29,x]*F[9,x]
F[29,x] = F[30,x]+F[6,x]
F[30,x] = F[27,x]+F[31,x]
F[31,x] = F[32,x]
F[32,x] = F[30,x]*F[9,x]
F[33,x] = F[34,x]
F[34,x] = F[35,x]*F[9,x]
F[35,x] = F[36,x]+F[37,x]
F[36,x] = F[27,x]
F[37,x] = F[38,x]
F[38,x] = F[39,x]*F[9,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[27,x]
F[41,x] = F[38,x]
F[42,x] = F[43,x]+F[44,x]+F[61,x]
F[43,x] = 0
F[44,x] = F[45,x]*F[9,x]
F[45,x] = F[46,x]+F[51,x]
F[46,x] = F[47,x]+F[7,x]
F[47,x] = F[48,x]
F[48,x] = F[49,x]*F[9,x]
F[49,x] = F[50,x]+F[7,x]
F[50,x] = F[48,x]
F[51,x] = F[52,x]+F[66,x]
F[52,x] = F[43,x]+F[53,x]+F[61,x]
F[53,x] = F[54,x]*F[9,x]
F[54,x] = F[55,x]+F[56,x]
F[55,x] = F[50,x]+F[7,x]
F[56,x] = F[52,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[59,x]*F[9,x]
F[59,x] = F[50,x]+F[60,x]
F[60,x] = F[58,x]
F[61,x] = F[62,x]*F[9,x]
F[62,x] = F[63,x]+F[7,x]
F[63,x] = F[43,x]+F[61,x]+F[64,x]
F[64,x] = F[65,x]*F[9,x]
F[65,x] = F[63,x]+F[7,x]
F[66,x] = F[58,x]
F[67,x] = F[68,x]
F[68,x] = F[69,x,1]
F[69,x,k[0]] = F[70,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]
F[71,x,k[0]] = F[72,x,k[0]]*F[81,x,k[0]]*F[9,x]
F[72,x,k[0]] = F[73,x,k[0]]+F[91,x,k[0]]
F[73,x,k[0]] = F[62,x]+F[74,x,k[0]]
F[74,x,k[0]] = F[75,x,k[0]]+F[82,x,k[0]]
F[75,x,k[0]] = F[76,x,k[0]]
F[76,x,k[0]] = F[77,x,k[0]]*F[9,x]
F[77,x,k[0]] = F[75,x,k[0]]+F[78,x,k[0]]
F[78,x,k[0]] = F[79,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]*F[81,x,k[0]]
F[80,x,k[0]] = k[0]*x
F[81,x,k[0]] = F[1,x]+F[78,x,k[0]]
F[82,x,k[0]] = 2*F[43,x]+F[83,x,k[0]]+F[90,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[43,x]+F[86,x,k[0]]+F[88,x,k[0]]
F[86,x,k[0]] = F[80,x,k[0]]*F[87,x,k[0]]
F[87,x,k[0]] = F[7,x]+F[85,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]*F[9,x]
F[89,x,k[0]] = F[78,x,k[0]]+F[85,x,k[0]]
F[90,x,k[0]] = F[74,x,k[0]]*F[9,x]
F[91,x,k[0]] = (F[70,x,k[0]]*k[0]-F[70,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_{67}\! \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_{42}\! \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_{26}\! \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_{18}\! \left(x \right)+F_{21}\! \left(x \right)
F_{18}\! \left(x \right) = F_{1}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{18}\! \left(x \right) F_{9}\! \left(x \right)
F_{21}\! \left(x \right) = F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right) F_{9}\! \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_{9}\! \left(x \right)
F_{25}\! \left(x \right) = F_{22}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{33}\! \left(x \right)
F_{27}\! \left(x \right) = F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right) F_{9}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{6}\! \left(x \right)
F_{30}\! \left(x \right) = F_{27}\! \left(x \right)+F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{30}\! \left(x \right) F_{9}\! \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_{36}\! \left(x \right)+F_{37}\! \left(x \right)
F_{36}\! \left(x \right) = F_{27}\! \left(x \right)
F_{37}\! \left(x \right) = F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right) F_{9}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{27}\! \left(x \right)
F_{41}\! \left(x \right) = F_{38}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)+F_{44}\! \left(x \right)+F_{61}\! \left(x \right)
F_{43}\! \left(x \right) = 0
F_{44}\! \left(x \right) = F_{45}\! \left(x \right) F_{9}\! \left(x \right)
F_{45}\! \left(x \right) = F_{46}\! \left(x \right)+F_{51}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \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_{50}\! \left(x \right)+F_{7}\! \left(x \right)
F_{50}\! \left(x \right) = F_{48}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)+F_{66}\! \left(x \right)
F_{52}\! \left(x \right) = F_{43}\! \left(x \right)+F_{53}\! \left(x \right)+F_{61}\! \left(x \right)
F_{53}\! \left(x \right) = F_{54}\! \left(x \right) F_{9}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right)+F_{56}\! \left(x \right)
F_{55}\! \left(x \right) = F_{50}\! \left(x \right)+F_{7}\! \left(x \right)
F_{56}\! \left(x \right) = F_{52}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right) F_{9}\! \left(x \right)
F_{59}\! \left(x \right) = F_{50}\! \left(x \right)+F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right) F_{9}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{7}\! \left(x \right)
F_{63}\! \left(x \right) = F_{43}\! \left(x \right)+F_{61}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right) F_{9}\! \left(x \right)
F_{65}\! \left(x \right) = F_{63}\! \left(x \right)+F_{7}\! \left(x \right)
F_{66}\! \left(x \right) = F_{58}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x , 1\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{72}\! \left(x , y\right) F_{81}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{62}\! \left(x \right)+F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{82}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{76}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{77}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{77}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{78}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right) F_{81}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = y x
F_{81}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{78}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = 2 F_{43}\! \left(x \right)+F_{83}\! \left(x , y\right)+F_{90}\! \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_{43}\! \left(x \right)+F_{86}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{80}\! \left(x , y\right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{7}\! \left(x \right)+F_{85}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{89}\! \left(x , y\right) = F_{78}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{74}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{91}\! \left(x , y\right) = \frac{F_{70}\! \left(x , y\right) y -F_{70}\! \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_67(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_42(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_26(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_18(x) + F_21(x))
Eq(F_18(x), F_1(x) + F_19(x))
Eq(F_19(x), F_20(x))
Eq(F_20(x), F_18(x)*F_9(x))
Eq(F_21(x), F_22(x))
Eq(F_22(x), F_23(x)*F_9(x))
Eq(F_23(x), F_24(x) + F_25(x))
Eq(F_24(x), F_1(x) + F_9(x))
Eq(F_25(x), F_22(x))
Eq(F_26(x), F_27(x) + F_33(x))
Eq(F_27(x), F_28(x))
Eq(F_28(x), F_29(x)*F_9(x))
Eq(F_29(x), F_30(x) + F_6(x))
Eq(F_30(x), F_27(x) + F_31(x))
Eq(F_31(x), F_32(x))
Eq(F_32(x), F_30(x)*F_9(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_35(x)*F_9(x))
Eq(F_35(x), F_36(x) + F_37(x))
Eq(F_36(x), F_27(x))
Eq(F_37(x), F_38(x))
Eq(F_38(x), F_39(x)*F_9(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_27(x))
Eq(F_41(x), F_38(x))
Eq(F_42(x), F_43(x) + F_44(x) + F_61(x))
Eq(F_43(x), 0)
Eq(F_44(x), F_45(x)*F_9(x))
Eq(F_45(x), F_46(x) + F_51(x))
Eq(F_46(x), F_47(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_50(x) + F_7(x))
Eq(F_50(x), F_48(x))
Eq(F_51(x), F_52(x) + F_66(x))
Eq(F_52(x), F_43(x) + F_53(x) + F_61(x))
Eq(F_53(x), F_54(x)*F_9(x))
Eq(F_54(x), F_55(x) + F_56(x))
Eq(F_55(x), F_50(x) + F_7(x))
Eq(F_56(x), F_52(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_59(x)*F_9(x))
Eq(F_59(x), F_50(x) + F_60(x))
Eq(F_60(x), F_58(x))
Eq(F_61(x), F_62(x)*F_9(x))
Eq(F_62(x), F_63(x) + F_7(x))
Eq(F_63(x), F_43(x) + F_61(x) + F_64(x))
Eq(F_64(x), F_65(x)*F_9(x))
Eq(F_65(x), F_63(x) + F_7(x))
Eq(F_66(x), F_58(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_69(x, 1))
Eq(F_69(x, k_0), F_70(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0))
Eq(F_71(x, k_0), F_72(x, k_0)*F_81(x, k_0)*F_9(x))
Eq(F_72(x, k_0), F_73(x, k_0) + F_91(x, k_0))
Eq(F_73(x, k_0), F_62(x) + F_74(x, k_0))
Eq(F_74(x, k_0), F_75(x, k_0) + F_82(x, k_0))
Eq(F_75(x, k_0), F_76(x, k_0))
Eq(F_76(x, k_0), F_77(x, k_0)*F_9(x))
Eq(F_77(x, k_0), F_75(x, k_0) + F_78(x, k_0))
Eq(F_78(x, k_0), F_79(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0)*F_81(x, k_0))
Eq(F_80(x, k_0), k_0*x)
Eq(F_81(x, k_0), F_1(x) + F_78(x, k_0))
Eq(F_82(x, k_0), 2*F_43(x) + F_83(x, k_0) + F_90(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_43(x) + F_86(x, k_0) + F_88(x, k_0))
Eq(F_86(x, k_0), F_80(x, k_0)*F_87(x, k_0))
Eq(F_87(x, k_0), F_7(x) + F_85(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0)*F_9(x))
Eq(F_89(x, k_0), F_78(x, k_0) + F_85(x, k_0))
Eq(F_90(x, k_0), F_74(x, k_0)*F_9(x))
Eq(F_91(x, k_0), (-k_0*F_70(x, k_0) + F_70(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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 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, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 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": [[{"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, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 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_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, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"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, 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": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[1, 2]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"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": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"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, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"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, 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": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"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, 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": [3, 0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [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, 0], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"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, 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": [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, 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": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 0], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], 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