0132_0213_0231_1230_3012
Counting sequence:
1, 1, 2, 6, 19, 57, 168, 506, 1585, 5165, 17382, 59919, 210213, 747203, 2682904, 9711578, 35390877, 129710869, 477770434, 1767526131, 6564645657, 24467316715, 91484662100, 343063809471, 1289912537679, 4861963180667, 18367386628858, 69533618027441, 263748085970985, 1002242485090071, 3814987038966840, 14544637112972762, 55534067024536309, 212336134707215333, 812944050739670778, 3116285512087176395, 11959798420220198369, 45950804393341226203, 176733862924445662604, 680425372004853715731, 2622127042826247931807, 10113918592737409771635, 39044429914103467225410, 150853479209483398183241, 583300119601792786122545, 2257117854094840259311335, 8740328711568357762149296, 33868773757261415630622287, 131327898242310102966363395, 509552245179898613031336475, 1978261657756723603577214142, 7684785670515442285137678329, 29869166945774877749956123533, 116157871455786937850181238423, 451959718027962478646864273788, 1759414616608836885390989382705, 6852456927844909526346677454459, 26700952856774923961839258868263, 104088460289122448148686394697154, 405944995127577273961019595109653, 1583850964596120619147525082494833, 6182127958584856803408585454097471, 24139737743045629131554467760003192, 94295850558771984399621403373805786, 368479169875816668702381079568362405, 1440418573150919687319233967953458565, 5632681584560312771887403853268291946, 22033725021956517537145528908895202107, 86218923998960285873759593253377569265, 337485502510215975851931698634411500603, 1321422108420282271080237987548935248636, 5175569924646105560599531814712477074443, 20276890389709399865290181809689463689631, 79463489365077377845930604115218914157763, 311496878311103321146981024484548424516754, 1221395654430378811847650187939440711710553, 4790408930363303911366165140257821622801537, 18793142726809884575286919142813459516739399, 73745243611532458459841267582099157886246944, 289450081175264899454586077484394424558144771, 1136359577947336271932237339914474771255046027, 4462290049988320482464450223325747812674442995, 17526585015616776834737558369554884894745731870, 68854441132780194707892887737947105659684119281, 270557451039395118028652134695725483454069021645, 1063353702922273835973056000856590292789898798535, 4180080073556524734514734513797135126562342010636, 16435314834665426797069222332015341479634771692457, 64633260585762914370496792228651092135215897757435, 254224158304000796523953750263851468431616096917303, 1000134600800354781929399869506561507052598539626386, 3935312233584004685417854810703388795154306579265413, 15487357822491889407128329439658421802774480926205441, 60960876535340415751462568532589806033490828504060383, 239993345518077005168915786526997037289323026681353064, 944973797977428207852605890261980225403315156621025583, 3721443204405954385563870580993327916841675494150807787, 14657929356129575437016877925885195275977292544443848219, 57743358069601357782187700766499181362549406811844659014, 227508830794229349661819540712601504013099032975717000681, 896519947090131496687170070707925932534952222287097668757
Generating function in Maple syntax:
1/2*(-2*(-1+x)^4*(x-1/2)*(1-4*x)^(1/2)+2*x^6+4*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^{6}+4 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**6 + 2*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^6+4*x^5-11*x^4+16*x^3-14*x^2+6*x-1)*(-1+x)^4*F(x)+x^11+8*x^10-44*x^9+148*x^8-332*x^7+508*x^6-541*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(-1+x \right)^{8} F \! \left(x \right)^{2}-\left(2 x -1\right) \left(2 x^{6}+4 x^{5}-11 x^{4}+16 x^{3}-14 x^{2}+6 x -1\right) \left(-1+x \right)^{4} F \! \left(x \right)+x^{11}+8 x^{10}-44 x^{9}+148 x^{8}-332 x^{7}+508 x^{6}-541 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) = 57
a(6) = 168
a(7) = 506
a(8) = 1585
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+48*n^2-8*n-16)/(n+4), n >= 9
Recurrence in latex format:
a \! \left(0\right) = 1
a \! \left(1\right) = 1
a \! \left(2\right) = 2
a \! \left(3\right) = 6
a \! \left(4\right) = 19
a \! \left(5\right) = 57
a \! \left(6\right) = 168
a \! \left(7\right) = 506
a \! \left(8\right) = 1585
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}+48 n^{2}-8 n -16}{2 \left(n +4\right)}, \quad n \geq 9
Specification 1
Strategy pack name: requirement_placements_tracked_fusion
Tree: http://permpal.com/tree/21575/
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[87,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[53,x]
F[11,x] = F[12,x]
F[12,x] = F[13,x]*F[9,x]
F[13,x] = F[14,x]+F[17,x]
F[14,x] = F[1,x]+F[15,x]
F[15,x] = F[16,x]
F[16,x] = F[14,x]*F[9,x]
F[17,x] = F[18,x]+F[30,x]
F[18,x] = F[19,x]
F[19,x] = F[20,x]*F[9,x]
F[20,x] = F[21,x]+F[22,x]
F[21,x] = F[1,x]+F[9,x]
F[22,x] = F[18,x]+F[23,x]
F[23,x] = F[24,x]+F[25,x]+F[29,x]
F[24,x] = 0
F[25,x] = F[26,x]*F[9,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[9,x]
F[28,x] = F[23,x]
F[29,x] = F[18,x]*F[9,x]
F[30,x] = F[24,x]+F[31,x]+F[51,x]
F[31,x] = F[32,x]*F[9,x]
F[32,x] = F[33,x]+F[36,x]
F[33,x] = F[15,x]+F[34,x]
F[34,x] = F[35,x]
F[35,x] = F[15,x]*F[9,x]
F[36,x] = F[30,x]+F[37,x]
F[37,x] = 2*F[24,x]+F[38,x]+F[42,x]
F[38,x] = F[39,x]*F[9,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[34,x]
F[41,x] = F[37,x]
F[42,x] = F[43,x]*F[9,x]
F[43,x] = F[44,x]
F[44,x] = F[45,x]*F[9,x]
F[45,x] = F[33,x]+F[46,x]
F[46,x] = F[43,x]+F[47,x]
F[47,x] = 2*F[24,x]+F[42,x]+F[48,x]
F[48,x] = F[49,x]*F[9,x]
F[49,x] = F[40,x]+F[50,x]
F[50,x] = F[47,x]
F[51,x] = F[52,x]*F[9,x]
F[52,x] = F[18,x]+F[43,x]
F[53,x] = F[24,x]+F[54,x]+F[77,x]
F[54,x] = F[55,x]*F[9,x]
F[55,x] = F[56,x]+F[61,x]
F[56,x] = F[57,x]+F[7,x]
F[57,x] = F[58,x]
F[58,x] = F[59,x]*F[9,x]
F[59,x] = F[60,x]+F[9,x]
F[60,x] = F[58,x]
F[61,x] = F[62,x]+F[82,x]
F[62,x] = F[24,x]+F[63,x]+F[77,x]
F[63,x] = F[64,x]*F[9,x]
F[64,x] = F[65,x]+F[66,x]
F[65,x] = F[60,x]+F[7,x]
F[66,x] = F[62,x]+F[67,x]
F[67,x] = 2*F[24,x]+F[68,x]+F[72,x]
F[68,x] = F[69,x]*F[9,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = F[60,x]
F[71,x] = F[67,x]
F[72,x] = F[73,x]*F[9,x]
F[73,x] = F[74,x]+F[76,x]
F[74,x] = F[75,x]
F[75,x] = F[7,x]*F[9,x]
F[76,x] = F[72,x]
F[77,x] = F[78,x]*F[9,x]
F[78,x] = F[7,x]+F[79,x]
F[79,x] = F[24,x]+F[77,x]+F[80,x]
F[80,x] = F[81,x]*F[9,x]
F[81,x] = F[7,x]+F[79,x]
F[82,x] = 2*F[24,x]+F[72,x]+F[83,x]
F[83,x] = F[84,x]*F[9,x]
F[84,x] = F[85,x]+F[86,x]
F[85,x] = F[57,x]
F[86,x] = F[82,x]
F[87,x] = F[88,x]
F[88,x] = F[89,x,1]
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[91,x,k[0]]
F[91,x,k[0]] = F[101,x,k[0]]*F[9,x]*F[92,x,k[0]]
F[92,x,k[0]] = F[111,x,k[0]]+F[93,x,k[0]]
F[93,x,k[0]] = F[78,x]+F[94,x,k[0]]
F[94,x,k[0]] = F[102,x,k[0]]+F[95,x,k[0]]
F[95,x,k[0]] = F[96,x,k[0]]
F[96,x,k[0]] = F[9,x]*F[97,x,k[0]]
F[97,x,k[0]] = F[95,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[99,x,k[0]]
F[99,x,k[0]] = F[100,x,k[0]]*F[101,x,k[0]]
F[100,x,k[0]] = k[0]*x
F[101,x,k[0]] = F[1,x]+F[98,x,k[0]]
F[102,x,k[0]] = 2*F[24,x]+F[103,x,k[0]]+F[110,x,k[0]]
F[103,x,k[0]] = F[104,x,k[0]]*F[9,x]
F[104,x,k[0]] = F[102,x,k[0]]+F[105,x,k[0]]
F[105,x,k[0]] = F[106,x,k[0]]+F[108,x,k[0]]+F[24,x]
F[106,x,k[0]] = F[100,x,k[0]]*F[107,x,k[0]]
F[107,x,k[0]] = F[105,x,k[0]]+F[7,x]
F[108,x,k[0]] = F[109,x,k[0]]*F[9,x]
F[109,x,k[0]] = F[105,x,k[0]]+F[98,x,k[0]]
F[110,x,k[0]] = F[9,x]*F[94,x,k[0]]
F[111,x,k[0]] = (F[90,x,k[0]]*k[0]-F[90,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_{87}\! \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_{53}\! \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_{17}\! \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_{14}\! \left(x \right) F_{9}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)+F_{30}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right) F_{9}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)
F_{21}\! \left(x \right) = F_{1}\! \left(x \right)+F_{9}\! \left(x \right)
F_{22}\! \left(x \right) = F_{18}\! \left(x \right)+F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{25}\! \left(x \right)+F_{29}\! \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_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{9}\! \left(x \right)
F_{28}\! \left(x \right) = F_{23}\! \left(x \right)
F_{29}\! \left(x \right) = F_{18}\! \left(x \right) F_{9}\! \left(x \right)
F_{30}\! \left(x \right) = F_{24}\! \left(x \right)+F_{31}\! \left(x \right)+F_{51}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right) F_{9}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{36}\! \left(x \right)
F_{33}\! \left(x \right) = F_{15}\! \left(x \right)+F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{15}\! \left(x \right) F_{9}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{38}\! \left(x \right)+F_{42}\! \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_{34}\! \left(x \right)
F_{41}\! \left(x \right) = F_{37}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right) F_{9}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right) F_{9}\! \left(x \right)
F_{45}\! \left(x \right) = F_{33}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{43}\! \left(x \right)+F_{47}\! \left(x \right)
F_{47}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{42}\! \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_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{47}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right) F_{9}\! \left(x \right)
F_{52}\! \left(x \right) = F_{18}\! \left(x \right)+F_{43}\! \left(x \right)
F_{53}\! \left(x \right) = F_{24}\! \left(x \right)+F_{54}\! \left(x \right)+F_{77}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x \right) F_{9}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{61}\! \left(x \right)
F_{56}\! \left(x \right) = F_{57}\! \left(x \right)+F_{7}\! \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_{60}\! \left(x \right)+F_{9}\! \left(x \right)
F_{60}\! \left(x \right) = F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{82}\! \left(x \right)
F_{62}\! \left(x \right) = F_{24}\! \left(x \right)+F_{63}\! \left(x \right)+F_{77}\! \left(x \right)
F_{63}\! \left(x \right) = F_{64}\! \left(x \right) F_{9}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)+F_{66}\! \left(x \right)
F_{65}\! \left(x \right) = F_{60}\! \left(x \right)+F_{7}\! \left(x \right)
F_{66}\! \left(x \right) = F_{62}\! \left(x \right)+F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{68}\! \left(x \right)+F_{72}\! \left(x \right)
F_{68}\! \left(x \right) = F_{69}\! \left(x \right) F_{9}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = F_{60}\! \left(x \right)
F_{71}\! \left(x \right) = F_{67}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right) F_{9}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)+F_{76}\! \left(x \right)
F_{74}\! \left(x \right) = F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{7}\! \left(x \right) F_{9}\! \left(x \right)
F_{76}\! \left(x \right) = F_{72}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right) F_{9}\! \left(x \right)
F_{78}\! \left(x \right) = F_{7}\! \left(x \right)+F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = F_{24}\! \left(x \right)+F_{77}\! \left(x \right)+F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{81}\! \left(x \right) F_{9}\! \left(x \right)
F_{81}\! \left(x \right) = F_{7}\! \left(x \right)+F_{79}\! \left(x \right)
F_{82}\! \left(x \right) = 2 F_{24}\! \left(x \right)+F_{72}\! \left(x \right)+F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right) F_{9}\! \left(x \right)
F_{84}\! \left(x \right) = F_{85}\! \left(x \right)+F_{86}\! \left(x \right)
F_{85}\! \left(x \right) = F_{57}\! \left(x \right)
F_{86}\! \left(x \right) = F_{82}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{89}\! \left(x , 1\right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{101}\! \left(x , y\right) F_{9}\! \left(x \right) F_{92}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{111}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{78}\! \left(x \right)+F_{94}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{9}\! \left(x \right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = F_{95}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{101}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = y x
F_{101}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{98}\! \left(x , y\right)
F_{102}\! \left(x , y\right) = 2 F_{24}\! \left(x \right)+F_{103}\! \left(x , y\right)+F_{110}\! \left(x , y\right)
F_{103}\! \left(x , y\right) = F_{104}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{104}\! \left(x , y\right) = F_{102}\! \left(x , y\right)+F_{105}\! \left(x , y\right)
F_{105}\! \left(x , y\right) = F_{106}\! \left(x , y\right)+F_{108}\! \left(x , y\right)+F_{24}\! \left(x \right)
F_{106}\! \left(x , y\right) = F_{100}\! \left(x , y\right) F_{107}\! \left(x , y\right)
F_{107}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{7}\! \left(x \right)
F_{108}\! \left(x , y\right) = F_{109}\! \left(x , y\right) F_{9}\! \left(x \right)
F_{109}\! \left(x , y\right) = F_{105}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{110}\! \left(x , y\right) = F_{9}\! \left(x \right) F_{94}\! \left(x , y\right)
F_{111}\! \left(x , y\right) = \frac{y F_{90}\! \left(x , y\right)-F_{90}\! \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_87(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_53(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_17(x))
Eq(F_14(x), F_1(x) + F_15(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_14(x)*F_9(x))
Eq(F_17(x), F_18(x) + F_30(x))
Eq(F_18(x), F_19(x))
Eq(F_19(x), F_20(x)*F_9(x))
Eq(F_20(x), F_21(x) + F_22(x))
Eq(F_21(x), F_1(x) + F_9(x))
Eq(F_22(x), F_18(x) + F_23(x))
Eq(F_23(x), F_24(x) + F_25(x) + F_29(x))
Eq(F_24(x), 0)
Eq(F_25(x), F_26(x)*F_9(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_9(x))
Eq(F_28(x), F_23(x))
Eq(F_29(x), F_18(x)*F_9(x))
Eq(F_30(x), F_24(x) + F_31(x) + F_51(x))
Eq(F_31(x), F_32(x)*F_9(x))
Eq(F_32(x), F_33(x) + F_36(x))
Eq(F_33(x), F_15(x) + F_34(x))
Eq(F_34(x), F_35(x))
Eq(F_35(x), F_15(x)*F_9(x))
Eq(F_36(x), F_30(x) + F_37(x))
Eq(F_37(x), 2*F_24(x) + F_38(x) + F_42(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_34(x))
Eq(F_41(x), F_37(x))
Eq(F_42(x), F_43(x)*F_9(x))
Eq(F_43(x), F_44(x))
Eq(F_44(x), F_45(x)*F_9(x))
Eq(F_45(x), F_33(x) + F_46(x))
Eq(F_46(x), F_43(x) + F_47(x))
Eq(F_47(x), 2*F_24(x) + F_42(x) + F_48(x))
Eq(F_48(x), F_49(x)*F_9(x))
Eq(F_49(x), F_40(x) + F_50(x))
Eq(F_50(x), F_47(x))
Eq(F_51(x), F_52(x)*F_9(x))
Eq(F_52(x), F_18(x) + F_43(x))
Eq(F_53(x), F_24(x) + F_54(x) + F_77(x))
Eq(F_54(x), F_55(x)*F_9(x))
Eq(F_55(x), F_56(x) + F_61(x))
Eq(F_56(x), F_57(x) + F_7(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_59(x)*F_9(x))
Eq(F_59(x), F_60(x) + F_9(x))
Eq(F_60(x), F_58(x))
Eq(F_61(x), F_62(x) + F_82(x))
Eq(F_62(x), F_24(x) + F_63(x) + F_77(x))
Eq(F_63(x), F_64(x)*F_9(x))
Eq(F_64(x), F_65(x) + F_66(x))
Eq(F_65(x), F_60(x) + F_7(x))
Eq(F_66(x), F_62(x) + F_67(x))
Eq(F_67(x), 2*F_24(x) + F_68(x) + F_72(x))
Eq(F_68(x), F_69(x)*F_9(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), F_60(x))
Eq(F_71(x), F_67(x))
Eq(F_72(x), F_73(x)*F_9(x))
Eq(F_73(x), F_74(x) + F_76(x))
Eq(F_74(x), F_75(x))
Eq(F_75(x), F_7(x)*F_9(x))
Eq(F_76(x), F_72(x))
Eq(F_77(x), F_78(x)*F_9(x))
Eq(F_78(x), F_7(x) + F_79(x))
Eq(F_79(x), F_24(x) + F_77(x) + F_80(x))
Eq(F_80(x), F_81(x)*F_9(x))
Eq(F_81(x), F_7(x) + F_79(x))
Eq(F_82(x), 2*F_24(x) + F_72(x) + F_83(x))
Eq(F_83(x), F_84(x)*F_9(x))
Eq(F_84(x), F_85(x) + F_86(x))
Eq(F_85(x), F_57(x))
Eq(F_86(x), F_82(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_89(x, 1))
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_91(x, k_0))
Eq(F_91(x, k_0), F_101(x, k_0)*F_9(x)*F_92(x, k_0))
Eq(F_92(x, k_0), F_111(x, k_0) + F_93(x, k_0))
Eq(F_93(x, k_0), F_78(x) + F_94(x, k_0))
Eq(F_94(x, k_0), F_102(x, k_0) + F_95(x, k_0))
Eq(F_95(x, k_0), F_96(x, k_0))
Eq(F_96(x, k_0), F_9(x)*F_97(x, k_0))
Eq(F_97(x, k_0), F_95(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_99(x, k_0))
Eq(F_99(x, k_0), F_100(x, k_0)*F_101(x, k_0))
Eq(F_100(x, k_0), k_0*x)
Eq(F_101(x, k_0), F_1(x) + F_98(x, k_0))
Eq(F_102(x, k_0), F_103(x, k_0) + F_110(x, k_0) + 2*F_24(x))
Eq(F_103(x, k_0), F_104(x, k_0)*F_9(x))
Eq(F_104(x, k_0), F_102(x, k_0) + F_105(x, k_0))
Eq(F_105(x, k_0), F_106(x, k_0) + F_108(x, k_0) + F_24(x))
Eq(F_106(x, k_0), F_100(x, k_0)*F_107(x, k_0))
Eq(F_107(x, k_0), F_105(x, k_0) + F_7(x))
Eq(F_108(x, k_0), F_109(x, k_0)*F_9(x))
Eq(F_109(x, k_0), F_105(x, k_0) + F_98(x, k_0))
Eq(F_110(x, k_0), F_9(x)*F_94(x, k_0))
Eq(F_111(x, k_0), (-k_0*F_90(x, k_0) + F_90(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, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [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, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [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, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [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"}}, {"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": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [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": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 2], [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}}, {"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": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [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": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [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": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 1], [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, 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