0132_0231_1023_1203_3012
Counting sequence:
1, 1, 2, 6, 19, 56, 165, 508, 1632, 5421, 18456, 63990, 224976, 799771, 2869084, 10371698, 37741360, 138127283, 508089121, 1877393851, 6965019708, 25933928737, 96882575863, 363017022246, 1363959128500, 5137734217165, 19397788037399, 73395126396516, 278258935750374, 1056908695451391, 4021406675025873, 15325750212967645, 58495764569084746, 223586621709213575, 855754697062106740, 3279452905594836138, 12582631959447524120, 48331629926380516667, 185846910260016314928, 715351208690398217771, 2756139945644326701622, 10628714365606154693585, 41024069277967539884106, 158473850430018404268343, 612661948147296849179350, 2370354395383735360515037, 9177415509869473217341474, 35557303734171600857386611, 137856098302553508065094958, 534810679624888447592852077, 2076060428862061769309947668, 8063717406109932933855917725, 31338352432494183089826824470, 121857789039914107692121943217, 474086882014385318484094101760, 1845363007914034282826086610467, 7186494070703820065682489269478, 27999888173947682344195791613105, 109142135285274902659409769170560, 425616874429290965945453030548887, 1660462706151415753387023104046682, 6480630721661224857609963521946733, 25303322147159249678427504545301108, 98833566226944681181392347585425684, 386182712851691315563668632393319340, 1509515797680335063550628442854969359, 5902475899262871860074013178591950833, 23087556841149377587482521637177303835, 90336778019644107695383733037756832164, 353581828304411109608511433611586896457, 1384363160274057932711443694328662605639, 5421769984878612353342616714035214402810, 21240242179115598742840740672809413677220, 83234173247946371516986111596104953096669, 326260395983303380405147635106132609873347, 1279217279215202174946200271415488398025604, 5016934808808273422403433837442102192676070, 19680848334932768554178683394160101988061335, 77224932148262366687305993579650975116673829, 303093676947038153135345783888151195073554082, 1189869127874385976002353146232298346916236904, 4672205679622739505492714035832899073670173645, 18350280019294712593531722874190384712951328245, 72087350486552416751522444753848985806347999294, 283249257165188065187241478654117911160121687922, 1113190898892107975680999263581300483953124559799, 4375820979044057113894103593632814831470304914835, 17204277146028832014933343222285505623742066349590, 67654754417223627328600490749943708665458216378004, 266099042239102492158637750662536739986020135580757, 1046814071618034197949294868377392998156719365447309, 4118843187158187497246698042322599011916482839185400, 16209092532380965323388697102951330941364138211367890, 63799637538860258242797337812208359998688643043682359, 251160980082872748889217705259648809132260031258609347, 988915097928702288884231028291205165016163470101985504, 3894369973250661186476942594372992759372019850442369380, 15338585083972811221991282019683947663310500532937674725, 60422940467919475727951670736085199985234063580914309939, 238059487712651160007004536712322544532432055707309826712, 938069192671861174695718242117440280848437110361079823994
Generating function in Maple syntax:
1/2/x*(-1+(1-4*x)^(1/2))*(x^7-x^6-x^5+x^4+3*x^2-3*x+1)/(x-1)^3
Generating function in latex syntax:
\frac{\left(-1+\sqrt{1-4 x}\right) \left(x^{7}-x^{6}-x^{5}+x^{4}+3 x^{2}-3 x +1\right)}{2 x \left(x -1\right)^{3}}
Generating function in sympy syntax:
(sqrt(1 - 4*x) - 1)*(x**7 - x**6 - x**5 + x**4 + 3*x**2 - 3*x + 1)/(2*x*(x - 1)**3)
Implicit equation for the generating function in Maple syntax:
x*(x-1)^6*F(x)^2+(x^7-x^6-x^5+x^4+3*x^2-3*x+1)*(x-1)^3*F(x)+(x^7-x^6-x^5+x^4+3*x^2-3*x+1)^2 = 0
Implicit equation for the generating function in latex syntax:
x \left(x -1\right)^{6} F \! \left(x \right)^{2}+\left(x^{7}-x^{6}-x^{5}+x^{4}+3 x^{2}-3 x +1\right) \left(x -1\right)^{3} F \! \left(x \right)+\left(x^{7}-x^{6}-x^{5}+x^{4}+3 x^{2}-3 x +1\right)^{2} = 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) = 165
a(7) = 508
a(8) = 1632
a(9) = 5421
a(10) = 18456
a(11) = 63990
a(12) = 224976
a(13) = 799771
a(14) = 2869084
a(n+9) = -2*(-7+2*n)/(10+n)*a(n)+3*(-10+3*n)/(10+n)*a(1+n)-2*(n-10)/(10+n)*a(n+2)-8*(1+n)/(10+n)*a(n+3)+6*(1+n)/(10+n)*a(n+4)-(80+13*n)/(10+n)*a(n+5)+9*(20+3*n)/(10+n)*a(n+6)-2*(84+11*n)/(10+n)*a(n+7)+2*(35+4*n)/(10+n)*a(n+8)+(n+4)/(10+n), n >= 15
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) = 165
a \! \left(7\right) = 508
a \! \left(8\right) = 1632
a \! \left(9\right) = 5421
a \! \left(10\right) = 18456
a \! \left(11\right) = 63990
a \! \left(12\right) = 224976
a \! \left(13\right) = 799771
a \! \left(14\right) = 2869084
a \! \left(n +9\right) = -\frac{2 \left(-7+2 n \right) a \! \left(n \right)}{10+n}+\frac{3 \left(-10+3 n \right) a \! \left(1+n \right)}{10+n}-\frac{2 \left(n -10\right) a \! \left(n +2\right)}{10+n}-\frac{8 \left(1+n \right) a \! \left(n +3\right)}{10+n}+\frac{6 \left(1+n \right) a \! \left(n +4\right)}{10+n}-\frac{\left(80+13 n \right) a \! \left(n +5\right)}{10+n}+\frac{9 \left(20+3 n \right) a \! \left(n +6\right)}{10+n}-\frac{2 \left(84+11 n \right) a \! \left(n +7\right)}{10+n}+\frac{2 \left(35+4 n \right) a \! \left(n +8\right)}{10+n}+\frac{n +4}{10+n}, \quad n \geq 15
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21691/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[13,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[53,x]
F[4,x] = F[5,x]
F[5,x] = F[13,x]*F[6,x]
F[6,x] = F[44,x]+F[7,x]
F[7,x] = F[23,x]+F[8,x]
F[8,x] = F[1,x]+F[9,x]
F[9,x] = F[10,x]
F[10,x] = F[11,x]*F[13,x]
F[11,x] = F[12,x]+F[14,x]
F[12,x] = F[1,x]+F[13,x]
F[13,x] = x
F[14,x] = F[15,x]+F[18,x]
F[15,x] = F[16,x]
F[16,x] = F[13,x]*F[17,x]
F[17,x] = F[1,x]+F[15,x]
F[18,x] = F[19,x]+F[20,x]+F[22,x]
F[19,x] = 0
F[20,x] = F[13,x]*F[21,x]
F[21,x] = F[13,x]+F[18,x]
F[22,x] = F[13,x]*F[15,x]
F[23,x] = F[15,x]+F[24,x]
F[24,x] = F[19,x]+F[25,x]+F[30,x]
F[25,x] = F[13,x]*F[26,x]
F[26,x] = F[15,x]+F[27,x]
F[27,x] = F[19,x]+F[25,x]+F[28,x]
F[28,x] = F[13,x]*F[29,x]
F[29,x] = F[15,x]+F[27,x]
F[30,x] = F[13,x]*F[31,x]
F[31,x] = F[32,x]+F[36,x]
F[32,x] = F[15,x]+F[33,x]
F[33,x] = F[34,x]
F[34,x] = F[13,x]*F[35,x]
F[35,x] = F[13,x]+F[33,x]
F[36,x] = F[27,x]+F[37,x]
F[37,x] = 2*F[19,x]+F[38,x]+F[42,x]
F[38,x] = F[13,x]*F[39,x]
F[39,x] = F[40,x]+F[41,x]
F[40,x] = F[22,x]
F[41,x] = F[38,x]
F[42,x] = F[13,x]*F[43,x]
F[43,x] = F[33,x]+F[37,x]
F[44,x] = F[45,x]
F[45,x] = F[13,x]*F[46,x]
F[46,x] = F[47,x]+F[49,x]
F[47,x] = F[17,x]*F[48,x]
F[48,x] = F[13,x]+F[17,x]
F[49,x] = F[50,x]
F[50,x] = F[13,x]^2*F[51,x]
F[51,x] = F[1,x]+F[52,x]
F[52,x] = F[13,x]*F[51,x]
F[53,x] = F[13,x]*F[54,x]
F[54,x] = F[55,x,1]
F[55,x,k[0]] = F[1,x]+F[56,x,k[0]]+F[90,x,k[0]]+F[92,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[13,x]*F[58,x,k[0]]
F[58,x,k[0]] = F[59,x,k[0]]+F[83,x]
F[59,x,k[0]] = F[60,x,k[0]]+F[70,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]+F[65,x,k[0]]
F[61,x,k[0]] = F[1,x]+F[62,x,k[0]]
F[62,x,k[0]] = F[63,x,k[0]]
F[63,x,k[0]] = F[61,x,k[0]]*F[64,x,k[0]]
F[64,x,k[0]] = k[0]*x
F[65,x,k[0]] = F[66,x,k[0]]+F[9,x]
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = F[64,x,k[0]]*F[68,x,k[0]]
F[68,x,k[0]] = F[15,x]+F[69,x,k[0]]
F[69,x,k[0]] = F[67,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]+F[76,x,k[0]]
F[71,x,k[0]] = F[15,x]+F[72,x,k[0]]
F[72,x,k[0]] = F[19,x]+F[73,x,k[0]]+F[75,x,k[0]]
F[73,x,k[0]] = F[13,x]*F[74,x,k[0]]
F[74,x,k[0]] = F[62,x,k[0]]+F[72,x,k[0]]
F[75,x,k[0]] = F[64,x,k[0]]*F[71,x,k[0]]
F[76,x,k[0]] = F[24,x]+F[77,x,k[0]]
F[77,x,k[0]] = 2*F[19,x]+F[78,x,k[0]]+F[81,x,k[0]]
F[78,x,k[0]] = F[13,x]*F[79,x,k[0]]
F[79,x,k[0]] = F[69,x,k[0]]+F[80,x,k[0]]
F[80,x,k[0]] = 2*F[19,x]+F[78,x,k[0]]+F[81,x,k[0]]
F[81,x,k[0]] = F[64,x,k[0]]*F[82,x,k[0]]
F[82,x,k[0]] = F[27,x]+F[80,x,k[0]]
F[83,x] = F[84,x]
F[84,x] = F[13,x]*F[85,x]
F[85,x] = F[86,x]+F[89,x]
F[86,x] = F[51,x]+F[87,x]
F[87,x] = F[88,x]
F[88,x] = F[12,x]*F[13,x]*F[17,x]
F[89,x] = F[15,x]*F[17,x]
F[90,x,k[0]] = F[13,x]*F[91,x,k[0]]
F[91,x,k[0]] = 1/(-1+k[0])*(F[55,x,k[0]]*k[0]-F[55,x,1])
F[92,x,k[0]] = F[55,x,k[0]]*F[64,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_{13}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{53}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{13}\! \left(x \right) F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{44}\! \left(x \right)+F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{23}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{1}\! \left(x \right)+F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)
F_{10}\! \left(x \right) = F_{11}\! \left(x \right) F_{13}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)+F_{14}\! \left(x \right)
F_{12}\! \left(x \right) = F_{1}\! \left(x \right)+F_{13}\! \left(x \right)
F_{13}\! \left(x \right) = x
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{18}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{13}\! \left(x \right) F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{1}\! \left(x \right)+F_{15}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right)+F_{20}\! \left(x \right)+F_{22}\! \left(x \right)
F_{19}\! \left(x \right) = 0
F_{20}\! \left(x \right) = F_{13}\! \left(x \right) F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{13}\! \left(x \right)+F_{18}\! \left(x \right)
F_{22}\! \left(x \right) = F_{13}\! \left(x \right) F_{15}\! \left(x \right)
F_{23}\! \left(x \right) = F_{15}\! \left(x \right)+F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{19}\! \left(x \right)+F_{25}\! \left(x \right)+F_{30}\! \left(x \right)
F_{25}\! \left(x \right) = F_{13}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{15}\! \left(x \right)+F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{19}\! \left(x \right)+F_{25}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{13}\! \left(x \right) F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{15}\! \left(x \right)+F_{27}\! \left(x \right)
F_{30}\! \left(x \right) = F_{13}\! \left(x \right) F_{31}\! \left(x \right)
F_{31}\! \left(x \right) = F_{32}\! \left(x \right)+F_{36}\! \left(x \right)
F_{32}\! \left(x \right) = F_{15}\! \left(x \right)+F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{13}\! \left(x \right) F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{13}\! \left(x \right)+F_{33}\! \left(x \right)
F_{36}\! \left(x \right) = F_{27}\! \left(x \right)+F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = 2 F_{19}\! \left(x \right)+F_{38}\! \left(x \right)+F_{42}\! \left(x \right)
F_{38}\! \left(x \right) = F_{13}\! \left(x \right) F_{39}\! \left(x \right)
F_{39}\! \left(x \right) = F_{40}\! \left(x \right)+F_{41}\! \left(x \right)
F_{40}\! \left(x \right) = F_{22}\! \left(x \right)
F_{41}\! \left(x \right) = F_{38}\! \left(x \right)
F_{42}\! \left(x \right) = F_{13}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{33}\! \left(x \right)+F_{37}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{13}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{47}\! \left(x \right)+F_{49}\! \left(x \right)
F_{47}\! \left(x \right) = F_{17}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{13}\! \left(x \right)+F_{17}\! \left(x \right)
F_{49}\! \left(x \right) = F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{13} \left(x \right)^{2} F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{1}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{13}\! \left(x \right) F_{51}\! \left(x \right)
F_{53}\! \left(x \right) = F_{13}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{55}\! \left(x , 1\right)
F_{55}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{56}\! \left(x , y\right)+F_{90}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{58}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{83}\! \left(x \right)
F_{59}\! \left(x , y\right) = F_{60}\! \left(x , y\right)+F_{70}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right)+F_{65}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{62}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{63}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{61}\! \left(x , y\right) F_{64}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = y x
F_{65}\! \left(x , y\right) = F_{66}\! \left(x , y\right)+F_{9}\! \left(x \right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{64}\! \left(x , y\right) F_{68}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)+F_{76}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{15}\! \left(x \right)+F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{19}\! \left(x \right)+F_{73}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{74}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{62}\! \left(x , y\right)+F_{72}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = F_{64}\! \left(x , y\right) F_{71}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{24}\! \left(x \right)+F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = 2 F_{19}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{79}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{69}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = 2 F_{19}\! \left(x \right)+F_{78}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{64}\! \left(x , y\right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{27}\! \left(x \right)+F_{80}\! \left(x , y\right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{13}\! \left(x \right) F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)+F_{89}\! \left(x \right)
F_{86}\! \left(x \right) = F_{51}\! \left(x \right)+F_{87}\! \left(x \right)
F_{87}\! \left(x \right) = F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{12}\! \left(x \right) F_{13}\! \left(x \right) F_{17}\! \left(x \right)
F_{89}\! \left(x \right) = F_{15}\! \left(x \right) F_{17}\! \left(x \right)
F_{90}\! \left(x , y\right) = F_{13}\! \left(x \right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = \frac{F_{55}\! \left(x , y\right) y -F_{55}\! \left(x , 1\right)}{-1+y}
F_{92}\! \left(x , y\right) = F_{55}\! \left(x , y\right) F_{64}\! \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_13(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_53(x))
Eq(F_4(x), F_5(x))
Eq(F_5(x), F_13(x)*F_6(x))
Eq(F_6(x), F_44(x) + F_7(x))
Eq(F_7(x), F_23(x) + F_8(x))
Eq(F_8(x), F_1(x) + F_9(x))
Eq(F_9(x), F_10(x))
Eq(F_10(x), F_11(x)*F_13(x))
Eq(F_11(x), F_12(x) + F_14(x))
Eq(F_12(x), F_1(x) + F_13(x))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x) + F_18(x))
Eq(F_15(x), F_16(x))
Eq(F_16(x), F_13(x)*F_17(x))
Eq(F_17(x), F_1(x) + F_15(x))
Eq(F_18(x), F_19(x) + F_20(x) + F_22(x))
Eq(F_19(x), 0)
Eq(F_20(x), F_13(x)*F_21(x))
Eq(F_21(x), F_13(x) + F_18(x))
Eq(F_22(x), F_13(x)*F_15(x))
Eq(F_23(x), F_15(x) + F_24(x))
Eq(F_24(x), F_19(x) + F_25(x) + F_30(x))
Eq(F_25(x), F_13(x)*F_26(x))
Eq(F_26(x), F_15(x) + F_27(x))
Eq(F_27(x), F_19(x) + F_25(x) + F_28(x))
Eq(F_28(x), F_13(x)*F_29(x))
Eq(F_29(x), F_15(x) + F_27(x))
Eq(F_30(x), F_13(x)*F_31(x))
Eq(F_31(x), F_32(x) + F_36(x))
Eq(F_32(x), F_15(x) + F_33(x))
Eq(F_33(x), F_34(x))
Eq(F_34(x), F_13(x)*F_35(x))
Eq(F_35(x), F_13(x) + F_33(x))
Eq(F_36(x), F_27(x) + F_37(x))
Eq(F_37(x), 2*F_19(x) + F_38(x) + F_42(x))
Eq(F_38(x), F_13(x)*F_39(x))
Eq(F_39(x), F_40(x) + F_41(x))
Eq(F_40(x), F_22(x))
Eq(F_41(x), F_38(x))
Eq(F_42(x), F_13(x)*F_43(x))
Eq(F_43(x), F_33(x) + F_37(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_13(x)*F_46(x))
Eq(F_46(x), F_47(x) + F_49(x))
Eq(F_47(x), F_17(x)*F_48(x))
Eq(F_48(x), F_13(x) + F_17(x))
Eq(F_49(x), F_50(x))
Eq(F_50(x), F_13(x)**2*F_51(x))
Eq(F_51(x), F_1(x) + F_52(x))
Eq(F_52(x), F_13(x)*F_51(x))
Eq(F_53(x), F_13(x)*F_54(x))
Eq(F_54(x), F_55(x, 1))
Eq(F_55(x, k_0), F_1(x) + F_56(x, k_0) + F_90(x, k_0) + F_92(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_13(x)*F_58(x, k_0))
Eq(F_58(x, k_0), F_59(x, k_0) + F_83(x))
Eq(F_59(x, k_0), F_60(x, k_0) + F_70(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0) + F_65(x, k_0))
Eq(F_61(x, k_0), F_1(x) + F_62(x, k_0))
Eq(F_62(x, k_0), F_63(x, k_0))
Eq(F_63(x, k_0), F_61(x, k_0)*F_64(x, k_0))
Eq(F_64(x, k_0), k_0*x)
Eq(F_65(x, k_0), F_66(x, k_0) + F_9(x))
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), F_64(x, k_0)*F_68(x, k_0))
Eq(F_68(x, k_0), F_15(x) + F_69(x, k_0))
Eq(F_69(x, k_0), F_67(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0) + F_76(x, k_0))
Eq(F_71(x, k_0), F_15(x) + F_72(x, k_0))
Eq(F_72(x, k_0), F_19(x) + F_73(x, k_0) + F_75(x, k_0))
Eq(F_73(x, k_0), F_13(x)*F_74(x, k_0))
Eq(F_74(x, k_0), F_62(x, k_0) + F_72(x, k_0))
Eq(F_75(x, k_0), F_64(x, k_0)*F_71(x, k_0))
Eq(F_76(x, k_0), F_24(x) + F_77(x, k_0))
Eq(F_77(x, k_0), 2*F_19(x) + F_78(x, k_0) + F_81(x, k_0))
Eq(F_78(x, k_0), F_13(x)*F_79(x, k_0))
Eq(F_79(x, k_0), F_69(x, k_0) + F_80(x, k_0))
Eq(F_80(x, k_0), 2*F_19(x) + F_78(x, k_0) + F_81(x, k_0))
Eq(F_81(x, k_0), F_64(x, k_0)*F_82(x, k_0))
Eq(F_82(x, k_0), F_27(x) + F_80(x, k_0))
Eq(F_83(x), F_84(x))
Eq(F_84(x), F_13(x)*F_85(x))
Eq(F_85(x), F_86(x) + F_89(x))
Eq(F_86(x), F_51(x) + F_87(x))
Eq(F_87(x), F_88(x))
Eq(F_88(x), F_12(x)*F_13(x)*F_17(x))
Eq(F_89(x), F_15(x)*F_17(x))
Eq(F_90(x, k_0), F_13(x)*F_91(x, k_0))
Eq(F_91(x, k_0), (k_0*F_55(x, k_0) - F_55(x, 1))/(k_0 - 1))
Eq(F_92(x, k_0), F_55(x, k_0)*F_64(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, 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, 0, 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], "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], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "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, 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, 0, 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_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"}}, {"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], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0, 3], "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], [2, 0]]}, {"patt": [1, 0, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 0], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [2, 0], [2, 0], [2, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [2, 0], [2, 0]]}, {"patt": [1, 2, 0, 3], "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}}, {"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], "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": [[0, 1], [2, 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], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [3, 1], [3, 1]]}, {"patt": [0, 1, 2], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [0, 2, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "pos": [[3, 1], [3, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[3, 1], [3, 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": [3, 0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1], [2, 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": [[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], [0, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [3, 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]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 1], [0, 1], [3, 1]]}, {"patt": [1, 0, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [1, 1], [1, 1], [1, 1]]}, {"patt": 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