0123_0213_0231_0312_1230
Counting sequence:
1, 1, 2, 6, 19, 61, 198, 651, 2171, 7345, 25194, 87516, 307462, 1091026, 3905580, 14088665, 51165715, 186923705, 686483650, 2532947000, 9385112530, 34905108470, 130262393140, 487635569270, 1830633108574, 6890248857626, 25996000238628, 98296251919656, 372439551601516, 1413839817188036, 5376675968066648, 20480759256616533, 78135960848962051, 298529351193892105, 1142132549248223666, 4375270420841774720, 16781109690486970906, 64436939824827929422, 247697139726180364388, 953134984070708085402, 3671237775900925777834, 14153841729433281780478, 54616067736856617277356, 210927266175256244122152, 815256742826519385712404, 3153477740932204799929788, 12206866219727338223564136, 47285059631035301870257722, 183288915035515748942031534, 710933403251288223574250250, 2759248320836950597239674484, 10715468409252439788031782096, 41637056436007028487351391092, 161878031711509548889883394396, 629688743049417509026680034824, 2450674513223917983347676590316, 9542431619655937121804922259548, 37173944551633033779312927091476, 144882939607768646190329293618056, 564921461197217122173558490878480, 2203660431573854997269747998616664, 8599652862008868616609160622043656, 33573064543882388365755926164105392, 131120113944906274043248697881101261, 512283809463811600951859594983096035, 2002211171643954231509264656550130345, 7828206184821484869660946081991993490, 30617037233888254798814039177947926480, 119786591860219965125461250699690866410, 468806037209739102618162101576682299070, 1835329756330584214443296946224834409540, 7187321826376775742258808115799446366130, 28154542009396563517537732428668238497010, 110320113069514999453935763727436039136470, 432396724695346542341270582773077302389980, 1695228736144891197532557358402958332659240, 6647973869911604173427203911674009861524740, 26077285881839410198908622172032738324483980, 102316263718038090370967648711230396234029000, 401544222272998737161317630318216685299864590, 1576252697706536388340294139756962730763615290, 6188985786278792087757912853985900421094879150, 24305906960238704255856092051376655838418723900, 95477379987652505902401854322000169999926764880, 375131184866303158290822979380584603641143369820, 1474204180482704839818152101480808452441733657620, 5794577280560265460149320909799879338168443944600, 22781035619307159146880054294148260902552623565300, 89579936916155281132672905285508909665990440682340, 352315456715883017621733468902950398812479127735340, 1385908095342357106278416110077454833438190438133880, 5452769665164363319521333101602875665201404094314160, 21457450318436256578823740343684203188280246546489320, 84453107116137034816563863731656362526742259192557240, 332451325392518769643452613542181455935781685838070480, 1308922226709048326219132757334996136810543573515377410, 5154320514328545824980614408970822613487082258686315470, 20300153382403284493561630252764491732140382012658787690, 79964292273872396946730212725535560376879034001795736980, 315036127916243210336075387392060085614066064029476155200, 1241340014058787209915313603854489093358907235371400561380
Generating function in Maple syntax:
((-x^2-x+1)*(1-4*x)^(1/2)+3*x^2+x-1)/(4*x^2-2*x)
Generating function in latex syntax:
\frac{\left(-x^{2}-x +1\right) \sqrt{1-4 x}+3 x^{2}+x -1}{4 x^{2}-2 x}
Generating function in sympy syntax:
(3*x**2 + x + sqrt(1 - 4*x)*(-x**2 - x + 1) - 1)/(4*x**2 - 2*x)
Implicit equation for the generating function in Maple syntax:
x*(2*x-1)^2*F(x)^2-(2*x-1)*(3*x^2+x-1)*F(x)+x^4+4*x^3-3*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(2 x -1\right)^{2} F \! \left(x \right)^{2}-\left(2 x -1\right) \left(3 x^{2}+x -1\right) F \! \left(x \right)+x^{4}+4 x^{3}-3 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 19
a(n+4) = 4*(2*n-1)/(n+5)*a(n)+2*(n+6)/(n+5)*a(1+n)-13*(n+3)/(n+5)*a(n+2)+(27+7*n)/(n+5)*a(n+3), n >= 5
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(n +4\right) = \frac{4 \left(2 n -1\right) a \! \left(n \right)}{n +5}+\frac{2 \left(n +6\right) a \! \left(1+n \right)}{n +5}-\frac{13 \left(n +3\right) a \! \left(n +2\right)}{n +5}+\frac{\left(27+7 n \right) a \! \left(n +3\right)}{n +5}, \quad n \geq 5
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://permpal.com/tree/21517/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[11,x]*F[3,x]
F[3,x] = F[1,x]+F[101,x]+F[4,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[6,x,1]
F[6,x,k[0]] = F[1,x]+F[12,x,k[0]]+F[7,x,k[0]]+F[9,x,k[0]]
F[7,x,k[0]] = F[6,x,k[0]]*F[8,x,k[0]]
F[8,x,k[0]] = k[0]*x
F[9,x,k[0]] = F[10,x,k[0]]*F[11,x]
F[10,x,k[0]] = (F[6,x,k[0]]*k[0]-F[6,x,1])/(-1+k[0])
F[11,x] = x
F[12,x,k[0]] = F[11,x]*F[13,x,k[0]]
F[13,x,k[0]] = F[14,x]+F[53,x,k[0]]
F[14,x] = F[15,x]+F[22,x]
F[15,x] = F[16,x]+F[19,x]
F[16,x] = F[1,x]+F[17,x]
F[17,x] = F[18,x]
F[18,x] = F[11,x]*F[16,x]
F[19,x] = F[11,x]+F[20,x]
F[20,x] = F[21,x]
F[21,x] = F[11,x]*F[17,x]
F[22,x] = F[23,x]+F[52,x]
F[23,x] = F[24,x]+F[36,x]
F[24,x] = F[25,x]
F[25,x] = F[11,x]*F[26,x]
F[26,x] = F[27,x]+F[28,x]
F[27,x] = F[1,x]+F[11,x]
F[28,x] = F[24,x]+F[29,x]
F[29,x] = F[30,x]+F[31,x]+F[35,x]
F[30,x] = 0
F[31,x] = F[11,x]*F[32,x]
F[32,x] = F[33,x]+F[34,x]
F[33,x] = F[11,x]
F[34,x] = F[29,x]
F[35,x] = F[11,x]*F[24,x]
F[36,x] = F[30,x]+F[37,x]+F[47,x]
F[37,x] = F[11,x]*F[38,x]
F[38,x] = F[39,x]+F[40,x]
F[39,x] = F[17,x]+F[20,x]
F[40,x] = F[36,x]+F[41,x]
F[41,x] = 2*F[30,x]+F[42,x]+F[46,x]
F[42,x] = F[11,x]*F[43,x]
F[43,x] = F[44,x]+F[45,x]
F[44,x] = F[20,x]
F[45,x] = F[41,x]
F[46,x] = F[11,x]*F[36,x]
F[47,x] = F[11,x]*F[48,x]
F[48,x] = F[17,x]+F[49,x]
F[49,x] = F[30,x]+F[47,x]+F[50,x]
F[50,x] = F[11,x]*F[51,x]
F[51,x] = F[17,x]+F[49,x]
F[52,x] = F[29,x]+F[41,x]
F[53,x,k[0]] = F[54,x,k[0]]+F[68,x,k[0]]
F[54,x,k[0]] = F[55,x,k[0]]+F[63,x,k[0]]
F[55,x,k[0]] = F[56,x,k[0]]+F[59,x,k[0]]
F[56,x,k[0]] = F[57,x,k[0]]
F[57,x,k[0]] = F[58,x,k[0]]*F[8,x,k[0]]
F[58,x,k[0]] = F[1,x]+F[56,x,k[0]]
F[59,x,k[0]] = F[30,x]+F[60,x,k[0]]+F[62,x,k[0]]
F[60,x,k[0]] = F[61,x,k[0]]*F[8,x,k[0]]
F[61,x,k[0]] = F[17,x]+F[59,x,k[0]]
F[62,x,k[0]] = F[11,x]*F[55,x,k[0]]
F[63,x,k[0]] = F[64,x,k[0]]+F[66,x,k[0]]
F[64,x,k[0]] = F[65,x,k[0]]
F[65,x,k[0]] = F[11,x]*F[56,x,k[0]]
F[66,x,k[0]] = F[67,x,k[0]]
F[67,x,k[0]] = F[11,x]*F[59,x,k[0]]
F[68,x,k[0]] = F[100,x,k[0]]+F[69,x,k[0]]
F[69,x,k[0]] = F[70,x,k[0]]+F[81,x,k[0]]
F[70,x,k[0]] = F[71,x,k[0]]
F[71,x,k[0]] = F[11,x]*F[72,x,k[0]]
F[72,x,k[0]] = F[73,x,k[0]]+F[74,x,k[0]]
F[73,x,k[0]] = F[56,x,k[0]]+F[64,x,k[0]]
F[74,x,k[0]] = F[70,x,k[0]]+F[75,x,k[0]]
F[75,x,k[0]] = 2*F[30,x]+F[76,x,k[0]]+F[80,x,k[0]]
F[76,x,k[0]] = F[11,x]*F[77,x,k[0]]
F[77,x,k[0]] = F[78,x,k[0]]+F[79,x,k[0]]
F[78,x,k[0]] = F[64,x,k[0]]
F[79,x,k[0]] = F[75,x,k[0]]
F[80,x,k[0]] = F[11,x]*F[70,x,k[0]]
F[81,x,k[0]] = 2*F[30,x]+F[82,x,k[0]]+F[92,x,k[0]]
F[82,x,k[0]] = F[11,x]*F[83,x,k[0]]
F[83,x,k[0]] = F[84,x,k[0]]+F[85,x,k[0]]
F[84,x,k[0]] = F[59,x,k[0]]+F[66,x,k[0]]
F[85,x,k[0]] = F[81,x,k[0]]+F[86,x,k[0]]
F[86,x,k[0]] = 3*F[30,x]+F[87,x,k[0]]+F[91,x,k[0]]
F[87,x,k[0]] = F[11,x]*F[88,x,k[0]]
F[88,x,k[0]] = F[89,x,k[0]]+F[90,x,k[0]]
F[89,x,k[0]] = F[66,x,k[0]]
F[90,x,k[0]] = F[86,x,k[0]]
F[91,x,k[0]] = F[11,x]*F[81,x,k[0]]
F[92,x,k[0]] = F[11,x]*F[93,x,k[0]]
F[93,x,k[0]] = F[94,x,k[0]]+F[97,x,k[0]]
F[94,x,k[0]] = F[95,x,k[0]]
F[95,x,k[0]] = F[11,x]*F[96,x,k[0]]
F[96,x,k[0]] = F[56,x,k[0]]+F[94,x,k[0]]
F[97,x,k[0]] = 2*F[30,x]+F[92,x,k[0]]+F[98,x,k[0]]
F[98,x,k[0]] = F[11,x]*F[99,x,k[0]]
F[99,x,k[0]] = F[59,x,k[0]]+F[97,x,k[0]]
F[100,x,k[0]] = F[75,x,k[0]]+F[86,x,k[0]]
F[101,x] = F[11,x]*F[14,x]
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_{11}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{101}\! \left(x \right)+F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{6}\! \left(x , 1\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{12}\! \left(x , y\right)+F_{7}\! \left(x , y\right)+F_{9}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{6}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = y x
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right) F_{11}\! \left(x \right)
F_{10}\! \left(x , y\right) = \frac{y F_{6}\! \left(x , y\right)-F_{6}\! \left(x , 1\right)}{-1+y}
F_{11}\! \left(x \right) = x
F_{12}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x \right)+F_{53}\! \left(x , y\right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)+F_{22}\! \left(x \right)
F_{15}\! \left(x \right) = F_{16}\! \left(x \right)+F_{19}\! \left(x \right)
F_{16}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right)
F_{19}\! \left(x \right) = F_{11}\! \left(x \right)+F_{20}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right)
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{52}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)+F_{36}\! \left(x \right)
F_{24}\! \left(x \right) = F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{11}\! \left(x \right) F_{26}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{28}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{28}\! \left(x \right) = F_{24}\! \left(x \right)+F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)+F_{35}\! \left(x \right)
F_{30}\! \left(x \right) = 0
F_{31}\! \left(x \right) = F_{11}\! \left(x \right) F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{33}\! \left(x \right)+F_{34}\! \left(x \right)
F_{33}\! \left(x \right) = F_{11}\! \left(x \right)
F_{34}\! \left(x \right) = F_{29}\! \left(x \right)
F_{35}\! \left(x \right) = F_{11}\! \left(x \right) F_{24}\! \left(x \right)
F_{36}\! \left(x \right) = F_{30}\! \left(x \right)+F_{37}\! \left(x \right)+F_{47}\! \left(x \right)
F_{37}\! \left(x \right) = F_{11}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{39}\! \left(x \right)+F_{40}\! \left(x \right)
F_{39}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{40}\! \left(x \right) = F_{36}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = 2 F_{30}\! \left(x \right)+F_{42}\! \left(x \right)+F_{46}\! \left(x \right)
F_{42}\! \left(x \right) = F_{11}\! \left(x \right) F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{44}\! \left(x \right)+F_{45}\! \left(x \right)
F_{44}\! \left(x \right) = F_{20}\! \left(x \right)
F_{45}\! \left(x \right) = F_{41}\! \left(x \right)
F_{46}\! \left(x \right) = F_{11}\! \left(x \right) F_{36}\! \left(x \right)
F_{47}\! \left(x \right) = F_{11}\! \left(x \right) F_{48}\! \left(x \right)
F_{48}\! \left(x \right) = F_{17}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{30}\! \left(x \right)+F_{47}\! \left(x \right)+F_{50}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{17}\! \left(x \right)+F_{49}\! \left(x \right)
F_{52}\! \left(x \right) = F_{29}\! \left(x \right)+F_{41}\! \left(x \right)
F_{53}\! \left(x , y\right) = F_{54}\! \left(x , y\right)+F_{68}\! \left(x , y\right)
F_{54}\! \left(x , y\right) = F_{55}\! \left(x , y\right)+F_{63}\! \left(x , y\right)
F_{55}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{59}\! \left(x , y\right)
F_{56}\! \left(x , y\right) = F_{57}\! \left(x , y\right)
F_{57}\! \left(x , y\right) = F_{58}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{58}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{56}\! \left(x , y\right)
F_{59}\! \left(x , y\right) = F_{30}\! \left(x \right)+F_{60}\! \left(x , y\right)+F_{62}\! \left(x , y\right)
F_{60}\! \left(x , y\right) = F_{61}\! \left(x , y\right) F_{8}\! \left(x , y\right)
F_{61}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{59}\! \left(x , y\right)
F_{62}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{55}\! \left(x , y\right)
F_{63}\! \left(x , y\right) = F_{64}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{64}\! \left(x , y\right) = F_{65}\! \left(x , y\right)
F_{65}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{56}\! \left(x , y\right)
F_{66}\! \left(x , y\right) = F_{67}\! \left(x , y\right)
F_{67}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{59}\! \left(x , y\right)
F_{68}\! \left(x , y\right) = F_{100}\! \left(x , y\right)+F_{69}\! \left(x , y\right)
F_{69}\! \left(x , y\right) = F_{70}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{70}\! \left(x , y\right) = F_{71}\! \left(x , y\right)
F_{71}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{72}\! \left(x , y\right)
F_{72}\! \left(x , y\right) = F_{73}\! \left(x , y\right)+F_{74}\! \left(x , y\right)
F_{73}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{64}\! \left(x , y\right)
F_{74}\! \left(x , y\right) = F_{70}\! \left(x , y\right)+F_{75}\! \left(x , y\right)
F_{75}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{76}\! \left(x , y\right)+F_{80}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{77}\! \left(x , y\right)
F_{77}\! \left(x , y\right) = F_{78}\! \left(x , y\right)+F_{79}\! \left(x , y\right)
F_{78}\! \left(x , y\right) = F_{64}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{75}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{70}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{82}\! \left(x , y\right)+F_{92}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{83}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{84}\! \left(x , y\right)+F_{85}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{66}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{81}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = 3 F_{30}\! \left(x \right)+F_{87}\! \left(x , y\right)+F_{91}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{89}\! \left(x , y\right)+F_{90}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{66}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{81}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{93}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{94}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{94}\! \left(x , y\right) = F_{95}\! \left(x , y\right)
F_{95}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{96}\! \left(x , y\right)
F_{96}\! \left(x , y\right) = F_{56}\! \left(x , y\right)+F_{94}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = 2 F_{30}\! \left(x \right)+F_{92}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{98}\! \left(x , y\right) = F_{11}\! \left(x \right) F_{99}\! \left(x , y\right)
F_{99}\! \left(x , y\right) = F_{59}\! \left(x , y\right)+F_{97}\! \left(x , y\right)
F_{100}\! \left(x , y\right) = F_{75}\! \left(x , y\right)+F_{86}\! \left(x , y\right)
F_{101}\! \left(x \right) = F_{11}\! \left(x \right) F_{14}\! \left(x \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_11(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_101(x) + F_4(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_6(x, 1))
Eq(F_6(x, k_0), F_1(x) + F_12(x, k_0) + F_7(x, k_0) + F_9(x, k_0))
Eq(F_7(x, k_0), F_6(x, k_0)*F_8(x, k_0))
Eq(F_8(x, k_0), k_0*x)
Eq(F_9(x, k_0), F_10(x, k_0)*F_11(x))
Eq(F_10(x, k_0), (-k_0*F_6(x, k_0) + F_6(x, 1))/(1 - k_0))
Eq(F_11(x), x)
Eq(F_12(x, k_0), F_11(x)*F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x) + F_53(x, k_0))
Eq(F_14(x), F_15(x) + F_22(x))
Eq(F_15(x), F_16(x) + F_19(x))
Eq(F_16(x), F_1(x) + F_17(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_11(x)*F_16(x))
Eq(F_19(x), F_11(x) + F_20(x))
Eq(F_20(x), F_21(x))
Eq(F_21(x), F_11(x)*F_17(x))
Eq(F_22(x), F_23(x) + F_52(x))
Eq(F_23(x), F_24(x) + F_36(x))
Eq(F_24(x), F_25(x))
Eq(F_25(x), F_11(x)*F_26(x))
Eq(F_26(x), F_27(x) + F_28(x))
Eq(F_27(x), F_1(x) + F_11(x))
Eq(F_28(x), F_24(x) + F_29(x))
Eq(F_29(x), F_30(x) + F_31(x) + F_35(x))
Eq(F_30(x), 0)
Eq(F_31(x), F_11(x)*F_32(x))
Eq(F_32(x), F_33(x) + F_34(x))
Eq(F_33(x), F_11(x))
Eq(F_34(x), F_29(x))
Eq(F_35(x), F_11(x)*F_24(x))
Eq(F_36(x), F_30(x) + F_37(x) + F_47(x))
Eq(F_37(x), F_11(x)*F_38(x))
Eq(F_38(x), F_39(x) + F_40(x))
Eq(F_39(x), F_17(x) + F_20(x))
Eq(F_40(x), F_36(x) + F_41(x))
Eq(F_41(x), 2*F_30(x) + F_42(x) + F_46(x))
Eq(F_42(x), F_11(x)*F_43(x))
Eq(F_43(x), F_44(x) + F_45(x))
Eq(F_44(x), F_20(x))
Eq(F_45(x), F_41(x))
Eq(F_46(x), F_11(x)*F_36(x))
Eq(F_47(x), F_11(x)*F_48(x))
Eq(F_48(x), F_17(x) + F_49(x))
Eq(F_49(x), F_30(x) + F_47(x) + F_50(x))
Eq(F_50(x), F_11(x)*F_51(x))
Eq(F_51(x), F_17(x) + F_49(x))
Eq(F_52(x), F_29(x) + F_41(x))
Eq(F_53(x, k_0), F_54(x, k_0) + F_68(x, k_0))
Eq(F_54(x, k_0), F_55(x, k_0) + F_63(x, k_0))
Eq(F_55(x, k_0), F_56(x, k_0) + F_59(x, k_0))
Eq(F_56(x, k_0), F_57(x, k_0))
Eq(F_57(x, k_0), F_58(x, k_0)*F_8(x, k_0))
Eq(F_58(x, k_0), F_1(x) + F_56(x, k_0))
Eq(F_59(x, k_0), F_30(x) + F_60(x, k_0) + F_62(x, k_0))
Eq(F_60(x, k_0), F_61(x, k_0)*F_8(x, k_0))
Eq(F_61(x, k_0), F_17(x) + F_59(x, k_0))
Eq(F_62(x, k_0), F_11(x)*F_55(x, k_0))
Eq(F_63(x, k_0), F_64(x, k_0) + F_66(x, k_0))
Eq(F_64(x, k_0), F_65(x, k_0))
Eq(F_65(x, k_0), F_11(x)*F_56(x, k_0))
Eq(F_66(x, k_0), F_67(x, k_0))
Eq(F_67(x, k_0), F_11(x)*F_59(x, k_0))
Eq(F_68(x, k_0), F_100(x, k_0) + F_69(x, k_0))
Eq(F_69(x, k_0), F_70(x, k_0) + F_81(x, k_0))
Eq(F_70(x, k_0), F_71(x, k_0))
Eq(F_71(x, k_0), F_11(x)*F_72(x, k_0))
Eq(F_72(x, k_0), F_73(x, k_0) + F_74(x, k_0))
Eq(F_73(x, k_0), F_56(x, k_0) + F_64(x, k_0))
Eq(F_74(x, k_0), F_70(x, k_0) + F_75(x, k_0))
Eq(F_75(x, k_0), 2*F_30(x) + F_76(x, k_0) + F_80(x, k_0))
Eq(F_76(x, k_0), F_11(x)*F_77(x, k_0))
Eq(F_77(x, k_0), F_78(x, k_0) + F_79(x, k_0))
Eq(F_78(x, k_0), F_64(x, k_0))
Eq(F_79(x, k_0), F_75(x, k_0))
Eq(F_80(x, k_0), F_11(x)*F_70(x, k_0))
Eq(F_81(x, k_0), 2*F_30(x) + F_82(x, k_0) + F_92(x, k_0))
Eq(F_82(x, k_0), F_11(x)*F_83(x, k_0))
Eq(F_83(x, k_0), F_84(x, k_0) + F_85(x, k_0))
Eq(F_84(x, k_0), F_59(x, k_0) + F_66(x, k_0))
Eq(F_85(x, k_0), F_81(x, k_0) + F_86(x, k_0))
Eq(F_86(x, k_0), 3*F_30(x) + F_87(x, k_0) + F_91(x, k_0))
Eq(F_87(x, k_0), F_11(x)*F_88(x, k_0))
Eq(F_88(x, k_0), F_89(x, k_0) + F_90(x, k_0))
Eq(F_89(x, k_0), F_66(x, k_0))
Eq(F_90(x, k_0), F_86(x, k_0))
Eq(F_91(x, k_0), F_11(x)*F_81(x, k_0))
Eq(F_92(x, k_0), F_11(x)*F_93(x, k_0))
Eq(F_93(x, k_0), F_94(x, k_0) + F_97(x, k_0))
Eq(F_94(x, k_0), F_95(x, k_0))
Eq(F_95(x, k_0), F_11(x)*F_96(x, k_0))
Eq(F_96(x, k_0), F_56(x, k_0) + F_94(x, k_0))
Eq(F_97(x, k_0), 2*F_30(x) + F_92(x, k_0) + F_98(x, k_0))
Eq(F_98(x, k_0), F_11(x)*F_99(x, k_0))
Eq(F_99(x, k_0), F_59(x, k_0) + F_97(x, k_0))
Eq(F_100(x, k_0), F_75(x, k_0) + F_86(x, k_0))
Eq(F_101(x), F_11(x)*F_14(x))
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, 2, 3], "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": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2, 3], "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": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_placement", "direction": 3, "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], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 2, 3, 0], "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, 0]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0, 1], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 0], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [2, 0, 1], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 1, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}], "requirements": [[{"patt": [0], "pos": [[1, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 1], [2, 1]], [[1, 0]]], "strategy_class": "FactorStrategy", "workable": true}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": 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