0123_0132_0213_0231_1023_3012
Counting sequence:
1, 1, 2, 6, 18, 55, 170, 540, 1763, 5897, 20121, 69769, 245114, 870510, 3119772, 11267594, 40967499, 149823450, 550747530, 2033807960, 7541267304, 28065954782, 104801109658, 392529781966, 1474304052788, 5551499852546, 20953440258862, 79258335527286, 300407324722206, 1140750526305254, 4339406442118602, 16534071563466323, 63094893367556736, 241119734790301729, 922695369339846350, 3535387953788364266, 13562443607934121996, 52087374738149087201, 200260109212291360605, 770725489312194040939, 2969107749948601493498, 11448602514035141138086, 44183497258816915186804, 170659690497512787514931, 659703001510265494601047, 2552096616070588793453421, 9880124811529416426286062, 38276381167140600125296978, 148384909770200307168560086, 575608392531872831135833243, 2234250272077813609801993041, 8677473832882597078337892223, 33721095707229289834399288452, 131113545062962453620142362452, 510061010808612266477789452562, 1985258349989600481799480531281, 7730798858481834105236793745719, 30118731294385784503626761968737, 117394253739861329992798475447774, 457770856618218044348148649474878, 1785805618475329827887254296339584, 6969456260138684603693191837413967, 27210498288520560287322507547551877, 106277535333400166843540143407992996, 415248994250409928744089324878621354, 1623053506332652230967653439425849803, 6346137002485630453195838644524565834, 24821832935301097794132288208999826801, 97118438955186873075606408734820887161, 380109575334983379856277494950533028600, 1488165424890564894670964531033546036061, 5828074218291231993439977057143397852223, 22831094960723782877149791347709763795108, 89464904139411621799149825968211265896667, 350670787477455521501032731038984380565163, 1374878028970345364130956404867361484061120, 5391918844468559144301168696068769952942605, 21151157111383265303948057957127048068676419, 82991508258236323549674394918833355836395390, 325716055724799921928838033840329206764269137, 1278639173062357678752213069971996946504911327, 5020623064605553310697891262366746823854191786, 19718121513380862836315497751512274309092405197, 77458556204701952423885716069227603227619929479, 304345514724583199204878286528138944864298056394, 1196067956890063792497624371062282000902294009633, 4701474849371987372859861183905414776761317444889, 18484156372430230416704886496960777828313951413646, 72685941386645268781198950611583769069682584930521, 285880514419340086779494126109345734880022591272475, 1124605452830833816630780559964055387022861694922786, 4424819055826327015638791666260166764411665453248473, 17412808037505129951151916918005638781552103195518553, 68535943412178239967763574317161553060390941233123402, 269800431178956037359438592090184692755644239237452413, 1062282361925666909340174480888183983249171367226395005, 4183202265016240426705288680433342995432255727497486890, 16475850485916774262768335005090141461075314623468452399, 64901610389348208269821992117610930757980041595219201825, 255699787803439000179849742607560317258881252172696954782, 1007560606324584188618700271562130745093268545584460497137
Generating function in Maple syntax:
1/2*((-x^5-x^4+3*x^2-3*x+1)*(1-4*x)^(1/2)-2*x^6+x^5-x^4+2*x^3-3*x^2+3*x-1)/x/(x^2+x-1)/(x-1)^2
Generating function in latex syntax:
\frac{\left(-x^{5}-x^{4}+3 x^{2}-3 x +1\right) \sqrt{1-4 x}-2 x^{6}+x^{5}-x^{4}+2 x^{3}-3 x^{2}+3 x -1}{2 x \left(x^{2}+x -1\right) \left(x -1\right)^{2}}
Generating function in sympy syntax:
(-x**6 + x**5/2 - x**4/2 + x**3 - 3*x**2/2 + 3*x/2 + sqrt(1 - 4*x)*(-x**5 - x**4 + 3*x**2 - 3*x + 1)/2 - 1/2)/(x*(x - 1)**2*(x**2 + x - 1))
Implicit equation for the generating function in Maple syntax:
x*(x^2+x-1)^2*(x-1)^4*F(x)^2+(x^2+x-1)*(2*x^6-x^5+x^4-2*x^3+3*x^2-3*x+1)*(x-1)^2*F(x)+x^11+3*x^9-2*x^8-2*x^7-4*x^6+9*x^5+x^4-14*x^3+14*x^2-6*x+1 = 0
Implicit equation for the generating function in latex syntax:
x \left(x^{2}+x -1\right)^{2} \left(x -1\right)^{4} F \! \left(x \right)^{2}+\left(x^{2}+x -1\right) \left(2 x^{6}-x^{5}+x^{4}-2 x^{3}+3 x^{2}-3 x +1\right) \left(x -1\right)^{2} F \! \left(x \right)+x^{11}+3 x^{9}-2 x^{8}-2 x^{7}-4 x^{6}+9 x^{5}+x^{4}-14 x^{3}+14 x^{2}-6 x +1 = 0
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 18
a(5) = 55
a(6) = 170
a(7) = 540
a(8) = 1763
a(9) = 5897
a(10) = 20121
a(11) = 69769
a(n+9) = -2*(-1+2*n)/(n+10)*a(n)-3*(n+3)/(n+10)*a(1+n)+(-8+9*n)/(n+10)*a(n+2)+2*(40+7*n)/(n+10)*a(n+3)-2*(53+10*n)/(n+10)*a(n+4)-4*(17+4*n)/(n+10)*a(n+5)+(257+41*n)/(n+10)*a(n+6)-(220+29*n)/(n+10)*a(n+7)+(79+9*n)/(n+10)*a(n+8)+2/(n+10), n >= 12
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) = 18
a \! \left(5\right) = 55
a \! \left(6\right) = 170
a \! \left(7\right) = 540
a \! \left(8\right) = 1763
a \! \left(9\right) = 5897
a \! \left(10\right) = 20121
a \! \left(11\right) = 69769
a \! \left(n +9\right) = -\frac{2 \left(-1+2 n \right) a \! \left(n \right)}{n +10}-\frac{3 \left(n +3\right) a \! \left(1+n \right)}{n +10}+\frac{\left(-8+9 n \right) a \! \left(n +2\right)}{n +10}+\frac{2 \left(40+7 n \right) a \! \left(n +3\right)}{n +10}-\frac{2 \left(53+10 n \right) a \! \left(n +4\right)}{n +10}-\frac{4 \left(17+4 n \right) a \! \left(n +5\right)}{n +10}+\frac{\left(257+41 n \right) a \! \left(n +6\right)}{n +10}-\frac{\left(220+29 n \right) a \! \left(n +7\right)}{n +10}+\frac{\left(79+9 n \right) a \! \left(n +8\right)}{n +10}+\frac{2}{n +10}, \quad n \geq 12
Specification 1
Strategy pack name: row_placements_tracked_fusion
Tree: http://www.permpal.com/tree/22049/
System of equations in Maple syntax:
F[0,x] = F[1,x]+F[2,x]
F[1,x] = 1
F[2,x] = F[21,x]*F[3,x]
F[3,x] = F[1,x]+F[4,x]+F[99,x]
F[4,x] = F[5,x,1]
F[5,x,k[0]] = F[21,x]*F[6,x,k[0]]
F[6,x,k[0]] = F[1,x]+F[7,x,k[0]]+F[96,x,k[0]]+F[98,x,k[0]]
F[7,x,k[0]] = F[8,x,k[0]]
F[8,x,k[0]] = F[21,x]*F[9,x,k[0]]
F[9,x,k[0]] = F[10,x,k[0]]+F[94,x]
F[10,x,k[0]] = F[11,x,k[0]]+F[38,x,k[0]]
F[11,x,k[0]] = F[12,x,k[0]]+F[16,x,k[0]]
F[12,x,k[0]] = F[1,x]+F[13,x,k[0]]
F[13,x,k[0]] = F[14,x,k[0]]
F[14,x,k[0]] = F[12,x,k[0]]*F[15,x,k[0]]
F[15,x,k[0]] = k[0]*x
F[16,x,k[0]] = F[17,x]+F[28,x,k[0]]
F[17,x] = F[18,x]
F[18,x] = F[19,x]*F[21,x]
F[19,x] = F[20,x]+F[22,x]
F[20,x] = F[1,x]+F[21,x]
F[21,x] = x
F[22,x] = F[23,x]+F[26,x]
F[23,x] = F[24,x]
F[24,x] = F[21,x]*F[25,x]
F[25,x] = F[1,x]+F[23,x]
F[26,x] = F[27,x]
F[27,x] = F[21,x]*F[23,x]
F[28,x,k[0]] = F[29,x]+F[30,x,k[0]]+F[35,x,k[0]]
F[29,x] = 0
F[30,x,k[0]] = F[21,x]*F[31,x,k[0]]
F[31,x,k[0]] = F[32,x,k[0]]+F[33,x,k[0]]
F[32,x,k[0]] = F[15,x,k[0]]
F[33,x,k[0]] = F[34,x,k[0]]
F[34,x,k[0]] = F[15,x,k[0]]*F[23,x]
F[35,x,k[0]] = F[15,x,k[0]]*F[36,x,k[0]]
F[36,x,k[0]] = F[23,x]+F[37,x,k[0]]
F[37,x,k[0]] = F[35,x,k[0]]
F[38,x,k[0]] = F[39,x,k[0]]+F[52,x,k[0]]
F[39,x,k[0]] = F[40,x]+F[46,x,k[0]]
F[40,x] = F[41,x]
F[41,x] = F[21,x]*F[42,x]
F[42,x] = F[20,x]+F[43,x]
F[43,x] = F[40,x]+F[44,x]
F[44,x] = F[45,x]
F[45,x] = F[21,x]*F[40,x]
F[46,x,k[0]] = F[29,x]+F[47,x,k[0]]+F[51,x,k[0]]
F[47,x,k[0]] = F[21,x]*F[48,x,k[0]]
F[48,x,k[0]] = F[49,x,k[0]]+F[50,x,k[0]]
F[49,x,k[0]] = F[13,x,k[0]]
F[50,x,k[0]] = F[46,x,k[0]]
F[51,x,k[0]] = F[15,x,k[0]]*F[39,x,k[0]]
F[52,x,k[0]] = F[53,x]+F[75,x,k[0]]
F[53,x] = F[29,x]+F[54,x]+F[61,x]
F[54,x] = F[21,x]*F[55,x]
F[55,x] = F[56,x]+F[57,x]
F[56,x] = F[23,x]
F[57,x] = F[58,x]
F[58,x] = F[29,x]+F[54,x]+F[59,x]
F[59,x] = F[21,x]*F[60,x]
F[60,x] = F[40,x]+F[58,x]
F[61,x] = F[21,x]*F[62,x]
F[62,x] = F[63,x]+F[69,x]
F[63,x] = F[40,x]+F[64,x]
F[64,x] = F[65,x]
F[65,x] = F[21,x]*F[66,x]
F[66,x] = F[67,x]+F[68,x]
F[67,x] = F[21,x]
F[68,x] = F[64,x]
F[69,x] = F[58,x]+F[70,x]
F[70,x] = F[71,x]
F[71,x] = F[21,x]*F[72,x]
F[72,x] = F[73,x]+F[74,x]
F[73,x] = F[26,x]
F[74,x] = F[70,x]
F[75,x,k[0]] = F[29,x]+F[76,x,k[0]]+F[81,x,k[0]]+F[83,x,k[0]]
F[76,x,k[0]] = F[21,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[37,x,k[0]]
F[79,x,k[0]] = F[80,x,k[0]]
F[80,x,k[0]] = 2*F[29,x]+F[76,x,k[0]]+F[81,x,k[0]]
F[81,x,k[0]] = F[15,x,k[0]]*F[82,x,k[0]]
F[82,x,k[0]] = F[58,x]+F[80,x,k[0]]
F[83,x,k[0]] = F[21,x]*F[84,x,k[0]]
F[84,x,k[0]] = F[85,x,k[0]]+F[89,x,k[0]]
F[85,x,k[0]] = F[86,x,k[0]]
F[86,x,k[0]] = F[21,x]*F[87,x,k[0]]
F[87,x,k[0]] = F[32,x,k[0]]+F[88,x,k[0]]
F[88,x,k[0]] = F[86,x,k[0]]
F[89,x,k[0]] = F[90,x,k[0]]
F[90,x,k[0]] = F[21,x]*F[91,x,k[0]]
F[91,x,k[0]] = F[92,x,k[0]]+F[93,x,k[0]]
F[92,x,k[0]] = F[34,x,k[0]]
F[93,x,k[0]] = F[90,x,k[0]]
F[94,x] = F[21,x]*F[95,x]
F[95,x] = F[1,x]+F[40,x]
F[96,x,k[0]] = F[21,x]*F[97,x,k[0]]
F[97,x,k[0]] = 1/(-1+k[0])*(F[6,x,k[0]]*k[0]-F[6,x,1])
F[98,x,k[0]] = F[15,x,k[0]]*F[6,x,k[0]]
F[99,x] = F[100,x]
F[100,x] = F[101,x]*F[21,x]
F[101,x] = F[102,x]+F[94,x]
F[102,x] = F[103,x]+F[104,x]
F[103,x] = F[1,x]+F[17,x]
F[104,x] = F[40,x]+F[53,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_{21}\! \left(x \right) F_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{1}\! \left(x \right)+F_{4}\! \left(x \right)+F_{99}\! \left(x \right)
F_{4}\! \left(x \right) = F_{5}\! \left(x , 1\right)
F_{5}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{6}\! \left(x , y\right)
F_{6}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{7}\! \left(x , y\right)+F_{96}\! \left(x , y\right)+F_{98}\! \left(x , y\right)
F_{7}\! \left(x , y\right) = F_{8}\! \left(x , y\right)
F_{8}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{9}\! \left(x , y\right)
F_{9}\! \left(x , y\right) = F_{10}\! \left(x , y\right)+F_{94}\! \left(x \right)
F_{10}\! \left(x , y\right) = F_{11}\! \left(x , y\right)+F_{38}\! \left(x , y\right)
F_{11}\! \left(x , y\right) = F_{12}\! \left(x , y\right)+F_{16}\! \left(x , y\right)
F_{12}\! \left(x , y\right) = F_{1}\! \left(x \right)+F_{13}\! \left(x , y\right)
F_{13}\! \left(x , y\right) = F_{14}\! \left(x , y\right)
F_{14}\! \left(x , y\right) = F_{12}\! \left(x , y\right) F_{15}\! \left(x , y\right)
F_{15}\! \left(x , y\right) = y x
F_{16}\! \left(x , y\right) = F_{17}\! \left(x \right)+F_{28}\! \left(x , y\right)
F_{17}\! \left(x \right) = F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{19}\! \left(x \right) F_{21}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{22}\! \left(x \right)
F_{20}\! \left(x \right) = F_{1}\! \left(x \right)+F_{21}\! \left(x \right)
F_{21}\! \left(x \right) = x
F_{22}\! \left(x \right) = F_{23}\! \left(x \right)+F_{26}\! \left(x \right)
F_{23}\! \left(x \right) = F_{24}\! \left(x \right)
F_{24}\! \left(x \right) = F_{21}\! \left(x \right) F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{1}\! \left(x \right)+F_{23}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{21}\! \left(x \right) F_{23}\! \left(x \right)
F_{28}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{30}\! \left(x , y\right)+F_{35}\! \left(x , y\right)
F_{29}\! \left(x \right) = 0
F_{30}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{31}\! \left(x , y\right)
F_{31}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{33}\! \left(x , y\right)
F_{32}\! \left(x , y\right) = F_{15}\! \left(x , y\right)
F_{33}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{34}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{23}\! \left(x \right)
F_{35}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{36}\! \left(x , y\right)
F_{36}\! \left(x , y\right) = F_{23}\! \left(x \right)+F_{37}\! \left(x , y\right)
F_{37}\! \left(x , y\right) = F_{35}\! \left(x , y\right)
F_{38}\! \left(x , y\right) = F_{39}\! \left(x , y\right)+F_{52}\! \left(x , y\right)
F_{39}\! \left(x , y\right) = F_{40}\! \left(x \right)+F_{46}\! \left(x , y\right)
F_{40}\! \left(x \right) = F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{21}\! \left(x \right) F_{42}\! \left(x \right)
F_{42}\! \left(x \right) = F_{20}\! \left(x \right)+F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{40}\! \left(x \right)+F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{21}\! \left(x \right) F_{40}\! \left(x \right)
F_{46}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{47}\! \left(x , y\right)+F_{51}\! \left(x , y\right)
F_{47}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{48}\! \left(x , y\right)
F_{48}\! \left(x , y\right) = F_{49}\! \left(x , y\right)+F_{50}\! \left(x , y\right)
F_{49}\! \left(x , y\right) = F_{13}\! \left(x , y\right)
F_{50}\! \left(x , y\right) = F_{46}\! \left(x , y\right)
F_{51}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{39}\! \left(x , y\right)
F_{52}\! \left(x , y\right) = F_{53}\! \left(x \right)+F_{75}\! \left(x , y\right)
F_{53}\! \left(x \right) = F_{29}\! \left(x \right)+F_{54}\! \left(x \right)+F_{61}\! \left(x \right)
F_{54}\! \left(x \right) = F_{21}\! \left(x \right) F_{55}\! \left(x \right)
F_{55}\! \left(x \right) = F_{56}\! \left(x \right)+F_{57}\! \left(x \right)
F_{56}\! \left(x \right) = F_{23}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{29}\! \left(x \right)+F_{54}\! \left(x \right)+F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{21}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{40}\! \left(x \right)+F_{58}\! \left(x \right)
F_{61}\! \left(x \right) = F_{21}\! \left(x \right) F_{62}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{69}\! \left(x \right)
F_{63}\! \left(x \right) = F_{40}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{65}\! \left(x \right)
F_{65}\! \left(x \right) = F_{21}\! \left(x \right) F_{66}\! \left(x \right)
F_{66}\! \left(x \right) = F_{67}\! \left(x \right)+F_{68}\! \left(x \right)
F_{67}\! \left(x \right) = F_{21}\! \left(x \right)
F_{68}\! \left(x \right) = F_{64}\! \left(x \right)
F_{69}\! \left(x \right) = F_{58}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)
F_{71}\! \left(x \right) = F_{21}\! \left(x \right) F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{73}\! \left(x \right)+F_{74}\! \left(x \right)
F_{73}\! \left(x \right) = F_{26}\! \left(x \right)
F_{74}\! \left(x \right) = F_{70}\! \left(x \right)
F_{75}\! \left(x , y\right) = F_{29}\! \left(x \right)+F_{76}\! \left(x , y\right)+F_{81}\! \left(x , y\right)+F_{83}\! \left(x , y\right)
F_{76}\! \left(x , y\right) = F_{21}\! \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_{37}\! \left(x , y\right)
F_{79}\! \left(x , y\right) = F_{80}\! \left(x , y\right)
F_{80}\! \left(x , y\right) = 2 F_{29}\! \left(x \right)+F_{76}\! \left(x , y\right)+F_{81}\! \left(x , y\right)
F_{81}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{82}\! \left(x , y\right)
F_{82}\! \left(x , y\right) = F_{58}\! \left(x \right)+F_{80}\! \left(x , y\right)
F_{83}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{84}\! \left(x , y\right)
F_{84}\! \left(x , y\right) = F_{85}\! \left(x , y\right)+F_{89}\! \left(x , y\right)
F_{85}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{86}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{87}\! \left(x , y\right)
F_{87}\! \left(x , y\right) = F_{32}\! \left(x , y\right)+F_{88}\! \left(x , y\right)
F_{88}\! \left(x , y\right) = F_{86}\! \left(x , y\right)
F_{89}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{90}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{91}\! \left(x , y\right)
F_{91}\! \left(x , y\right) = F_{92}\! \left(x , y\right)+F_{93}\! \left(x , y\right)
F_{92}\! \left(x , y\right) = F_{34}\! \left(x , y\right)
F_{93}\! \left(x , y\right) = F_{90}\! \left(x , y\right)
F_{94}\! \left(x \right) = F_{21}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{1}\! \left(x \right)+F_{40}\! \left(x \right)
F_{96}\! \left(x , y\right) = F_{21}\! \left(x \right) F_{97}\! \left(x , y\right)
F_{97}\! \left(x , y\right) = \frac{F_{6}\! \left(x , y\right) y -F_{6}\! \left(x , 1\right)}{-1+y}
F_{98}\! \left(x , y\right) = F_{15}\! \left(x , y\right) F_{6}\! \left(x , y\right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{21}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{94}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{104}\! \left(x \right)
F_{103}\! \left(x \right) = F_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{104}\! \left(x \right) = F_{40}\! \left(x \right)+F_{53}\! \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_21(x)*F_3(x))
Eq(F_3(x), F_1(x) + F_4(x) + F_99(x))
Eq(F_4(x), F_5(x, 1))
Eq(F_5(x, k_0), F_21(x)*F_6(x, k_0))
Eq(F_6(x, k_0), F_1(x) + F_7(x, k_0) + F_96(x, k_0) + F_98(x, k_0))
Eq(F_7(x, k_0), F_8(x, k_0))
Eq(F_8(x, k_0), F_21(x)*F_9(x, k_0))
Eq(F_9(x, k_0), F_10(x, k_0) + F_94(x))
Eq(F_10(x, k_0), F_11(x, k_0) + F_38(x, k_0))
Eq(F_11(x, k_0), F_12(x, k_0) + F_16(x, k_0))
Eq(F_12(x, k_0), F_1(x) + F_13(x, k_0))
Eq(F_13(x, k_0), F_14(x, k_0))
Eq(F_14(x, k_0), F_12(x, k_0)*F_15(x, k_0))
Eq(F_15(x, k_0), k_0*x)
Eq(F_16(x, k_0), F_17(x) + F_28(x, k_0))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_19(x)*F_21(x))
Eq(F_19(x), F_20(x) + F_22(x))
Eq(F_20(x), F_1(x) + F_21(x))
Eq(F_21(x), x)
Eq(F_22(x), F_23(x) + F_26(x))
Eq(F_23(x), F_24(x))
Eq(F_24(x), F_21(x)*F_25(x))
Eq(F_25(x), F_1(x) + F_23(x))
Eq(F_26(x), F_27(x))
Eq(F_27(x), F_21(x)*F_23(x))
Eq(F_28(x, k_0), F_29(x) + F_30(x, k_0) + F_35(x, k_0))
Eq(F_29(x), 0)
Eq(F_30(x, k_0), F_21(x)*F_31(x, k_0))
Eq(F_31(x, k_0), F_32(x, k_0) + F_33(x, k_0))
Eq(F_32(x, k_0), F_15(x, k_0))
Eq(F_33(x, k_0), F_34(x, k_0))
Eq(F_34(x, k_0), F_15(x, k_0)*F_23(x))
Eq(F_35(x, k_0), F_15(x, k_0)*F_36(x, k_0))
Eq(F_36(x, k_0), F_23(x) + F_37(x, k_0))
Eq(F_37(x, k_0), F_35(x, k_0))
Eq(F_38(x, k_0), F_39(x, k_0) + F_52(x, k_0))
Eq(F_39(x, k_0), F_40(x) + F_46(x, k_0))
Eq(F_40(x), F_41(x))
Eq(F_41(x), F_21(x)*F_42(x))
Eq(F_42(x), F_20(x) + F_43(x))
Eq(F_43(x), F_40(x) + F_44(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_21(x)*F_40(x))
Eq(F_46(x, k_0), F_29(x) + F_47(x, k_0) + F_51(x, k_0))
Eq(F_47(x, k_0), F_21(x)*F_48(x, k_0))
Eq(F_48(x, k_0), F_49(x, k_0) + F_50(x, k_0))
Eq(F_49(x, k_0), F_13(x, k_0))
Eq(F_50(x, k_0), F_46(x, k_0))
Eq(F_51(x, k_0), F_15(x, k_0)*F_39(x, k_0))
Eq(F_52(x, k_0), F_53(x) + F_75(x, k_0))
Eq(F_53(x), F_29(x) + F_54(x) + F_61(x))
Eq(F_54(x), F_21(x)*F_55(x))
Eq(F_55(x), F_56(x) + F_57(x))
Eq(F_56(x), F_23(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_29(x) + F_54(x) + F_59(x))
Eq(F_59(x), F_21(x)*F_60(x))
Eq(F_60(x), F_40(x) + F_58(x))
Eq(F_61(x), F_21(x)*F_62(x))
Eq(F_62(x), F_63(x) + F_69(x))
Eq(F_63(x), F_40(x) + F_64(x))
Eq(F_64(x), F_65(x))
Eq(F_65(x), F_21(x)*F_66(x))
Eq(F_66(x), F_67(x) + F_68(x))
Eq(F_67(x), F_21(x))
Eq(F_68(x), F_64(x))
Eq(F_69(x), F_58(x) + F_70(x))
Eq(F_70(x), F_71(x))
Eq(F_71(x), F_21(x)*F_72(x))
Eq(F_72(x), F_73(x) + F_74(x))
Eq(F_73(x), F_26(x))
Eq(F_74(x), F_70(x))
Eq(F_75(x, k_0), F_29(x) + F_76(x, k_0) + F_81(x, k_0) + F_83(x, k_0))
Eq(F_76(x, k_0), F_21(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_37(x, k_0))
Eq(F_79(x, k_0), F_80(x, k_0))
Eq(F_80(x, k_0), 2*F_29(x) + F_76(x, k_0) + F_81(x, k_0))
Eq(F_81(x, k_0), F_15(x, k_0)*F_82(x, k_0))
Eq(F_82(x, k_0), F_58(x) + F_80(x, k_0))
Eq(F_83(x, k_0), F_21(x)*F_84(x, k_0))
Eq(F_84(x, k_0), F_85(x, k_0) + F_89(x, k_0))
Eq(F_85(x, k_0), F_86(x, k_0))
Eq(F_86(x, k_0), F_21(x)*F_87(x, k_0))
Eq(F_87(x, k_0), F_32(x, k_0) + F_88(x, k_0))
Eq(F_88(x, k_0), F_86(x, k_0))
Eq(F_89(x, k_0), F_90(x, k_0))
Eq(F_90(x, k_0), F_21(x)*F_91(x, k_0))
Eq(F_91(x, k_0), F_92(x, k_0) + F_93(x, k_0))
Eq(F_92(x, k_0), F_34(x, k_0))
Eq(F_93(x, k_0), F_90(x, k_0))
Eq(F_94(x), F_21(x)*F_95(x))
Eq(F_95(x), F_1(x) + F_40(x))
Eq(F_96(x, k_0), F_21(x)*F_97(x, k_0))
Eq(F_97(x, k_0), (k_0*F_6(x, k_0) - F_6(x, 1))/(k_0 - 1))
Eq(F_98(x, k_0), F_15(x, k_0)*F_6(x, k_0))
Eq(F_99(x), F_100(x))
Eq(F_100(x), F_101(x)*F_21(x))
Eq(F_101(x), F_102(x) + F_94(x))
Eq(F_102(x), F_103(x) + F_104(x))
Eq(F_103(x), F_1(x) + F_17(x))
Eq(F_104(x), F_40(x) + F_53(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, 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, 0, 2, 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, 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], [2, 1], [2, 1]]}, {"patt": [0, 1, 2], "pos": [[2, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1], "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": [[0, 1], [2, 1], [2, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [3, 0, 1, 2], "pos": [[0, 1], [0, 1], [0, 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, 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, 0, 2, 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": 3, "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": false, "include_empty": true, "indices": [0], "own_col": true, "own_row": true, "strategy_class": "RequirementPlacementStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1], "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": [[0, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 1, 3, 2], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1, 3], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [1, 0, 2, 3], "pos": [[0, 0], [0, 0], [0, 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], [0, 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]]}, 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