0123_0231_1230_2301
Counting sequence:
1, 1, 2, 6, 20, 65, 198, 563, 1506, 3830, 9354, 22128, 51056, 115527, 257446, 566833, 1236094, 2674708, 5750890, 12299494, 26186972, 55539597, 117396518, 247409087, 520025946, 1090436066, 2281600554, 4764607724, 9931966152, 20669356611, 42949467590, 89120329629, 184683310582, 382251759328, 790273599562, 1632087130114, 3367253851060, 6940666566889, 14293650494726, 29411935284555, 60473138667218, 124244812965518, 255086696546634, 523367533587368, 1073123347325472, 2199023254003967, 4503599625643110, 9218305485350985, 18858823437477998, 38562071806992492, 78812993476365226, 161003686675604830, 328762772794861708, 671036344474701829, 1369094286716786278, 2792231768965494295, 5692549928991697226, 11601272640101362170, 23634890844434870762, 48134472817329879716, 97998327891575487864, 199455420296977462139, 405828369621602473350, 825491797298494135349, 1678653710707560218598, 3412647653636257347768, 6935975771714780937866, 14093312472314086148346, 28629346802397211955044, 58144137320332493621473, 118059162071741116296262, 239660099005634479517731, 486403747735573440842434, 986974594919755832341030, 2002283388736729552067594, 4061235175267894863953376, 8235807146124661231504592, 16698287883427065453018551, 33849922949209616867656998, 68606540263130205638874977, 139026469255682355063842910, 281679715970208597677419460, 570612986858104970430354666, 1155733083551585490986211030, 2340480386773922082196235324, 4738989212889346364811161469, 9594035304461697130428934822, 19420184366289403062438397807, 39304596247310823728003135290, 79537647524085682662222113554, 160932205107099435736836854698, 325578230332055012298417578332, 658584100899822306246279070760, 1332023482271069175791399594931, 2693757525484987478180433053510, 5446936172855673209556082001357, 11012714589482742925502541043158, 22263113666508278863785778374032, 45001596308102143753132888351434, 90953930566375459557388375620338, 183809337033093263217021881326356
Generating function in Maple syntax:
-(7*x^7-33*x^6+76*x^5-97*x^4+75*x^3-35*x^2+9*x-1)/(2*x-1)^2/(-1+x)^6
Generating function in latex syntax:
-\frac{7 x^{7}-33 x^{6}+76 x^{5}-97 x^{4}+75 x^{3}-35 x^{2}+9 x -1}{\left(2 x -1\right)^{2} \left(-1+x \right)^{6}}
Generating function in sympy syntax:
(-7*x**7 + 33*x**6 - 76*x**5 + 97*x**4 - 75*x**3 + 35*x**2 - 9*x + 1)/((x - 1)**6*(2*x - 1)**2)
Implicit equation for the generating function in Maple syntax:
(2*x-1)^2*(-1+x)^6*F(x)+7*x^7-33*x^6+76*x^5-97*x^4+75*x^3-35*x^2+9*x-1 = 0
Implicit equation for the generating function in latex syntax:
\left(2 x -1\right)^{2} \left(-1+x \right)^{6} F \! \left(x \right)+7 x^{7}-33 x^{6}+76 x^{5}-97 x^{4}+75 x^{3}-35 x^{2}+9 x -1 = 0
Explicit closed form in Maple syntax:
6+3*2^(-1+n)*n-5*2^n+1/2*n^2+49/30*n-1/8*n^3-1/120*n^5
Explicit closed form in latex syntax:
6+3 \,2^{-1+n} n -5 \,2^{n}+\frac{n^{2}}{2}+\frac{49 n}{30}-\frac{n^{3}}{8}-\frac{n^{5}}{120}
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 65
a(6) = 198
a(7) = 563
a(n+2) = -1/120*n^5+1/12*n^4-1/8*n^3+11/12*n^2-4*a(n)+4*a(n+1)-13/15*n+2, n >= 8
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) = 20
a \! \left(5\right) = 65
a \! \left(6\right) = 198
a \! \left(7\right) = 563
a \! \left(n +2\right) = -\frac{n^{5}}{120}+\frac{n^{4}}{12}-\frac{n^{3}}{8}+\frac{11 n^{2}}{12}-4 a \! \left(n \right)+4 a \! \left(n +1\right)-\frac{13 n}{15}+2, \quad n \geq 8
Specification 1
Strategy pack name: insertion_row_and_col_placements
Tree: http://permpal.com/tree/21156/
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[13,x]*F[4,x]
F[4,x] = F[29,x]+F[5,x]
F[5,x] = F[1,x]+F[6,x]
F[6,x] = F[13,x]*F[7,x]
F[7,x] = F[5,x]+F[8,x]
F[8,x] = F[13,x]*F[9,x]
F[9,x] = F[10,x]+F[14,x]+F[8,x]
F[10,x] = F[1,x]+F[11,x]
F[11,x] = F[12,x]
F[12,x] = F[10,x]*F[13,x]
F[13,x] = x
F[14,x] = F[15,x]
F[15,x] = F[10,x]*F[13,x]*F[16,x]
F[16,x] = F[17,x]+F[24,x]
F[17,x] = F[10,x]+F[18,x]
F[18,x] = F[11,x]+F[19,x]
F[19,x] = F[20,x]+F[21,x]+F[23,x]
F[20,x] = 0
F[21,x] = F[13,x]*F[22,x]
F[22,x] = F[11,x]+F[19,x]
F[23,x] = F[13,x]*F[18,x]
F[24,x] = F[11,x]+F[25,x]
F[25,x] = F[20,x]+F[26,x]+F[28,x]
F[26,x] = F[13,x]*F[27,x]
F[27,x] = F[11,x]+F[25,x]
F[28,x] = F[13,x]*F[24,x]
F[29,x] = F[30,x]+F[31,x]
F[30,x] = F[6,x]
F[31,x] = F[100,x]+F[20,x]+F[32,x]
F[32,x] = F[13,x]*F[33,x]
F[33,x] = F[34,x]+F[41,x]
F[34,x] = F[11,x]+F[35,x]
F[35,x] = F[20,x]+F[36,x]+F[39,x]
F[36,x] = F[13,x]*F[37,x]
F[37,x] = F[11,x]+F[38,x]
F[38,x] = F[36,x]
F[39,x] = F[13,x]*F[40,x]
F[40,x] = F[11,x]+F[35,x]
F[41,x] = F[42,x]+F[73,x]
F[42,x] = F[43,x]
F[43,x] = F[13,x]*F[44,x]
F[44,x] = F[45,x]+F[47,x]
F[45,x] = F[34,x]+F[46,x]
F[46,x] = F[10,x]*F[11,x]
F[47,x] = F[48,x]+F[66,x]
F[48,x] = F[49,x]+F[50,x]
F[49,x] = F[11,x]*F[30,x]
F[50,x] = F[20,x]+F[51,x]+F[55,x]
F[51,x] = F[52,x]
F[52,x] = F[11,x]*F[13,x]*F[53,x]
F[53,x] = F[18,x]+F[54,x]
F[54,x] = F[11,x]*F[17,x]
F[55,x] = F[13,x]*F[56,x]
F[56,x] = F[50,x]+F[57,x]
F[57,x] = F[58,x]
F[58,x] = F[13,x]*F[59,x]
F[59,x] = F[60,x]+F[62,x]
F[60,x] = 2*F[61,x]
F[61,x] = F[10,x]*F[11,x]
F[62,x] = F[63,x]+F[65,x]
F[63,x] = F[57,x]+F[64,x]
F[64,x] = F[11,x]*F[18,x]
F[65,x] = F[11,x]*F[25,x]
F[66,x] = F[10,x]*F[67,x]
F[67,x] = F[68,x]
F[68,x] = F[13,x]*F[69,x]
F[69,x] = F[70,x]+F[71,x]
F[70,x] = 2*F[46,x]
F[71,x] = F[64,x]+F[72,x]
F[72,x] = F[65,x]+F[67,x]
F[73,x] = F[74,x]
F[74,x] = F[13,x]*F[75,x]
F[75,x] = F[76,x]+F[97,x]
F[76,x] = F[77,x]+F[82,x]
F[77,x] = F[78,x]+F[79,x]
F[78,x] = F[35,x]+F[73,x]
F[79,x] = F[80,x]
F[80,x] = F[11,x]^2*F[81,x]
F[81,x] = F[10,x]+F[24,x]
F[82,x] = F[11,x]*F[83,x]
F[83,x] = F[84,x]+F[95,x]
F[84,x] = F[40,x]+F[85,x]
F[85,x] = F[25,x]+F[86,x]
F[86,x] = F[20,x]+F[87,x]+F[89,x]+F[94,x]
F[87,x] = F[13,x]*F[88,x]
F[88,x] = F[35,x]+F[86,x]
F[89,x] = F[13,x]*F[90,x]
F[90,x] = F[38,x]+F[91,x]
F[91,x] = 2*F[20,x]+F[89,x]+F[92,x]
F[92,x] = F[13,x]*F[93,x]
F[93,x] = F[38,x]+F[91,x]
F[94,x] = F[13,x]*F[85,x]
F[95,x] = F[96,x]
F[96,x] = F[10,x]*F[11,x]*F[81,x]
F[97,x] = F[98,x]
F[98,x] = F[11,x]*F[18,x]*F[99,x]
F[99,x] = F[11,x]+F[46,x]
F[100,x] = F[101,x]*F[13,x]
F[101,x] = F[102,x]+F[104,x]
F[102,x] = F[103,x]
F[103,x] = F[10,x]*F[30,x]
F[104,x] = F[105,x]+F[31,x]
F[105,x] = F[106,x]
F[106,x] = F[10,x]*F[107,x]*F[13,x]*F[30,x]
F[107,x] = F[11,x]+F[18,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_{3}\! \left(x \right)
F_{3}\! \left(x \right) = F_{13}\! \left(x \right) F_{4}\! \left(x \right)
F_{4}\! \left(x \right) = F_{29}\! \left(x \right)+F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)
F_{6}\! \left(x \right) = F_{13}\! \left(x \right) F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{5}\! \left(x \right)+F_{8}\! \left(x \right)
F_{8}\! \left(x \right) = F_{13}\! \left(x \right) F_{9}\! \left(x \right)
F_{9}\! \left(x \right) = F_{10}\! \left(x \right)+F_{14}\! \left(x \right)+F_{8}\! \left(x \right)
F_{10}\! \left(x \right) = F_{1}\! \left(x \right)+F_{11}\! \left(x \right)
F_{11}\! \left(x \right) = F_{12}\! \left(x \right)
F_{12}\! \left(x \right) = F_{10}\! \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_{15}\! \left(x \right) = F_{10}\! \left(x \right) F_{13}\! \left(x \right) F_{16}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{24}\! \left(x \right)
F_{17}\! \left(x \right) = F_{10}\! \left(x \right)+F_{18}\! \left(x \right)
F_{18}\! \left(x \right) = F_{11}\! \left(x \right)+F_{19}\! \left(x \right)
F_{19}\! \left(x \right) = F_{20}\! \left(x \right)+F_{21}\! \left(x \right)+F_{23}\! \left(x \right)
F_{20}\! \left(x \right) = 0
F_{21}\! \left(x \right) = F_{13}\! \left(x \right) F_{22}\! \left(x \right)
F_{22}\! \left(x \right) = F_{11}\! \left(x \right)+F_{19}\! \left(x \right)
F_{23}\! \left(x \right) = F_{13}\! \left(x \right) F_{18}\! \left(x \right)
F_{24}\! \left(x \right) = F_{11}\! \left(x \right)+F_{25}\! \left(x \right)
F_{25}\! \left(x \right) = F_{20}\! \left(x \right)+F_{26}\! \left(x \right)+F_{28}\! \left(x \right)
F_{26}\! \left(x \right) = F_{13}\! \left(x \right) F_{27}\! \left(x \right)
F_{27}\! \left(x \right) = F_{11}\! \left(x \right)+F_{25}\! \left(x \right)
F_{28}\! \left(x \right) = F_{13}\! \left(x \right) F_{24}\! \left(x \right)
F_{29}\! \left(x \right) = F_{30}\! \left(x \right)+F_{31}\! \left(x \right)
F_{30}\! \left(x \right) = F_{6}\! \left(x \right)
F_{31}\! \left(x \right) = F_{100}\! \left(x \right)+F_{20}\! \left(x \right)+F_{32}\! \left(x \right)
F_{32}\! \left(x \right) = F_{13}\! \left(x \right) F_{33}\! \left(x \right)
F_{33}\! \left(x \right) = F_{34}\! \left(x \right)+F_{41}\! \left(x \right)
F_{34}\! \left(x \right) = F_{11}\! \left(x \right)+F_{35}\! \left(x \right)
F_{35}\! \left(x \right) = F_{20}\! \left(x \right)+F_{36}\! \left(x \right)+F_{39}\! \left(x \right)
F_{36}\! \left(x \right) = F_{13}\! \left(x \right) F_{37}\! \left(x \right)
F_{37}\! \left(x \right) = F_{11}\! \left(x \right)+F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = F_{13}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{11}\! \left(x \right)+F_{35}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{73}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{13}\! \left(x \right) F_{44}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)+F_{47}\! \left(x \right)
F_{45}\! \left(x \right) = F_{34}\! \left(x \right)+F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{66}\! \left(x \right)
F_{48}\! \left(x \right) = F_{49}\! \left(x \right)+F_{50}\! \left(x \right)
F_{49}\! \left(x \right) = F_{11}\! \left(x \right) F_{30}\! \left(x \right)
F_{50}\! \left(x \right) = F_{20}\! \left(x \right)+F_{51}\! \left(x \right)+F_{55}\! \left(x \right)
F_{51}\! \left(x \right) = F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{11}\! \left(x \right) F_{13}\! \left(x \right) F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{18}\! \left(x \right)+F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right)
F_{55}\! \left(x \right) = F_{13}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{50}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{13}\! \left(x \right) F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{60}\! \left(x \right)+F_{62}\! \left(x \right)
F_{60}\! \left(x \right) = 2 F_{61}\! \left(x \right)
F_{61}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)+F_{65}\! \left(x \right)
F_{63}\! \left(x \right) = F_{57}\! \left(x \right)+F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right)
F_{65}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \left(x \right)
F_{66}\! \left(x \right) = F_{10}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{68}\! \left(x \right)
F_{68}\! \left(x \right) = F_{13}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{70}\! \left(x \right)+F_{71}\! \left(x \right)
F_{70}\! \left(x \right) = 2 F_{46}\! \left(x \right)
F_{71}\! \left(x \right) = F_{64}\! \left(x \right)+F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{65}\! \left(x \right)+F_{67}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{13}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{76}\! \left(x \right)+F_{97}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)+F_{82}\! \left(x \right)
F_{77}\! \left(x \right) = F_{78}\! \left(x \right)+F_{79}\! \left(x \right)
F_{78}\! \left(x \right) = F_{35}\! \left(x \right)+F_{73}\! \left(x \right)
F_{79}\! \left(x \right) = F_{80}\! \left(x \right)
F_{80}\! \left(x \right) = F_{11} \left(x \right)^{2} F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = F_{10}\! \left(x \right)+F_{24}\! \left(x \right)
F_{82}\! \left(x \right) = F_{11}\! \left(x \right) F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{84}\! \left(x \right)+F_{95}\! \left(x \right)
F_{84}\! \left(x \right) = F_{40}\! \left(x \right)+F_{85}\! \left(x \right)
F_{85}\! \left(x \right) = F_{25}\! \left(x \right)+F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{20}\! \left(x \right)+F_{87}\! \left(x \right)+F_{89}\! \left(x \right)+F_{94}\! \left(x \right)
F_{87}\! \left(x \right) = F_{13}\! \left(x \right) F_{88}\! \left(x \right)
F_{88}\! \left(x \right) = F_{35}\! \left(x \right)+F_{86}\! \left(x \right)
F_{89}\! \left(x \right) = F_{13}\! \left(x \right) F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{38}\! \left(x \right)+F_{91}\! \left(x \right)
F_{91}\! \left(x \right) = 2 F_{20}\! \left(x \right)+F_{89}\! \left(x \right)+F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{13}\! \left(x \right) F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{38}\! \left(x \right)+F_{91}\! \left(x \right)
F_{94}\! \left(x \right) = F_{13}\! \left(x \right) F_{85}\! \left(x \right)
F_{95}\! \left(x \right) = F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{10}\! \left(x \right) F_{11}\! \left(x \right) F_{81}\! \left(x \right)
F_{97}\! \left(x \right) = F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{11}\! \left(x \right) F_{18}\! \left(x \right) F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{11}\! \left(x \right)+F_{46}\! \left(x \right)
F_{100}\! \left(x \right) = F_{101}\! \left(x \right) F_{13}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{104}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)
F_{103}\! \left(x \right) = F_{10}\! \left(x \right) F_{30}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right)+F_{31}\! \left(x \right)
F_{105}\! \left(x \right) = F_{106}\! \left(x \right)
F_{106}\! \left(x \right) = F_{10}\! \left(x \right) F_{107}\! \left(x \right) F_{13}\! \left(x \right) F_{30}\! \left(x \right)
F_{107}\! \left(x \right) = F_{11}\! \left(x \right)+F_{18}\! \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_3(x))
Eq(F_3(x), F_13(x)*F_4(x))
Eq(F_4(x), F_29(x) + F_5(x))
Eq(F_5(x), F_1(x) + F_6(x))
Eq(F_6(x), F_13(x)*F_7(x))
Eq(F_7(x), F_5(x) + F_8(x))
Eq(F_8(x), F_13(x)*F_9(x))
Eq(F_9(x), F_10(x) + F_14(x) + F_8(x))
Eq(F_10(x), F_1(x) + F_11(x))
Eq(F_11(x), F_12(x))
Eq(F_12(x), F_10(x)*F_13(x))
Eq(F_13(x), x)
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_10(x)*F_13(x)*F_16(x))
Eq(F_16(x), F_17(x) + F_24(x))
Eq(F_17(x), F_10(x) + F_18(x))
Eq(F_18(x), F_11(x) + F_19(x))
Eq(F_19(x), F_20(x) + F_21(x) + F_23(x))
Eq(F_20(x), 0)
Eq(F_21(x), F_13(x)*F_22(x))
Eq(F_22(x), F_11(x) + F_19(x))
Eq(F_23(x), F_13(x)*F_18(x))
Eq(F_24(x), F_11(x) + F_25(x))
Eq(F_25(x), F_20(x) + F_26(x) + F_28(x))
Eq(F_26(x), F_13(x)*F_27(x))
Eq(F_27(x), F_11(x) + F_25(x))
Eq(F_28(x), F_13(x)*F_24(x))
Eq(F_29(x), F_30(x) + F_31(x))
Eq(F_30(x), F_6(x))
Eq(F_31(x), F_100(x) + F_20(x) + F_32(x))
Eq(F_32(x), F_13(x)*F_33(x))
Eq(F_33(x), F_34(x) + F_41(x))
Eq(F_34(x), F_11(x) + F_35(x))
Eq(F_35(x), F_20(x) + F_36(x) + F_39(x))
Eq(F_36(x), F_13(x)*F_37(x))
Eq(F_37(x), F_11(x) + F_38(x))
Eq(F_38(x), F_36(x))
Eq(F_39(x), F_13(x)*F_40(x))
Eq(F_40(x), F_11(x) + F_35(x))
Eq(F_41(x), F_42(x) + F_73(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_13(x)*F_44(x))
Eq(F_44(x), F_45(x) + F_47(x))
Eq(F_45(x), F_34(x) + F_46(x))
Eq(F_46(x), F_10(x)*F_11(x))
Eq(F_47(x), F_48(x) + F_66(x))
Eq(F_48(x), F_49(x) + F_50(x))
Eq(F_49(x), F_11(x)*F_30(x))
Eq(F_50(x), F_20(x) + F_51(x) + F_55(x))
Eq(F_51(x), F_52(x))
Eq(F_52(x), F_11(x)*F_13(x)*F_53(x))
Eq(F_53(x), F_18(x) + F_54(x))
Eq(F_54(x), F_11(x)*F_17(x))
Eq(F_55(x), F_13(x)*F_56(x))
Eq(F_56(x), F_50(x) + F_57(x))
Eq(F_57(x), F_58(x))
Eq(F_58(x), F_13(x)*F_59(x))
Eq(F_59(x), F_60(x) + F_62(x))
Eq(F_60(x), 2*F_61(x))
Eq(F_61(x), F_10(x)*F_11(x))
Eq(F_62(x), F_63(x) + F_65(x))
Eq(F_63(x), F_57(x) + F_64(x))
Eq(F_64(x), F_11(x)*F_18(x))
Eq(F_65(x), F_11(x)*F_25(x))
Eq(F_66(x), F_10(x)*F_67(x))
Eq(F_67(x), F_68(x))
Eq(F_68(x), F_13(x)*F_69(x))
Eq(F_69(x), F_70(x) + F_71(x))
Eq(F_70(x), 2*F_46(x))
Eq(F_71(x), F_64(x) + F_72(x))
Eq(F_72(x), F_65(x) + F_67(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_13(x)*F_75(x))
Eq(F_75(x), F_76(x) + F_97(x))
Eq(F_76(x), F_77(x) + F_82(x))
Eq(F_77(x), F_78(x) + F_79(x))
Eq(F_78(x), F_35(x) + F_73(x))
Eq(F_79(x), F_80(x))
Eq(F_80(x), F_11(x)**2*F_81(x))
Eq(F_81(x), F_10(x) + F_24(x))
Eq(F_82(x), F_11(x)*F_83(x))
Eq(F_83(x), F_84(x) + F_95(x))
Eq(F_84(x), F_40(x) + F_85(x))
Eq(F_85(x), F_25(x) + F_86(x))
Eq(F_86(x), F_20(x) + F_87(x) + F_89(x) + F_94(x))
Eq(F_87(x), F_13(x)*F_88(x))
Eq(F_88(x), F_35(x) + F_86(x))
Eq(F_89(x), F_13(x)*F_90(x))
Eq(F_90(x), F_38(x) + F_91(x))
Eq(F_91(x), 2*F_20(x) + F_89(x) + F_92(x))
Eq(F_92(x), F_13(x)*F_93(x))
Eq(F_93(x), F_38(x) + F_91(x))
Eq(F_94(x), F_13(x)*F_85(x))
Eq(F_95(x), F_96(x))
Eq(F_96(x), F_10(x)*F_11(x)*F_81(x))
Eq(F_97(x), F_98(x))
Eq(F_98(x), F_11(x)*F_18(x)*F_99(x))
Eq(F_99(x), F_11(x) + F_46(x))
Eq(F_100(x), F_101(x)*F_13(x))
Eq(F_101(x), F_102(x) + F_104(x))
Eq(F_102(x), F_103(x))
Eq(F_103(x), F_10(x)*F_30(x))
Eq(F_104(x), F_105(x) + F_31(x))
Eq(F_105(x), F_106(x))
Eq(F_106(x), F_10(x)*F_107(x)*F_13(x)*F_30(x))
Eq(F_107(x), F_11(x) + F_18(x))
Pack JSON:
{"expansion_strats": [[{"class_module": "tilings.strategies.requirement_placement", "dirs": [0, 1, 2, 3], "ignore_parent": false, "partial": false, "place_col": true, "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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}, {"class_module": "tilings.strategies.requirement_insertion", "extra_basis": [], "ignore_parent": true, "maxreqlen": 1, "one_cell_only": true, "strategy_class": "CellInsertionFactory"}], "iterative": false, "name": "insertion_row_and_col_placements", "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, 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": [2, 3, 0, 1], "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, 2, 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": [2, 3, 0, 1], "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, 2, 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": [2, 3, 0, 1], "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": true, "strategy_class": "RequirementInsertionStrategy"}}, {"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": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "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, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 2], [0, 2]]}, {"patt": [0, 1, 2], "pos": [[0, 2], [0, 2], [0, 2]]}, {"patt": [1, 2, 0], "pos": [[0, 2], [0, 2], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 2], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 2], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 2], [0, 2], [0, 2], [0, 2]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.factor", "ignore_parent": true, "partition": [[[0, 0], [0, 2]], [[1, 1]]], "strategy_class": "FactorStrategy", "workable": true}}, {"class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1], "pos": [[0, 0], [0, 0]]}, {"patt": [1, 0], "pos": [[0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "VerificationRule", "strategy": {"class_module": "tilings.strategies.verification", "strategy_class": "BasicVerificationStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "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, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "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, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": []}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 0]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0, 1, 2], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, {"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": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}], [{"patt": [0], "pos": [[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, 0]]}, {"patt": [0, 1, 2], "pos": [[0, 0], [0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[0, 1], [0, 1], [0, 1]]}, {"patt": [1, 2, 0], "pos": [[0, 1], [0, 1], [0, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [1, 2, 3, 0], "pos": [[0, 0], [0, 0], [0, 1], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 0], [0, 1], [0, 0], [0, 0]]}, {"patt": [2, 3, 0, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}], "requirements": [[{"patt": [0], "pos": [[0, 0]]}]]}, "rule_class": "Rule", "strategy": {"class_module": "tilings.strategies.requirement_insertion", "gps": [{"patt": [0], "pos": [[0, 1]]}], "ignore_parent": true, "strategy_class": "RequirementInsertionStrategy"}}, {"children": [{"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [], "pos": []}], "requirements": []}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 0]]}, {"patt": [0], "pos": [[0, 2]]}, {"patt": [0], "pos": [[0, 3]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0, 1], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1], "pos": [[1, 2], [1, 2]]}, {"patt": [0, 1], "pos": [[1, 3], [1, 3]]}, {"patt": [1, 0], "pos": [[0, 1], [0, 1]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 0]]}, {"patt": [0, 1, 2], "pos": [[1, 0], [1, 0], [1, 2]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 3], [1, 0]]}, {"patt": [1, 2, 0], "pos": [[1, 2], [1, 3], [1, 2]]}, {"patt": [2, 0, 1], "pos": [[1, 2], [1, 0], [1, 0]]}, {"patt": [2, 0, 1], "pos": [[1, 3], [1, 0], [1, 0]]}, {"patt": [0, 2, 3, 1], "pos": [[1, 0], [1, 0], [1, 3], [1, 0]]}, {"patt": [1, 2, 3, 0], 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