0213_0231_0321_3120
Counting sequence:
1, 1, 2, 6, 20, 64, 190, 528, 1394, 3540, 8726, 21016, 49690, 115740, 266270, 606240, 1368098, 3063844, 6815782, 15073320, 33161258, 72613932, 158335022, 343932976, 744489010, 1606418484, 3456106550, 7415529528, 15871246394, 33889976380, 72209137726, 153545080896, 325880643650, 690415992900, 1460288880710, 3083786518600, 6502580486218, 13692355739724, 28793460752462, 60473139527760, 126856154054738, 265806936014932, 556352883654742, 1163283302187096, 2429920697385050, 5070947627303004, 10572903812694110, 22025416927608928, 45845236831748194, 95349648360734820, 198158383604301926, 411516415950979176, 853995079340130410, 1771040553463447660, 3670433696306954350, 7602076171001397360, 15735577098032513138, 32552018106633945204, 67301792831424692342, 139071156493200916600, 287221569835180753018, 592889883744071057532, 1223249716387864641662, 2522592252079781183616, 5199675985776879861890, 10712946620806822101124, 22062305912156623732870, 45415883909472916078728, 93451205477412588486794, 192215073248053527838860, 395203045035153433821326, 812247035053578976755856, 1668766255884060877389970, 3427257474942645013840020, 7036326059475771368407190, 14440996704615375063482520, 29628127313524154070728858, 60767411901566594609840284, 124594917284032719318155422, 255385579393590413156679840, 523313764165682604000936098, 1072014970543272420670701732, 2195409288420166581266415782, 4494786197327191271557562536, 9199925487267328019513999530, 18825392863039005508524572844, 38511540909643626989439942830, 78763934999532319990456778928, 161048261985782440137657942194, 329214679197455816855985848500, 672820411351604179407674015926, 1374732413626414795275477450936, 2808266979118885153608663302330, 5735376202009166813607642529980, 11710912771639697400545715159230, 23907098038679263868851887014080, 48794644588472548915423880413378, 99569993239801706270686359584964, 203141008686573761589846688661702, 414363289949602485614234860257480, 845047581377143424772739774283978
Generating function in Maple syntax:
(2*x^6+2*x^5-12*x^4+23*x^3-19*x^2+7*x-1)/(x-1)^2/(2*x-1)^3
Generating function in latex syntax:
\frac{2 x^{6}+2 x^{5}-12 x^{4}+23 x^{3}-19 x^{2}+7 x -1}{\left(x -1\right)^{2} \left(2 x -1\right)^{3}}
Generating function in sympy syntax:
(2*x**6 + 2*x**5 - 12*x**4 + 23*x**3 - 19*x**2 + 7*x - 1)/((x - 1)**2*(2*x - 1)**3)
Implicit equation for the generating function in Maple syntax:
-(x-1)^2*(2*x-1)^3*F(x)+2*x^6+2*x^5-12*x^4+23*x^3-19*x^2+7*x-1 = 0
Implicit equation for the generating function in latex syntax:
-\left(x -1\right)^{2} \left(2 x -1\right)^{3} F \! \left(x \right)+2 x^{6}+2 x^{5}-12 x^{4}+23 x^{3}-19 x^{2}+7 x -1 = 0
Explicit closed form in Maple syntax:
piecewise(Or(n = 0,n = 1),1,1/16*(n^2+7*n-34)*2^n+2*n+2)
Explicit closed form in latex syntax:
\left\{\begin{array}{cc}1 & n =0\text{ or } n =1 \\ \frac{\left(n^{2}+7 n -34\right) 2^{n}}{16}+2 n +2 & \mathit{\text{otherwise}} \end{array}\right.
Recurrence in maple format:
a(0) = 1
a(1) = 1
a(2) = 2
a(3) = 6
a(4) = 20
a(5) = 64
a(6) = 190
a(n+3) = 8*a(n)-12*a(n+1)+6*a(n+2)-2*n+4, n >= 7
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) = 64
a \! \left(6\right) = 190
a \! \left(n +3\right) = 8 a \! \left(n \right)-12 a \! \left(n +1\right)+6 a \! \left(n +2\right)-2 n +4, \quad n \geq 7
Specification 1
Strategy pack name: row_placements
Tree: http://permpal.com/tree/21315/
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[4,x]+F[91,x]
F[4,x] = F[11,x]*F[5,x]
F[5,x] = F[1,x]+F[6,x]+F[76,x]+F[78,x]
F[6,x] = F[7,x]
F[7,x] = F[11,x]*F[25,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[12,x]
F[11,x] = x
F[12,x] = F[13,x]+F[16,x]
F[13,x] = F[1,x]+F[14,x]
F[14,x] = F[15,x]
F[15,x] = F[11,x]*F[13,x]
F[16,x] = F[17,x]+F[20,x]
F[17,x] = F[18,x]
F[18,x] = F[11,x]*F[19,x]
F[19,x] = F[1,x]+F[17,x]
F[20,x] = F[21,x]+F[22,x]+F[24,x]
F[21,x] = 0
F[22,x] = F[11,x]*F[23,x]
F[23,x] = F[14,x]+F[20,x]
F[24,x] = F[11,x]*F[16,x]
F[25,x] = F[26,x]+F[47,x]
F[26,x] = F[27,x]+F[35,x]
F[27,x] = F[1,x]+F[28,x]
F[28,x] = F[29,x]
F[29,x] = F[11,x]*F[30,x]
F[30,x] = F[27,x]+F[31,x]
F[31,x] = F[11,x]+F[32,x]
F[32,x] = F[33,x]
F[33,x] = F[11,x]*F[34,x]
F[34,x] = F[31,x]
F[35,x] = F[17,x]+F[36,x]
F[36,x] = F[21,x]+F[37,x]+F[39,x]
F[37,x] = F[11,x]*F[38,x]
F[38,x] = F[28,x]+F[36,x]
F[39,x] = F[11,x]*F[40,x]
F[40,x] = F[35,x]+F[41,x]
F[41,x] = F[42,x]+F[44,x]
F[42,x] = F[43,x]
F[43,x] = F[11,x]*F[17,x]
F[44,x] = F[45,x]
F[45,x] = F[11,x]*F[46,x]
F[46,x] = F[41,x]
F[47,x] = F[48,x]+F[61,x]
F[48,x] = F[17,x]+F[49,x]
F[49,x] = F[21,x]+F[50,x]+F[55,x]
F[50,x] = F[11,x]*F[51,x]
F[51,x] = F[14,x]+F[52,x]
F[52,x] = F[21,x]+F[50,x]+F[53,x]
F[53,x] = F[11,x]*F[54,x]
F[54,x] = F[17,x]+F[52,x]
F[55,x] = F[11,x]*F[56,x]
F[56,x] = F[48,x]+F[57,x]
F[57,x] = F[42,x]+F[58,x]
F[58,x] = F[59,x]
F[59,x] = F[11,x]*F[60,x]
F[60,x] = F[57,x]
F[61,x] = F[62,x]+F[65,x]
F[62,x] = F[63,x]
F[63,x] = F[11,x]*F[64,x]
F[64,x] = F[17,x]+F[62,x]
F[65,x] = 2*F[21,x]+F[66,x]+F[68,x]
F[66,x] = F[11,x]*F[67,x]
F[67,x] = F[49,x]+F[65,x]
F[68,x] = F[11,x]*F[69,x]
F[69,x] = F[61,x]+F[70,x]
F[70,x] = F[71,x]+F[73,x]
F[71,x] = F[72,x]
F[72,x] = F[11,x]*F[62,x]
F[73,x] = F[74,x]
F[74,x] = F[11,x]*F[75,x]
F[75,x] = F[70,x]
F[76,x] = F[77,x]
F[77,x] = F[11,x]*F[26,x]*F[8,x]
F[78,x] = F[11,x]*F[79,x]
F[79,x] = 2*F[88,x]+F[1,x]+F[80,x]+F[89,x]
F[80,x] = F[11,x]*F[81,x]
F[81,x] = 2*F[85,x]+F[1,x]+F[82,x]+F[87,x]
F[82,x] = F[83,x]
F[83,x] = F[11,x]*F[8,x]*F[84,x]
F[84,x] = F[13,x]+F[54,x]
F[85,x] = F[86,x]
F[86,x] = F[11,x]*F[13,x]*F[8,x]
F[87,x] = F[11,x]*F[81,x]
F[88,x] = F[11,x]*F[79,x]
F[89,x] = F[90,x]
F[90,x] = F[11,x]*F[13,x]*F[8,x]
F[91,x] = F[11,x]*F[92,x]
F[92,x] = F[1,x]+F[108,x]+F[110,x]+F[93,x]
F[93,x] = F[94,x]
F[94,x] = F[11,x]*F[8,x]*F[95,x]
F[95,x] = F[101,x]+F[96,x]
F[96,x] = F[13,x]+F[97,x]
F[97,x] = F[14,x]+F[98,x]
F[98,x] = F[99,x]
F[99,x] = F[100,x]*F[11,x]
F[100,x] = F[14,x]+F[98,x]
F[101,x] = F[102,x]+F[54,x]
F[102,x] = F[103,x]+F[52,x]
F[103,x] = 2*F[21,x]+F[104,x]+F[106,x]
F[104,x] = F[105,x]*F[11,x]
F[105,x] = F[103,x]+F[98,x]
F[106,x] = F[107,x]*F[11,x]
F[107,x] = F[103,x]+F[52,x]
F[108,x] = F[109,x]*F[11,x]
F[109,x] = F[1,x]+F[108,x]+F[82,x]
F[110,x] = F[11,x]*F[92,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_{4}\! \left(x \right)+F_{91}\! \left(x \right)
F_{4}\! \left(x \right) = F_{11}\! \left(x \right) F_{5}\! \left(x \right)
F_{5}\! \left(x \right) = F_{1}\! \left(x \right)+F_{6}\! \left(x \right)+F_{76}\! \left(x \right)+F_{78}\! \left(x \right)
F_{6}\! \left(x \right) = F_{7}\! \left(x \right)
F_{7}\! \left(x \right) = F_{11}\! \left(x \right) F_{25}\! \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_{12}\! \left(x \right)
F_{11}\! \left(x \right) = x
F_{12}\! \left(x \right) = F_{13}\! \left(x \right)+F_{16}\! \left(x \right)
F_{13}\! \left(x \right) = F_{1}\! \left(x \right)+F_{14}\! \left(x \right)
F_{14}\! \left(x \right) = F_{15}\! \left(x \right)
F_{15}\! \left(x \right) = F_{11}\! \left(x \right) F_{13}\! \left(x \right)
F_{16}\! \left(x \right) = F_{17}\! \left(x \right)+F_{20}\! \left(x \right)
F_{17}\! \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_{1}\! \left(x \right)+F_{17}\! \left(x \right)
F_{20}\! \left(x \right) = F_{21}\! \left(x \right)+F_{22}\! \left(x \right)+F_{24}\! \left(x \right)
F_{21}\! \left(x \right) = 0
F_{22}\! \left(x \right) = F_{11}\! \left(x \right) F_{23}\! \left(x \right)
F_{23}\! \left(x \right) = F_{14}\! \left(x \right)+F_{20}\! \left(x \right)
F_{24}\! \left(x \right) = F_{11}\! \left(x \right) F_{16}\! \left(x \right)
F_{25}\! \left(x \right) = F_{26}\! \left(x \right)+F_{47}\! \left(x \right)
F_{26}\! \left(x \right) = F_{27}\! \left(x \right)+F_{35}\! \left(x \right)
F_{27}\! \left(x \right) = F_{1}\! \left(x \right)+F_{28}\! \left(x \right)
F_{28}\! \left(x \right) = F_{29}\! \left(x \right)
F_{29}\! \left(x \right) = F_{11}\! \left(x \right) F_{30}\! \left(x \right)
F_{30}\! \left(x \right) = F_{27}\! \left(x \right)+F_{31}\! \left(x \right)
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_{33}\! \left(x \right) = F_{11}\! \left(x \right) F_{34}\! \left(x \right)
F_{34}\! \left(x \right) = F_{31}\! \left(x \right)
F_{35}\! \left(x \right) = F_{17}\! \left(x \right)+F_{36}\! \left(x \right)
F_{36}\! \left(x \right) = F_{21}\! \left(x \right)+F_{37}\! \left(x \right)+F_{39}\! \left(x \right)
F_{37}\! \left(x \right) = F_{11}\! \left(x \right) F_{38}\! \left(x \right)
F_{38}\! \left(x \right) = F_{28}\! \left(x \right)+F_{36}\! \left(x \right)
F_{39}\! \left(x \right) = F_{11}\! \left(x \right) F_{40}\! \left(x \right)
F_{40}\! \left(x \right) = F_{35}\! \left(x \right)+F_{41}\! \left(x \right)
F_{41}\! \left(x \right) = F_{42}\! \left(x \right)+F_{44}\! \left(x \right)
F_{42}\! \left(x \right) = F_{43}\! \left(x \right)
F_{43}\! \left(x \right) = F_{11}\! \left(x \right) F_{17}\! \left(x \right)
F_{44}\! \left(x \right) = F_{45}\! \left(x \right)
F_{45}\! \left(x \right) = F_{11}\! \left(x \right) F_{46}\! \left(x \right)
F_{46}\! \left(x \right) = F_{41}\! \left(x \right)
F_{47}\! \left(x \right) = F_{48}\! \left(x \right)+F_{61}\! \left(x \right)
F_{48}\! \left(x \right) = F_{17}\! \left(x \right)+F_{49}\! \left(x \right)
F_{49}\! \left(x \right) = F_{21}\! \left(x \right)+F_{50}\! \left(x \right)+F_{55}\! \left(x \right)
F_{50}\! \left(x \right) = F_{11}\! \left(x \right) F_{51}\! \left(x \right)
F_{51}\! \left(x \right) = F_{14}\! \left(x \right)+F_{52}\! \left(x \right)
F_{52}\! \left(x \right) = F_{21}\! \left(x \right)+F_{50}\! \left(x \right)+F_{53}\! \left(x \right)
F_{53}\! \left(x \right) = F_{11}\! \left(x \right) F_{54}\! \left(x \right)
F_{54}\! \left(x \right) = F_{17}\! \left(x \right)+F_{52}\! \left(x \right)
F_{55}\! \left(x \right) = F_{11}\! \left(x \right) F_{56}\! \left(x \right)
F_{56}\! \left(x \right) = F_{48}\! \left(x \right)+F_{57}\! \left(x \right)
F_{57}\! \left(x \right) = F_{42}\! \left(x \right)+F_{58}\! \left(x \right)
F_{58}\! \left(x \right) = F_{59}\! \left(x \right)
F_{59}\! \left(x \right) = F_{11}\! \left(x \right) F_{60}\! \left(x \right)
F_{60}\! \left(x \right) = F_{57}\! \left(x \right)
F_{61}\! \left(x \right) = F_{62}\! \left(x \right)+F_{65}\! \left(x \right)
F_{62}\! \left(x \right) = F_{63}\! \left(x \right)
F_{63}\! \left(x \right) = F_{11}\! \left(x \right) F_{64}\! \left(x \right)
F_{64}\! \left(x \right) = F_{17}\! \left(x \right)+F_{62}\! \left(x \right)
F_{65}\! \left(x \right) = 2 F_{21}\! \left(x \right)+F_{66}\! \left(x \right)+F_{68}\! \left(x \right)
F_{66}\! \left(x \right) = F_{11}\! \left(x \right) F_{67}\! \left(x \right)
F_{67}\! \left(x \right) = F_{49}\! \left(x \right)+F_{65}\! \left(x \right)
F_{68}\! \left(x \right) = F_{11}\! \left(x \right) F_{69}\! \left(x \right)
F_{69}\! \left(x \right) = F_{61}\! \left(x \right)+F_{70}\! \left(x \right)
F_{70}\! \left(x \right) = F_{71}\! \left(x \right)+F_{73}\! \left(x \right)
F_{71}\! \left(x \right) = F_{72}\! \left(x \right)
F_{72}\! \left(x \right) = F_{11}\! \left(x \right) F_{62}\! \left(x \right)
F_{73}\! \left(x \right) = F_{74}\! \left(x \right)
F_{74}\! \left(x \right) = F_{11}\! \left(x \right) F_{75}\! \left(x \right)
F_{75}\! \left(x \right) = F_{70}\! \left(x \right)
F_{76}\! \left(x \right) = F_{77}\! \left(x \right)
F_{77}\! \left(x \right) = F_{11}\! \left(x \right) F_{26}\! \left(x \right) F_{8}\! \left(x \right)
F_{78}\! \left(x \right) = F_{11}\! \left(x \right) F_{79}\! \left(x \right)
F_{79}\! \left(x \right) = 2 F_{88}\! \left(x \right)+F_{1}\! \left(x \right)+F_{80}\! \left(x \right)+F_{89}\! \left(x \right)
F_{80}\! \left(x \right) = F_{11}\! \left(x \right) F_{81}\! \left(x \right)
F_{81}\! \left(x \right) = 2 F_{85}\! \left(x \right)+F_{1}\! \left(x \right)+F_{82}\! \left(x \right)+F_{87}\! \left(x \right)
F_{82}\! \left(x \right) = F_{83}\! \left(x \right)
F_{83}\! \left(x \right) = F_{11}\! \left(x \right) F_{8}\! \left(x \right) F_{84}\! \left(x \right)
F_{84}\! \left(x \right) = F_{13}\! \left(x \right)+F_{54}\! \left(x \right)
F_{85}\! \left(x \right) = F_{86}\! \left(x \right)
F_{86}\! \left(x \right) = F_{11}\! \left(x \right) F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{87}\! \left(x \right) = F_{11}\! \left(x \right) F_{81}\! \left(x \right)
F_{88}\! \left(x \right) = F_{11}\! \left(x \right) F_{79}\! \left(x \right)
F_{89}\! \left(x \right) = F_{90}\! \left(x \right)
F_{90}\! \left(x \right) = F_{11}\! \left(x \right) F_{13}\! \left(x \right) F_{8}\! \left(x \right)
F_{91}\! \left(x \right) = F_{11}\! \left(x \right) F_{92}\! \left(x \right)
F_{92}\! \left(x \right) = F_{1}\! \left(x \right)+F_{108}\! \left(x \right)+F_{110}\! \left(x \right)+F_{93}\! \left(x \right)
F_{93}\! \left(x \right) = F_{94}\! \left(x \right)
F_{94}\! \left(x \right) = F_{11}\! \left(x \right) F_{8}\! \left(x \right) F_{95}\! \left(x \right)
F_{95}\! \left(x \right) = F_{101}\! \left(x \right)+F_{96}\! \left(x \right)
F_{96}\! \left(x \right) = F_{13}\! \left(x \right)+F_{97}\! \left(x \right)
F_{97}\! \left(x \right) = F_{14}\! \left(x \right)+F_{98}\! \left(x \right)
F_{98}\! \left(x \right) = F_{99}\! \left(x \right)
F_{99}\! \left(x \right) = F_{100}\! \left(x \right) F_{11}\! \left(x \right)
F_{100}\! \left(x \right) = F_{14}\! \left(x \right)+F_{98}\! \left(x \right)
F_{101}\! \left(x \right) = F_{102}\! \left(x \right)+F_{54}\! \left(x \right)
F_{102}\! \left(x \right) = F_{103}\! \left(x \right)+F_{52}\! \left(x \right)
F_{103}\! \left(x \right) = 2 F_{21}\! \left(x \right)+F_{104}\! \left(x \right)+F_{106}\! \left(x \right)
F_{104}\! \left(x \right) = F_{105}\! \left(x \right) F_{11}\! \left(x \right)
F_{105}\! \left(x \right) = F_{103}\! \left(x \right)+F_{98}\! \left(x \right)
F_{106}\! \left(x \right) = F_{107}\! \left(x \right) F_{11}\! \left(x \right)
F_{107}\! \left(x \right) = F_{103}\! \left(x \right)+F_{52}\! \left(x \right)
F_{108}\! \left(x \right) = F_{109}\! \left(x \right) F_{11}\! \left(x \right)
F_{109}\! \left(x \right) = F_{1}\! \left(x \right)+F_{108}\! \left(x \right)+F_{82}\! \left(x \right)
F_{110}\! \left(x \right) = F_{11}\! \left(x \right) F_{92}\! \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_4(x) + F_91(x))
Eq(F_4(x), F_11(x)*F_5(x))
Eq(F_5(x), F_1(x) + F_6(x) + F_76(x) + F_78(x))
Eq(F_6(x), F_7(x))
Eq(F_7(x), F_11(x)*F_25(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_12(x))
Eq(F_11(x), x)
Eq(F_12(x), F_13(x) + F_16(x))
Eq(F_13(x), F_1(x) + F_14(x))
Eq(F_14(x), F_15(x))
Eq(F_15(x), F_11(x)*F_13(x))
Eq(F_16(x), F_17(x) + F_20(x))
Eq(F_17(x), F_18(x))
Eq(F_18(x), F_11(x)*F_19(x))
Eq(F_19(x), F_1(x) + F_17(x))
Eq(F_20(x), F_21(x) + F_22(x) + F_24(x))
Eq(F_21(x), 0)
Eq(F_22(x), F_11(x)*F_23(x))
Eq(F_23(x), F_14(x) + F_20(x))
Eq(F_24(x), F_11(x)*F_16(x))
Eq(F_25(x), F_26(x) + F_47(x))
Eq(F_26(x), F_27(x) + F_35(x))
Eq(F_27(x), F_1(x) + F_28(x))
Eq(F_28(x), F_29(x))
Eq(F_29(x), F_11(x)*F_30(x))
Eq(F_30(x), F_27(x) + F_31(x))
Eq(F_31(x), F_11(x) + F_32(x))
Eq(F_32(x), F_33(x))
Eq(F_33(x), F_11(x)*F_34(x))
Eq(F_34(x), F_31(x))
Eq(F_35(x), F_17(x) + F_36(x))
Eq(F_36(x), F_21(x) + F_37(x) + F_39(x))
Eq(F_37(x), F_11(x)*F_38(x))
Eq(F_38(x), F_28(x) + F_36(x))
Eq(F_39(x), F_11(x)*F_40(x))
Eq(F_40(x), F_35(x) + F_41(x))
Eq(F_41(x), F_42(x) + F_44(x))
Eq(F_42(x), F_43(x))
Eq(F_43(x), F_11(x)*F_17(x))
Eq(F_44(x), F_45(x))
Eq(F_45(x), F_11(x)*F_46(x))
Eq(F_46(x), F_41(x))
Eq(F_47(x), F_48(x) + F_61(x))
Eq(F_48(x), F_17(x) + F_49(x))
Eq(F_49(x), F_21(x) + F_50(x) + F_55(x))
Eq(F_50(x), F_11(x)*F_51(x))
Eq(F_51(x), F_14(x) + F_52(x))
Eq(F_52(x), F_21(x) + F_50(x) + F_53(x))
Eq(F_53(x), F_11(x)*F_54(x))
Eq(F_54(x), F_17(x) + F_52(x))
Eq(F_55(x), F_11(x)*F_56(x))
Eq(F_56(x), F_48(x) + F_57(x))
Eq(F_57(x), F_42(x) + F_58(x))
Eq(F_58(x), F_59(x))
Eq(F_59(x), F_11(x)*F_60(x))
Eq(F_60(x), F_57(x))
Eq(F_61(x), F_62(x) + F_65(x))
Eq(F_62(x), F_63(x))
Eq(F_63(x), F_11(x)*F_64(x))
Eq(F_64(x), F_17(x) + F_62(x))
Eq(F_65(x), 2*F_21(x) + F_66(x) + F_68(x))
Eq(F_66(x), F_11(x)*F_67(x))
Eq(F_67(x), F_49(x) + F_65(x))
Eq(F_68(x), F_11(x)*F_69(x))
Eq(F_69(x), F_61(x) + F_70(x))
Eq(F_70(x), F_71(x) + F_73(x))
Eq(F_71(x), F_72(x))
Eq(F_72(x), F_11(x)*F_62(x))
Eq(F_73(x), F_74(x))
Eq(F_74(x), F_11(x)*F_75(x))
Eq(F_75(x), F_70(x))
Eq(F_76(x), F_77(x))
Eq(F_77(x), F_11(x)*F_26(x)*F_8(x))
Eq(F_78(x), F_11(x)*F_79(x))
Eq(F_79(x), F_1(x) + F_80(x) + 2*F_88(x) + F_89(x))
Eq(F_80(x), F_11(x)*F_81(x))
Eq(F_81(x), F_1(x) + F_82(x) + 2*F_85(x) + F_87(x))
Eq(F_82(x), F_83(x))
Eq(F_83(x), F_11(x)*F_8(x)*F_84(x))
Eq(F_84(x), F_13(x) + F_54(x))
Eq(F_85(x), F_86(x))
Eq(F_86(x), F_11(x)*F_13(x)*F_8(x))
Eq(F_87(x), F_11(x)*F_81(x))
Eq(F_88(x), F_11(x)*F_79(x))
Eq(F_89(x), F_90(x))
Eq(F_90(x), F_11(x)*F_13(x)*F_8(x))
Eq(F_91(x), F_11(x)*F_92(x))
Eq(F_92(x), F_1(x) + F_108(x) + F_110(x) + F_93(x))
Eq(F_93(x), F_94(x))
Eq(F_94(x), F_11(x)*F_8(x)*F_95(x))
Eq(F_95(x), F_101(x) + F_96(x))
Eq(F_96(x), F_13(x) + F_97(x))
Eq(F_97(x), F_14(x) + F_98(x))
Eq(F_98(x), F_99(x))
Eq(F_99(x), F_100(x)*F_11(x))
Eq(F_100(x), F_14(x) + F_98(x))
Eq(F_101(x), F_102(x) + F_54(x))
Eq(F_102(x), F_103(x) + F_52(x))
Eq(F_103(x), F_104(x) + F_106(x) + 2*F_21(x))
Eq(F_104(x), F_105(x)*F_11(x))
Eq(F_105(x), F_103(x) + F_98(x))
Eq(F_106(x), F_107(x)*F_11(x))
Eq(F_107(x), F_103(x) + F_52(x))
Eq(F_108(x), F_109(x)*F_11(x))
Eq(F_109(x), F_1(x) + F_108(x) + F_82(x))
Eq(F_110(x), F_11(x)*F_92(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.factor", "ignore_parent": true, "interleaving": null, "strategy_class": "FactorFactory", "tracked": false, "unions": false, "workable": true}], "iterative": false, "name": "row_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, 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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 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": [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], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 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, 1, 3], "pos": [[0, 1], [0, 1], [2, 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": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 2, 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, 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, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [3, 1, 2, 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": [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], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 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, 1, 3], "pos": [[0, 0], [0, 0], [1, 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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": [3, 1, 2, 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": [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], [0, 1], [0, 1]]}, {"patt": [2, 1, 0], "pos": [[2, 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, 1, 3], "pos": [[0, 1], [0, 1], [2, 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": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [0, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [0, 1], [2, 1]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 1], [0, 1], [2, 1], [2, 1]]}, {"patt": [3, 1, 2, 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}}, {"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, 1]]}, {"patt": [0], "pos": [[1, 0]]}, {"patt": [0], "pos": [[2, 1]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 1], "pos": [[2, 0], [2, 0]]}, {"patt": [1, 0], "pos": [[1, 1], [1, 1]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [2, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [2, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [3, 0], [3, 0]]}, {"patt": [1, 0, 2], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[2, 0], [3, 0], [3, 0]]}, {"patt": [1, 2, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [2, 0]]}, {"patt": [2, 1, 0], "pos": [[3, 0], [3, 0], [3, 0]]}, {"patt": [3, 1, 2, 0], "pos": [[0, 0], [0, 0], [3, 0], [3, 0]]}], "requirements": [[{"patt": [0], "pos": [[1, 1]]}]]}, {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"patt": [0], "pos": [[0, 1]]}, {"patt": [0], "pos": [[1, 1]]}, {"patt": [0], "pos": [[2, 0]]}, {"patt": [0], "pos": [[3, 1]]}, {"patt": [0, 1], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[1, 0], [1, 0]]}, {"patt": [1, 0], "pos": [[1, 0], [3, 0]]}, {"patt": [1, 0], "pos": [[2, 1], [2, 1]]}, {"patt": [1, 0], "pos": [[3, 0], [3, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [0, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [1, 0]]}, {"patt": [0, 2, 1], "pos": [[0, 0], [0, 0], [3, 0]]}, {"patt": [2, 0, 1], "pos": [[0, 0], [0, 0], [0, 0]]}], "requirements": [[{"patt": [0], "pos": [[2, 1]]}]]}], "class_module": "comb_spec_searcher.strategies.rule", "comb_class": {"assumptions": [], "class_module": "tilings.tiling", "comb_class": "Tiling", "obstructions": [{"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], [0, 0], [0, 0]]}, {"patt": [2, 1, 0], "pos": [[1, 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, 1, 3], "pos": [[0, 0], [0, 0], [1, 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": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [0, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [0, 0], [1, 0]]}, {"patt": [0, 3, 2, 1], "pos": [[0, 0], [0, 0], [1, 0], [1, 0]]}, {"patt": 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