A116829 Number of permutations of length n which avoid the patterns 1234, 1324, 3421.

1, 2, 6, 21, 73, 229, 629, 1521, 3304, 6578, 12201, 21353, 35607, 57007, 88153, 132293, 193422, 276388, 387005, 532173, 720005, 959961, 1262989, 1641673, 2110388, 2685462, 3385345, 4230785, 5245011, 6453923

Offset

1,2

Links

Table of n, a(n) for n=1..30.

D. Callan, T. Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 (2017), Table 2 No 63.

Lara Pudwell, Systematic Studies in Pattern Avoidance, 2005.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: x*(x^9-5*x^8+6*x^7+x^6+2*x^5-17*x^4+14*x^3-13*x^2+5*x-1)/(x-1)^7.

For n >= 4, a(n) = (7*n^6 - 15*n^5 - 125*n^4 + 255*n^3 + 3358*n^2 - 11400*n + 9360)/720. - Franklin T. Adams-Watters, Sep 16 2006

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). - Wesley Ivan Hurt, Jun 26 2022

Mathematica

CoefficientList[Series[(x^9 - 5*x^8 + 6*x^7 + x^6 + 2*x^5 - 17*x^4 + 14*x^3 - 13*x^2 + 5*x - 1)/(x - 1)^7, {x, 0, 50}], x] (* Wesley Ivan Hurt, Jun 26 2022 *)

Crossrefs

Sequence in context: A116834 A116762 A116803 * A116824 A116789 A116783

Adjacent sequences: A116826 A116827 A116828 * A116830 A116831 A116832

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Status

approved