A116803 Number of permutations of length n which avoid the patterns 1234, 3421, 4231.

1, 2, 6, 21, 73, 228, 616, 1460, 3110, 6082, 11102, 19155, 31539, 49924, 76416, 113626, 164744, 233618, 324838, 443825, 596925, 791508, 1036072, 1340352, 1715434, 2173874, 2729822, 3399151, 4199591, 5150868, 6274848, 7595686, 9139980, 10936930, 13018502

Offset

1,2

Links

Table of n, a(n) for n=1..35.

David Callan and Toufik Mansour, Enumeration of small Wilf classes avoiding 1324 and two other 4-letter patterns, arXiv:1705.00933 [math.CO], 2017, Table 2 No 62.

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*(3*x^7-7*x^6-3*x^5+17*x^4-14*x^3+13*x^2-5*x+1)/(x-1)^7.

For n >= 2, a(n) = (5*n^6 + 9*n^5 - 205*n^4 + 315*n^3 + 3080*n^2 - 10404*n + 10080)/720. - Franklin T. Adams-Watters, Sep 16 2006

Crossrefs

Sequence in context: A294760 A116834 A116762 * A116829 A116824 A116789

Adjacent sequences: A116800 A116801 A116802 * A116804 A116805 A116806

Keyword

nonn,easy

Author

Lara Pudwell, Feb 26 2006

Extensions

More terms from Jason Yuen, Sep 18 2025

Status

approved