Voozh

A289446

a(n) is the number of permutations of length n that avoid the pattern 231 and the mesh pattern (21, 204) or the same sequence for the mesh patterns (21, 206), (21, 236), (21, 238).

1, 1, 1, 2, 7, 25, 85, 285, 964, 3310, 11527, 40619, 144545, 518680, 1874713, 6819033, 24942773, 91692355, 338580112, 1255267919, 4670808304, 17437517562, 65296399663, 245186344749, 923016310851, 3482917631642, 13171095703465, 49908870565766, 189474155924628

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OFFSET

0,4

LINKS

Table of n, a(n) for n=0..28.

Christian Sievers, RFE Dec 2025: Mesh patterns avoiding 321, SeqFan thread.

Murray Tannock, Equivalence classes of mesh patterns with a dominating pattern, MSc Thesis, Reykjavik Univ., May 2016. See Appendix B1.

FORMULA

G.f.: (2*(x - 1))/(-2*x^2 + sqrt(1 - 4*x)*x + x - sqrt(1 - 4*x) - 1). - Thomas Scheuerle, Dec 23 2025

PROG

(PARI) listA(max_n) = my(x='x+O(x^max_n)); Vec((2*(x-1))/(-2*x^2+sqrt(1-4*x)*x+x-sqrt(1-4*x)-1)) \\ Thomas Scheuerle, Dec 23 2025

CROSSREFS