A289451 a(n) is the number of permutations of length n that avoid the pattern 231 and the mesh pattern (12, 409) or the same sequence for the mesh pattern (12, 473).

1, 1, 1, 2, 8, 32, 117, 408, 1402, 4826, 16751, 58731, 207946, 742822, 2674349, 9694740, 35357550, 129644654, 477638547, 1767263019, 6564120230, 24466266810, 91482563409, 343059613397, 1289904147048, 4861946401152, 18367353071827, 69533550915653, 263747951749982

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

From Vladimir Kruchinin, Jan 06 2022: (Start)

a(n) = binomial(2*n, n)/(n+1) - (n-1)*n/2.

G.f.: (1-sqrt(1-4*x))/(2*x) - x^2/((1-x))^3. (End)

a(n) ~ 4^n/(n^(3/2)*sqrt(Pi)). - Stefano Spezia, Dec 19 2025

Prog

(PARI) listA(max_n) = my(x='x+O(x^max_n)); Vec((1-sqrt(1-4*x))/(2*x) - x^2/((1-x))^3) \\ Thomas Scheuerle, Dec 19 2025

Crossrefs

Cf. A000108.

Related to mesh patterns: A280891, A289446-A289453, A289587-A289616, A289652-A289654.

Sequence in context: A067897 A145682 A363109 * A230509 A099752 A230393

Adjacent sequences: A289448 A289449 A289450 * A289452 A289453 A289454

Keyword

nonn

Author

N. J. A. Sloane, Jul 08 2017

Extensions

More terms, name and offset changed by Thomas Scheuerle, Dec 19 2025

Status

approved