A289449 a(n) is the number of permutations of length n that avoid the pattern 231 and the mesh pattern (12, 281) or the same sequence for the mesh patterns (12, 313), (12, 345), (12, 377), (12, 401), (12, 403), (12, 465), (12, 467).

1, 1, 1, 2, 7, 26, 93, 325, 1129, 3935, 13813, 48885, 174397, 626785, 2267813, 8254806, 30209779, 111094202, 410327745, 1521547078, 5662360451, 21141200004, 79170069157, 297293424680, 1119201700227, 4223248082578, 15970754734177

Offset

0,4

Links

Table of n, a(n) for n=0..26.

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 Thomas Scheuerle, Dec 10 2025: (Start)

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

a(n) = A127156(n+1, 1). (End)

Prog

(PARI) listA(max_n) = my(x='x+O(x^max_n)); Vec((2-4*x)/((1+sqrt(1-4*x))*(x-1)^2)) \\ Thomas Scheuerle, Dec 10 2025

Crossrefs

Cf. A127156, A104496 (First differences up to sign).

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

Sequence in context: A027417 A134063 A087448 * A188860 A129273 A055988

Adjacent sequences: A289446 A289447 A289448 * A289450 A289451 A289452

Keyword

nonn

Author

N. J. A. Sloane, Jul 08 2017

Extensions

More terms, name and offset changed by Thomas Scheuerle, Dec 10 2025

Status

approved