A289602 a(n) is the number of permutations of length n that avoid the pattern 321 and the mesh pattern (21, 257) or the same sequence for the mesh patterns (21, 261), (21, 273), (21, 277), (21, 321), (21, 325), (21, 337), (21, 341).

1, 1, 1, 3, 9, 30, 104, 365, 1286, 4542, 16092, 57250, 204684, 735732, 2659080, 9662077, 35288038, 129497334, 477327404, 1766607830, 6562744164, 24463383436, 91476534328, 343047030738, 1289877932924, 4861891875500, 18367239825944, 69533316034980, 263747465211096

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 B2.

Formula

From Thomas Scheuerle, Dec 17 2025: (Start)

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

a(n) = A000108(n) - A045623(n-2), for n > 1. (End)

Prog

(PARI) listA(max_n) = my(x='x+O(x^max_n)); Vec(((1-sqrt(1-4*x))/(2*x))-(x^2*(1-x)^2/(1-2*x)^2)) \\ Thomas Scheuerle, Dec 17 2025

Crossrefs

Cf. A000108, A045623.

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

Sequence in context: A148952 A148953 A148954 * A148955 A119372 A145268

Adjacent sequences: A289599 A289600 A289601 * A289603 A289604 A289605

Keyword

nonn

Author

N. J. A. Sloane, Jul 08 2017

Extensions

More terms, name and offset changed by Thomas Scheuerle, Dec 17 2025

Status

approved