A289588 a(n) is the number of permutations of length n that avoid the pattern 321 and the mesh pattern (12, 117) or the same sequence for the mesh patterns (12, 213), (12, 342), (12, 348).

1, 1, 1, 2, 4, 11, 34, 110, 365, 1234, 4237, 14741, 51869, 184299, 660401, 2383929, 8661434, 31649819, 116242094, 428878334, 1588858034, 5908076564, 22042959974, 82495136174, 309605919164, 1164967889198, 4393950529676, 16609453053052, 62913704495452, 238760752257656

Offset

0,4

Links

Table of n, a(n) for n=0..29.

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

G.f.: (x^3+x^2-x)*C(x)/(x-1) - (x^3-x+1)/(x-1) where C(x) is the g.f. for the Catalan numbers (A000108). - Michael D. Weiner, Aug 08 2019

Prog

(PARI) listA(max_n) = my(x='x+O(x^max_n)); Vec((x^3+x^2-x)*((1-sqrt(1-4*x))/(2*x))/(x-1)-(x^3-x+1)/(x-1)) \\ Thomas Scheuerle, Dec 21 2025

Crossrefs

Cf. A000108.

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

Sequence in context: A369843 A099215 A089407 * A362638 A344489 A238425

Adjacent sequences: A289585 A289586 A289587 * A289589 A289590 A289591

Keyword

nonn

Author

N. J. A. Sloane, Jul 08 2017

Extensions

More terms, name and offset changed by Thomas Scheuerle, Dec 21 2025

Status

approved