A289587 a(n) is the number of permutations of length n that avoid the pattern 321 and the mesh pattern (12, 174) or the same sequence for the mesh pattern (12, 234).

1, 1, 1, 3, 6, 18, 47, 139, 405, 1225, 3740, 11602, 36357, 115049, 366969, 1178791, 3809802

Offset

0,4

Links

Table of n, a(n) for n=0..16.

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

Conjectured g.f.: (x^4 + 4*x^3 + 11*x^2 - (x^2 + 5*x + 3)*sqrt(x^4 - 2*x^3 - 5*x^2 - 2*x + 1) + 10*x + 3)/(8*x*(x + 1)^2). - Thomas Scheuerle, Dec 23 2025

Crossrefs

Cf. A000108.

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

Sequence in context: A115344 A223044 A317078 * A151262 A148555 A148556

Adjacent sequences: A289584 A289585 A289586 * A289588 A289589 A289590

Keyword

nonn,more

Author

N. J. A. Sloane, Jul 08 2017

Extensions

More terms, name and offset changed by Thomas Scheuerle, Dec 23 2025

Status

approved