A289592 a(n) is the number of permutations of length n that avoid the pattern 321 and the mesh pattern (12, 187) or the same sequence for the mesh pattern (12, 442).

1, 1, 1, 2, 7, 22, 71, 235, 794, 2728, 9503, 33488, 119170, 427652, 1545878, 5623753, 20573960, 75644700, 279369615, 1035917700, 3855226650, 14394913860, 53911007250, 202462899990, 762283780284, 2876774770464, 10880208950246, 41232833427280, 156553609661204

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

G.f.: -(3*x^3 - 6*x^2 + sqrt(1 - 4*x)*(-x^3 + 2*x^2 - 2*x + 1) + 2*x - 1)/(2*x). - Thomas Scheuerle, Dec 19 2025

Prog

(PARI) listA(max_n) = my(x='x+O(x^max_n)); Vec(-(3*x^3-6*x^2+sqrt(1-4*x)*(-x^3+2*x^2-2*x+1)+2*x-1)/(2*x)) \\ Thomas Scheuerle, Dec 19 2025

Crossrefs

Cf. A000108.

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

Sequence in context: A109999 A092690 A030186 * A292230 A162770 A116387

Adjacent sequences: A289589 A289590 A289591 * A289593 A289594 A289595

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