A289598 a(n) is the number of permutations of length n that avoid the pattern 321 and the mesh pattern (12, 363) or the same sequence for the mesh patterns (12, 399), (12, 429), (12, 483).

1, 1, 1, 2, 7, 25, 86, 292, 995, 3425, 11926, 41981, 149216, 534877, 1931528, 7020392, 25662811, 94287105, 347993894, 1289624473, 4796857212, 17902146581, 67016296600, 251577049989, 946844533652, 3572042254105, 13505406670676, 51166197843827, 194214400834330

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

For n >= 1, a(n) = C(n) - C(n-1) - n + 2, where C = A000108. - Ruud H.G. van Tol, Dec 05 2025

From Thomas Scheuerle, Dec 10 2025: (Start)

G.f.: -(5*x^3 - 5*x^2 + 3*x + sqrt(1 - 4*x)*(1 - x)*(x - 1)^2 - 1)/(2*(x - 1)^2*x).

a(n) = A289601(n) + A289590(n) - A289595(n). (End)

Prog

(PARI) C(n)= binomial(2*n, n)/(n+1);
a(n)= if(n<1, 1, C(n)-C(n-1)-n+2); \\ Ruud H.G. van Tol, Dec 05 2025

Crossrefs

Cf. A000108.

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

Sequence in context: A169651 A289446 A370022 * A030017 A131430 A007484

Adjacent sequences: A289595 A289596 A289597 * A289599 A289600 A289601

Keyword

nonn

Author

N. J. A. Sloane, Jul 08 2017

Extensions

Name and offset changed by Thomas Scheuerle, Dec 10 2025

Status

approved