A289597 a(n) is the number of permutations of length n that avoid the pattern 321 and the mesh pattern (12, 271) or the same sequence for the mesh patterns (12, 303), (12, 331), (12, 421), (12, 423), (12, 459), (12, 481), (12, 489).

1, 1, 1, 2, 6, 21, 75, 266, 938, 3305, 11679, 41479, 148203, 532841, 1927445, 7012214, 25646442, 94254353, 347928375, 1289493419, 4796595087, 17901622313, 67015248045, 251574952859, 946840339371, 3572033865521, 13505389893485, 51166164289421, 194214333725493

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.

Murray Tannock and Henning Ulfarsson, Equivalence classes of mesh patterns with a dominating pattern, arXiv:1704.07104 [math.CO], 2017-2018.

Formula

G.f.: (1-x)*C(x) + x*(x^2-3*x+1)/((x-1)*(2*x-1)), where C(x) is the g.f. for the Catalan numbers (A000108). - Michael D. Weiner, Jan 02 2019

Prog

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

Crossrefs

Cf. A000108.

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

Sequence in context: A294815 A116751 A116823 * A116743 A294816 A263790

Adjacent sequences: A289594 A289595 A289596 * A289598 A289599 A289600

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