A289453 a(n) is the number of permutations of length n that avoid the pattern 321 and the mesh pattern (12, 106) or the same sequence for the mesh patterns (12, 122), (12, 142), (12, 158), (12, 172), (12, 188), (12, 226), (12, 242).

1, 1, 1, 2, 5, 13, 36, 103, 303, 910, 2779, 8603, 26936, 85149, 271389, 871154, 2813849, 9138849, 29826476, 97770747, 321753155, 1062627518, 3520815927, 11700046071, 38985853424, 130229025017, 436020282425, 1462951328322, 4918258874829, 16565024099733

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^2 + sqrt(x^4 - 2*x^3 - 5*x^2 - 2*x + 1) - 3*x - 1)/(4*x). - Thomas Scheuerle, Dec 23 2025

G.f.: (2-sqrt(2))/2+1/sqrt(2)*C(sqrt(2)*x/(x^2+(2*sqrt(2)-1)*x+1)), where C(x) is the g.f. for the Catalan numbers, A000108. - Michael D. Weiner, Jul 20 2022

Prog

(PARI) listA(max_n) = my(x='x+O(x^max_n)); Vec(-(-x^2+sqrt(x^4-2*x^3-5*x^2-2*x+1)-3*x-1)/(4*x)) \\ Thomas Scheuerle, Dec 23 2025

Crossrefs

Cf. A000108.

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

Sequence in context: A370168 A099164 A358460 * A339290 A036765 A246555

Adjacent sequences: A289450 A289451 A289452 * A289454 A289455 A289456

Keyword

nonn

Author

N. J. A. Sloane, Jul 08 2017

Extensions

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

Status

approved