A289596 a(n) is the number of permutations of length n that avoid the pattern 321 and the mesh pattern (12, 299) or the same sequence for the mesh patterns (12, 395), (12, 419), (12, 425).

1, 1, 1, 1, 5, 20, 74, 265, 937, 3304, 11678, 41478, 148202, 532840, 1927444, 7012213, 25646441, 94254352, 347928374, 1289493418, 4796595086, 17901622312, 67015248044, 251574952858, 946840339370, 3572033865520, 13505389893484, 51166164289420, 194214333725492

Offset

0,5

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

From Thomas Scheuerle, Dec 19 2025: (Start)

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

a(n) = A289594(n) + A289598(n) - A289597(n). (End)

Prog

(PARI) listA(max_n) = my(x='x+O(x^max_n)); Vec((sqrt(1-4*x)*(x-1)-x/2+3*x^2+2*x^3+(5*x-2)/(2*(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: A392266 A273718 A094806 * A026639 A248326 A022633

Adjacent sequences: A289593 A289594 A289595 * A289597 A289598 A289599

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