A289604 a(n) is the number of permutations of length n that avoid the pattern 321 and the mesh pattern (12, 277) or the same sequence for the mesh pattern (12, 337).

1, 1, 1, 2, 6, 25, 96, 357, 1289, 4587, 16258, 57728, 205921, 738751, 2666184, 9678385, 35324813, 129579151, 477507510, 1767000912, 6563595981, 24465218275, 91480466300, 343055419138, 1289895758487, 4861929623985, 18367319517446, 69533483806842, 263747817532309

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

From Thomas Scheuerle, Dec 17 2025: (Start)

G.f.: -(4*x^9 - 10*x^8 + 8*x^7 - 6*x^6 + 4*x^5 - 6*x^4 + 9*x^3 - 9*x^2 + sqrt(1 - 4*x)*(2*x^4 - 7*x^3 + 9*x^2 - 5*x + 1) + 5*x - 1)/(2*(x - 1)^3*x*(2*x - 1)).

a(n) = A289607(n) + A289610(n) - A289614(n).

a(n) = floor((A289603(n) + A289605(n))/2). (End)

Prog

(PARI) listA(max_n) = my(x='x+O(x^max_n)); Vec(-(4*x^9-10*x^8+8*x^7-6*x^6+4*x^5-6*x^4+9*x^3-9*x^2+sqrt(1-4*x)*(2*x^4-7*x^3+9*x^2-5*x+1)+5*x-1)/(2*(x-1)^3*x*(2*x-1))) \\ Thomas Scheuerle, Dec 18 2025

Crossrefs

Cf. A000108.

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

Sequence in context: A066317 A027104 A019048 * A028302 A064811 A074418

Adjacent sequences: A289601 A289602 A289603 * A289605 A289606 A289607

Keyword

nonn

Author

N. J. A. Sloane, Jul 08 2017

Extensions

More terms, name and offset changed by Thomas Scheuerle, Dec 18 2025

Status

approved