A289609 - OEIS

A289609

a(n) is the number of permutations of length n that avoid the pattern 321 and the mesh pattern (12, 285) or the same sequence for the mesh patterns (12, 339), (12, 369), (12, 405).

1, 1, 1, 2, 7, 29, 109, 388, 1355, 4721, 16525, 58257, 206969, 740831, 2670321, 9686628, 35341259, 129611993, 477573133, 1767132085, 6563858241, 24465742695, 91481515025, 343057516457, 1289899952977, 4861938012799, 18367336294889, 69533517361523, 263747884641445

(list; graph; refs; listen; history; text; internal format)

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 18 2025: (Start)

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

a(n) = C(n) - 2^(n-2) - 2*n + 5, for n > 2, where C(n) is the Catalan number A000108.

a(n) = A289610 - n + 3, for n > 2. (End)

PROG

(PARI) listA(max_n) = my(x='x+O(x^max_n)); Vec(-(8*x^6+4*x^4-8*x^3+10*x^2-8*x+2*sqrt(1-4*x)*(x-1)^2*(2*x-1)+2)/(4*(x-1)^2*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: A155186 A203969 A199581 * A278815 A263367 A120757

Adjacent sequences: A289606 A289607 A289608 * A289610 A289611 A289612

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane, Jul 09 2017

EXTENSIONS

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

STATUS

approved