A289595 a(n) is the number of permutations of length n that avoid the pattern 321 and the mesh pattern (12, 189) or the same sequence for the mesh patterns (12, 243), (12, 378), (12, 414).

1, 1, 1, 2, 8, 26, 85, 283, 959, 3300, 11505, 40560, 144364, 518092, 1872754, 6812393, 24919925, 91612680, 338299065, 1254266820, 4667212440, 17424507900, 65249033430, 245012929590, 922378266654, 3480559690488, 13162347057050, 49876293696528, 189352454432904, 720126911828856

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

a(n+4) = A000245(n+2) - A000108(n). - Michael D. Weiner, Jul 24 2020

From Thomas Scheuerle, Dec 17 2025: (Start)

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

a(n) = A289590(n) - A289598(n) + A289601(n). (End)

Prog

(PARI) listA(max_n) = my(x='x+O(x^max_n)); Vec(-(x^3-2*x^2+x-1-sqrt(1-4*x)*(-1+x+x^3))/(2*x)) \\ Thomas Scheuerle, Dec 17 2025

Crossrefs

Cf. A000108, A000245.

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

Sequence in context: A060410 A128634 A230904 * A343485 A298189 A053956

Adjacent sequences: A289592 A289593 A289594 * A289596 A289597 A289598

Keyword

nonn

Author

N. J. A. Sloane, Jul 08 2017

Extensions

More terms, name and offset changed by Thomas Scheuerle, Dec 17 2025

Status

approved