A289590 a(n) is the number of permutations of length n that avoid the pattern 321 and the mesh pattern (12, 179) or the same sequence for the mesh patterns (12, 185), (12, 314), (12, 410).

1, 1, 1, 1, 5, 17, 57, 193, 662, 2299, 8073, 28626, 102374, 368866, 1337866, 4880853, 17899520, 65949855, 244011945, 906272910, 3377587950, 12627650670, 47346886830, 177996632970, 670801216644, 2533715156814, 9590304802922, 36370887025828, 138186256589052, 525912510994500

Offset

0,5

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

From Thomas Scheuerle, Dec 10 2025: (Start)

G.f.: 2*x + ((sqrt(1 - 4*x) - 1)*(x*((x - 1)*x + 2) - 1))/(2*x) = 2*x - (x^3 - x^2 + 2*x - 1)*C(x), where C(x) is (1-sqrt(1-4*x))/(2*x) (A000108).

a(n) = A289595(n) + A289598(n) - A289601(n). (End)

Prog

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

Crossrefs

Cf. A000108.

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

Sequence in context: A027034 A027097 A098184 * A054113 A146697 A009229

Adjacent sequences: A289587 A289588 A289589 * A289591 A289592 A289593

Keyword

nonn

Author

N. J. A. Sloane, Jul 08 2017

Extensions

More terms, name and offset changed by Thomas Scheuerle, Dec 10 2025

Status

approved