A289601 a(n) is the number of permutations of length n that avoid the pattern 321 and the mesh pattern (12, 431) or the same sequence for the mesh pattern (12, 491).

1, 1, 1, 3, 10, 34, 114, 382, 1292, 4426, 15358, 53915, 191206, 684103, 2466416, 8951932, 32683216, 119949930, 442281014, 1637618383, 6086481702, 22699003811, 84918443200, 318593346609, 1198421583662, 4518886787779, 17077448924804, 64671604514527, 245380598678182, 932708665735337

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

From Thomas Scheuerle, Dec 11 2025: (Start)

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

a(n) = A289600(n)+1, for n > 2.

a(n) = A289595(n) + A289598(n) - A289590(n). (End)

Prog

(PARI) listA(max_n) = my(x='x+O(x^max_n)); Vec((-(2*x^4)/(x-1)^2+(sqrt(1-4*x)-1)*x^2-sqrt(1-4*x)+1)/(2*x)) \\ Thomas Scheuerle, Dec 11 2025

Crossrefs

Cf. A000108.

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

Sequence in context: A193036 A083580 A255631 * A291337 A255813 A113300

Adjacent sequences: A289598 A289599 A289600 * A289602 A289603 A289604

Keyword

nonn

Author

N. J. A. Sloane, Jul 08 2017

Extensions

More terms, name and offset changed by Thomas Scheuerle, Dec 11 2025

Status

approved