A289615 A246604 (Catalan(n)-n) with initial terms 1,0,0,2 changed to 1,1,1,3.

1, 1, 1, 3, 10, 37, 126, 422, 1422, 4853, 16786, 58775, 208000, 742887, 2674426, 9694830, 35357654, 129644773, 477638682, 1767263171, 6564120400, 24466266999, 91482563618, 343059613627, 1289904147300, 4861946401427, 18367353072126, 69533550915977, 263747951750332, 1002242216651339

Offset

0,4

Comments

a(n) is the number of permutations of length n that avoid the pattern 321 and the mesh pattern (12, 287) or the same sequence for the mesh patterns (12, 347), (12, 437), (12, 497). - Thomas Scheuerle, Dec 18 2025

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.

Mathematica

Join[{1, 1, 1, 3}, Array[CatalanNumber[#]-#&, 30, 4]] (* Paolo Xausa, Dec 08 2023 *)

Prog

(PARI) listA(max_n) = my(x='x+O(x^max_n)); Vec(-(-2*x^6+2*x^5+2*x^3-x^2+2*x+sqrt(1-4*x)*(x-1)^2-1)/(2*(x-1)^2*x)) \\ Thomas Scheuerle, Dec 23 2025

Crossrefs

A variant of A246604.

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

Sequence in context: A104603 A337341 A080625 * A359721 A138807 A149043

Adjacent sequences: A289612 A289613 A289614 * A289616 A289617 A289618

Keyword

nonn

Author

N. J. A. Sloane, Jul 09 2017

Extensions

Offset changed by Thomas Scheuerle, Dec 18 2025

Status

approved