A289652 - OEIS

A289652

Catalan numbers - 2 (A120304) with first three terms changed to 1,1,1.

1, 1, 1, 3, 12, 40, 130, 427, 1428, 4860, 16794, 58784, 208010, 742898, 2674438, 9694843, 35357668, 129644788, 477638698, 1767263188, 6564120418, 24466267018, 91482563638, 343059613648, 1289904147322, 4861946401450, 18367353072150, 69533550916002, 263747951750358

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

OFFSET

0,4

COMMENTS

a(n) is the number of permutations of length n that avoid the pattern 321 and the mesh pattern (12, 379) or the same sequence for the mesh patterns (12, 415), (12, 445), (12, 499). - Thomas Scheuerle, Dec 18 2025

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.

MATHEMATICA

Join[{1, 1, 1}, CatalanNumber[Range[3, 30]]-2] (* Paolo Xausa, Dec 08 2023 *)

PROG

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

CROSSREFS

A variant of A120304.

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

Sequence in context: A247002 A027991 A120304 * A026071 A102839 A050182