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A289447
a(n) is the number of permutations of length n that avoid the pattern 231 and the mesh pattern (12, 174) or the same sequence for the mesh pattern (12, 238).
0
1, 1, 1, 4, 10, 31, 97, 316, 1054, 3586, 12394, 43396, 153604, 548731, 1975873, 7163908, 26131510, 95829358, 353100382, 1306618696, 4853643916, 18092491990, 67655720026, 253727789944, 954081100780, 3596374863316, 13587079466692, 51439504808596, 195124852324504, 741507897774643
OFFSET
0,4
COMMENTS
From Thomas Scheuerle, Dec 08 2025: (Start)
a(n) is the number of permutations of length n that avoid the mesh pattern:
|#| or same sequence: |#|#
-O-+- -O-+-
#| |# #| |#
-+-O- -+-O-
#|#| #|#|
The binary encoding of the mesh patterns, as it is used here in the name, is explained by Christian Sievers in the SeqFan thread. (End)
LINKS
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 B1.
FORMULA
From Thomas Scheuerle, Dec 08 2025: (Start)
G.f.: -2*(4*x + 3*sqrt(1 - 4*x) - 3)/((sqrt(1 - 4*x) - 3)^2*x).
a(n) = A065601(n) - A126983(n+1). (End)
PROG
(PARI) listA(max_n) = my(x='x+O(x^max_n)); Vec(-(2*(4*x+3*sqrt(1-4*x)-3))/((sqrt(1-4*x)-3)^2*x)) \\ Thomas Scheuerle, Dec 08 2025
CROSSREFS
Related to mesh patterns: A280891, A289446-A289453, A289587-A289616, A289652-A289654.
Sequence in context: A095127 A006342 A258041 * A135831 A213106 A360919
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 08 2017
EXTENSIONS
More terms, name and offset changed by Thomas Scheuerle, Dec 08 2025
STATUS
approved