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A289452
a(n) is the number of permutations of length n that avoid the pattern 321 and the mesh pattern (12, 170).
0
1, 1, 1, 2, 3, 9, 16, 48, 102, 289, 693, 1902, 4883, 13296, 35415, 96778, 263217, 724590, 1996899, 5539806, 15410025, 43051125, 120615282, 339009948, 955322052, 2699027073, 7642788987, 21688832038, 61670656557, 175682146971, 501331661840, 1432930274400, 4101872293710
OFFSET
0,4
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 B2.
FORMULA
G.f.: (3 + 15*x + 26*x^2 + 17*x^3 + 3*x^4 - (3 + 7*x + 3*x^2)*sqrt(-(1 + x)^3*(3*x - 1)))/(2*x*(2 + 3*x)^2). - Thomas Scheuerle, Dec 23 2025
PROG
(PARI) listA(max_n) = my(x='x+O(x^max_n)); Vec((3+15*x+26*x^2+17*x^3+3*x^4-(3+7*x+3*x^2)*sqrt(-(1+x)^3*(3*x-1)))/(2*x*(2+3*x)^2)) \\ Thomas Scheuerle, Dec 25 2025
CROSSREFS
Cf. A000108.
Related to mesh patterns: A280891, A289446-A289453, A289587-A289616, A289652-A289654.
Sequence in context: A095742 A011951 A324014 * A086771 A156066 A143890
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 08 2017
EXTENSIONS
More terms, name and offset changed by Thomas Scheuerle, Dec 23 2025
STATUS
approved