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A356695
Expansion of x*(1+x-7*x^3-3*x^4+x^5)/(1-2*x^2-9*x^3+3*x^5).
0
1, 1, 2, 4, 10, 24, 53, 132, 310, 711, 1736, 4053, 9475, 22800, 53294, 125667, 299629, 702555, 1661861, 3941889, 9269716, 21941640, 51908768, 122325141, 289466629, 684020046, 1614034607, 3817513449, 9017274205, 21292938474, 50340109313, 118899240972
OFFSET
1,3
COMMENTS
Number of Catalan words of length n avoiding the pattern 1111 of length 4.
LINKS
Mansour, Toufik; Shattuck, Mark Avoidance of classical patterns by Catalan sequences. Filomat 31, No. 3, 543-558 (2017). Corollary 2.2
FORMULA
G.f.: x*(1+x-7*x^3-3*x^4+x^5)/(1-2*x^2-9*x^3+3*x^5).
a(n) = 2*a(n-2) + 9*a(n-3) - 3*a(n-5). - Wesley Ivan Hurt, Apr 20 2023
CROSSREFS
Cf. A131572 (length 3).
Sequence in context: A136427 A350881 A018114 * A089484 A132732 A275447
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Aug 23 2022
STATUS
approved