A356695 Expansion of x*(1+x-7*x^3-3*x^4+x^5)/(1-2*x^2-9*x^3+3*x^5).

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

Author

R. J. Mathar, Aug 23 2022

Keywords

• nonn
• easy

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
• Index entries for linear recurrences with constant coefficients, signature (0,2,9,0,-3).

Crossrefs

Cf. A131572 (length 3).

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