A307466 Number of Catalan words of length n avoiding the pattern 210.

1, 1, 2, 5, 14, 41, 121, 355, 1032, 2974, 8509, 24210, 68595, 193753, 546041, 1536358, 4317652, 12123685, 34021810, 95431301, 267601625, 750221859, 2102913404, 5893910702, 16517729313, 46288368894, 129710571239, 363467837569, 1018468044881, 2853791650010

Offset

0,3

Links

Table of n, a(n) for n=0..29.

J.-L. Baril, S. Kirgizov, V. Vanjovszki, Descent distribution on Catalan words avoiding a pattern of length at most three, Disc. Math. 341 (2018) 2608-2615, Table 2.

Index entries for linear recurrences with constant coefficients, signature (6,-11,5,2).

Formula

a(n) = A215404(n+2) -2*A215404(n+1) - A215404(n) -2^(n-1), n>0.

G.f.: (1-5*x+7*x^2-x^3-x^4)/(1-2*x)/(1-4*x+3*x^2+x^3) .

Maple

(1-5*x+7*x^2-x^3-x^4)/(1-2*x)/(1-4*x+3*x^2+x^3) ;
taylor(%, x=0, 30) ;
gfun[seriestolist](%) ;

Crossrefs

Sequence in context: A122055 A244885 A116845 * A116849 A371427 A123183

Adjacent sequences: A307463 A307464 A307465 * A307467 A307468 A307469

Keyword

nonn,easy

Author

R. J. Mathar, Apr 09 2019

Status

approved