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Number of Catalan words of length n avoiding the pattern 110.
1

%I #6 Oct 18 2019 04:12:26

%S 1,1,2,5,13,33,82,201,489,1185,2866,6925,16725,40385,97506,235409,

%T 568337,1372097,3312546,7997205,19306973,46611169,112529330,271669849,

%U 655869049,1583407969,3822685010,9228778013,22280241061,53789260161,129858761410

%N Number of Catalan words of length n avoiding the pattern 110.

%H J.-L. Baril, S. Kirgizov, V. Vanjovszki, <a href="http://doi.org/10.1016/j.disc.2018.06.001">Descent distribution on Catalan words avoiding a pattern of length at most three</a>, Disc. Math. 341 (2018) 2608-2615, Table 2.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,0,1).

%F 2*a(n) = A000129(n+1)-n+1 .

%F a(n) = A048776(n-2)+1.

%F G.f.: (1-3*x+2*x^2+x^3)/((1-x)^2*(1-2*x-x^2)).

%p (1-3*x+2*x^2+x^3)/(1-x)^2/(1-2*x-x^2) ;

%p taylor(%,x=0,30) ;

%p gfun[seriestolist](%) ;

%K nonn,easy

%O 0,3

%A _R. J. Mathar_, Apr 09 2019