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%I #4 Apr 09 2019 12:05:09
%S 1,1,2,5,14,41,121,355,1032,2974,8509,24210,68595,193753,546041,
%T 1536358,4317652,12123685,34021810,95431301,267601625,750221859,
%U 2102913404,5893910702,16517729313,46288368894,129710571239,363467837569,1018468044881,2853791650010
%N Number of Catalan words of length n avoiding the pattern 210.
%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 (6,-11,5,2).
%F a(n) = A215404(n+2) -2*A215404(n+1) - A215404(n) -2^(n-1), n>0.
%F G.f.: (1-5*x+7*x^2-x^3-x^4)/(1-2*x)/(1-4*x+3*x^2+x^3) .
%p (1-5*x+7*x^2-x^3-x^4)/(1-2*x)/(1-4*x+3*x^2+x^3) ;
%p taylor(%,x=0,30) ;
%p gfun[seriestolist](%) ;
%K nonn,easy
%O 0,3
%A _R. J. Mathar_, Apr 09 2019