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%I #11 Jun 12 2024 08:22:02
%S 1,1,2,5,9,21,43,92,196,414,882,1869,3970,8427,17887,37975,80608,
%T 171121,363254,771119,1636944,3474913,7376591,15659094,33241289,
%U 70564951,149795989,317988473,675029164,1432958824,3041899638,6457375642,13707783053,29099021980
%N a(n) = Sum_{k=0..floor(n/2)} binomial(3*n-5*k,k).
%H Seiichi Manyama, <a href="/A373638/b373638.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,0,-3,0,1).
%F G.f.: 1 / (1 - x^2 - x/(1 - x^2)^2).
%F a(n) = a(n-1) + 3*a(n-2) - 3*a(n-4) + a(n-6) for n > 5.
%o (PARI) a(n) = sum(k=0, n\2, binomial(3*n-5*k, k));
%Y Cf. A000045, A052535.
%K nonn,easy
%O 0,3
%A _Seiichi Manyama_, Jun 12 2024