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%I #21 Sep 29 2024 19:39:01
%S 1,1,1,2,4,6,9,16,27,43,71,119,196,322,533,882,1455,2402,3970,6558,
%T 10829,17887,29548,48804,80608,133146,219925,363254,599998,991044,
%U 1636944,2703794,4465957,7376591,12184181,20125051,33241289,54905857,90690002,149795989
%N a(n) = Sum_{k=0..floor(n/3)} binomial(2*n-5*k,k).
%H Harvey P. Dale, <a href="/A373639/b373639.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 (1,0,2,0,0,-1).
%F G.f.: 1 / (1 - x^3 - x/(1 - x^3)).
%F a(n) = a(n-1) + 2*a(n-3) - a(n-6) for n > 5.
%t LinearRecurrence[{1,0,2,0,0,-1},{1, 1, 1, 2, 4, 6},40] (* _James C. McMahon_, Jun 14 2024 *)
%t Table[Sum[Binomial[2n-5k,k],{k,0,Floor[n/3]}],{n,0,40}] (* _Harvey P. Dale_, Sep 29 2024 *)
%o (PARI) a(n) = sum(k=0, n\3, binomial(2*n-5*k, k));
%Y Cf. A000930, A373640.
%Y Cf. A052535, A122367, A373644.
%K nonn,easy
%O 0,4
%A _Seiichi Manyama_, Jun 12 2024