%I #8 Apr 06 2024 10:04:27

%S 1,5,28,166,1015,6324,39901,254035,1628380,10493680,67914088,

%T 441086947,2873255906,18763759019,122803467241,805241108334,

%U 5288922607095,34789875710568,229147231044397,1511104857207706,9975701630282920,65920216186587257

%N a(n) = Sum_{k=0..floor(n/3)} binomial(3*n+2,n-3*k).

%F a(n) = [x^n] 1/(((1-x)^3-x^3) * (1-x)^(2*n)).

%o (PARI) a(n) = sum(k=0, n\3, binomial(3*n+2, n-3*k));

%Y Cf. A371777, A371779, A371780.

%Y Cf. A066380.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 05 2024