A367113 - OEIS

%I #11 Nov 05 2023 09:01:07

%S 1,2,4,10,32,112,396,1416,5184,19424,73984,285056,1108848,4350816,

%T 17203008,68473504,274122752,1103014912,4458611968,18096793088,

%U 73724852224,301360575488,1235633545216,5080554352640,20943623880448,86541514460672,358386391051264

%N G.f. satisfies A(x) = 1 + 2*x*A(x) + 2*x^3*A(x)^3.

%F a(n) = Sum_{k=0..floor(n/3)} 2^(n-2*k) * binomial(n,3*k) * A001764(k).

%o (PARI) a(n) = sum(k=0, n\3, 2^(n-2*k)*binomial(n, 3*k)*binomial(3*k, k)/(2*k+1));

%Y Cf. A001764, A071879, A367111, A367112.

%Y Cf. A071356, A367115.

%Y Cf. A367074.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Nov 05 2023