login
G.f. satisfies A(x) = 1 - x^3 + x*A(x)^3.
1

%I #12 Nov 03 2023 11:18:15

%S 1,1,3,11,52,258,1344,7260,40290,228363,1316414,7694154,45491247,

%T 271594897,1635068538,9914851401,60503259435,371269891422,

%U 2289545742174,14181772631025,88194284530464,550444913949048,3446737067467311,21647081264988312

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

%F a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*(n-3*k)+1,k) * binomial(3*(n-3*k),n-3*k)/(2*(n-3*k)+1).

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

%Y Cf. A226022, A367047.

%Y Cf. A366676.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 03 2023