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%I #10 Nov 05 2023 09:01:29
%S 1,1,1,3,9,21,53,155,449,1273,3721,11155,33529,101245,309037,950587,
%T 2936833,9117169,28448209,89134435,280252585,884123429,2797933733,
%U 8879167067,28249550913,90091462761,287946752601,922194331891,2959055180953,9511538457229
%N G.f. satisfies A(x) = 1 + x*A(x) + 2*x^3*A(x)^3.
%F a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(n,3*k) * A001764(k).
%o (PARI) a(n) = sum(k=0, n\3, 2^k*binomial(n, 3*k)*binomial(3*k, k)/(2*k+1));
%Y Cf. A001764, A071879, A367112, A367113.
%Y Cf. A190590.
%K nonn,easy
%O 0,4
%A _Seiichi Manyama_, Nov 05 2023