%I #9 Nov 26 2023 08:38:01
%S 1,1,2,4,8,16,32,65,131,264,534,1078,2176,4396,8877,17925,36202,73108,
%T 147636,298152,602108,1215933,2455552,4958915,10014374,20223760,
%U 40841302,82477816,166561622,336366426,679282324,1371791274,2770293218,5594527784,11297988864
%N G.f. A(x) satisfies A(x) = 1 / (1 - x * (1 + x + x^2) * A(x^3)).
%F a(0) = 1; a(n) = Sum_{k=0..n-1} a(floor(k/3)) * a(n-1-k).
%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, v[j\3+1]*v[i-j])); v;
%Y Cf. A127680, A367653, A367654.
%Y Cf. A367659.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Nov 26 2023