A360890 - OEIS

%I #14 Feb 26 2023 06:56:00

%S 1,1,1,1,2,4,7,12,25,55,115,245,564,1331,3103,7407,18388,46198,116503,

%T 299966,789426,2095941,5616114,15299205,42255533,117689096,331204936,

%U 944052610,2718150015,7891518587,23137661717,68524545717,204645635263,616098009473

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

%H Seiichi Manyama, <a href="/A360890/b360890.txt">Table of n, a(n) for n = 0..1000</a>

%F a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n-1-2*k,k) * a(n-1-3*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)\3, binomial(i-1-2*j, j)*v[i-3*j])); v;

%Y Cf. A000110, A172383, A360891.

%Y Cf. A360898.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Feb 25 2023