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G.f. satisfies A(x) = 1 + x * (1 + x^3)^2 * A(x * (1 + x^3)).
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%I #7 Feb 25 2023 08:40:58

%S 1,1,1,1,3,6,10,16,37,85,175,365,865,2090,4826,11447,28797,73086,

%T 183422,471462,1249792,3329832,8898534,24244771,67210802,187336493,

%U 526399475,1501301887,4329346255,12565028776,36807317140,109047854266,325773015735,980062229742

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

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

%Y Cf. A360887, A360888.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Feb 25 2023