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%I #8 Jun 03 2022 12:59:31
%S 1,1,3,6,11,21,42,87,189,432,1018,2415,5694,13297,30768,70626,161011,
%T 364977,823536,1851706,4152972,9298653,20800758,46516437,104044590,
%U 232856189,521601174,1169670645,2626188319,5904269526,13292581605,29968831278,67663806228
%N G.f. A(x) satisfies: A(x) = 1 + x * A(x^3/(1 - x)^3) / (1 - x)^3.
%F a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} binomial(n+1,3*k+2) * a(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+2)*v[j+1])); v;
%Y Cf. A119685, A354696.
%Y Cf. A351816, A352045.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jun 03 2022
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