A360885 - OEIS

%I #14 Feb 26 2023 06:56:07

%S 1,1,1,1,2,4,7,16,39,93,246,671,1884,5578,16887,52854,170649,563703,

%T 1914366,6649798,23610987,85689987,317054427,1196183592,4595744763,

%U 17965311672,71426213637,288535755417,1183807706841,4929801601890,20825803784129,89210585925338

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

%H Seiichi Manyama, <a href="/A360885/b360885.txt">Table of n, a(n) for n = 0..934</a>

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

%Y Cf. A127782, A360886.

%Y Cf. A360896.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Feb 25 2023