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%I #9 Sep 16 2023 10:43:12
%S 1,0,0,0,0,1,1,1,1,1,3,6,10,15,21,33,57,101,175,291,477,791,1341,2310,
%T 3986,6839,11681,19966,34300,59245,102647,177963,308483,534973,929147,
%U 1616981,2818967,4920299,8594665,15023561,26283971,46030771,80695333,141593087
%N G.f. satisfies A(x) = 1 + x^5*A(x)^2 / (1 - x*A(x)).
%F a(n) = Sum_{k=0..floor(n/5)} binomial(n-4*k-1,n-5*k) * binomial(n-3*k+1,k) / (n-3*k+1).
%o (PARI) a(n) = sum(k=0, n\5, binomial(n-4*k-1, n-5*k)*binomial(n-3*k+1, k)/(n-3*k+1));
%Y Cf. A212364, A365698, A365700, A365701, A365702.
%K nonn
%O 0,11
%A _Seiichi Manyama_, Sep 16 2023
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