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%I #14 Sep 16 2023 12:02:22
%S 1,0,0,0,0,1,1,1,1,1,1,2,4,7,11,16,22,31,47,76,126,207,331,517,801,
%T 1251,1987,3206,5212,8465,13677,21997,35341,56937,92169,149860,244274,
%U 398383,649379,1058055,1724575,2814475,4600923,7533150,12347908,20252837,33230545
%N G.f. satisfies A(x) = 1 + x^5 / (1 - x*A(x)).
%F G.f.: A(x) = 2*(1+x^5) / (1+x+sqrt( (1+x)^2 - 4*x*(1+x^5) )).
%F a(n) = Sum_{k=0..floor(n/5)} binomial(n-4*k-1,n-5*k) * binomial(n-5*k+1,k) / (n-5*k+1).
%o (PARI) a(n) = sum(k=0, n\5, binomial(n-4*k-1, n-5*k)*binomial(n-5*k+1, k)/(n-5*k+1));
%Y Cf. A212364, A365699, A365700, A365701, A365702.
%Y Cf. A001006, A023426, A025246, A357308.
%K nonn
%O 0,12
%A _Seiichi Manyama_, Sep 16 2023