A365698 G.f. satisfies A(x) = 1 + x^5 / (1 - x*A(x)).

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, 1251, 1987, 3206, 5212, 8465, 13677, 21997, 35341, 56937, 92169, 149860, 244274, 398383, 649379, 1058055, 1724575, 2814475, 4600923, 7533150, 12347908, 20252837, 33230545

Offset

0,12

Links

Table of n, a(n) for n=0..46.

Formula

G.f.: A(x) = 2*(1+x^5) / (1+x+sqrt( (1+x)^2 - 4*x*(1+x^5) )).

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).

Prog

(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));

Crossrefs

Cf. A212364, A365699, A365700, A365701, A365702.

Cf. A001006, A023426, A025246, A357308.

Sequence in context: A005689 A212365 A131075 * A133523 A114805 A196722

Adjacent sequences: A365695 A365696 A365697 * A365699 A365700 A365701

Keyword

nonn

Author

Seiichi Manyama, Sep 16 2023

Status

approved