A365268 G.f. satisfies A(x) = 1 + x*A(x)^2*(1 + x^3*A(x)^2).

1, 1, 2, 5, 15, 48, 160, 549, 1929, 6909, 25134, 92612, 344924, 1296376, 4910656, 18728645, 71857133, 277160183, 1074085446, 4180057725, 16329796959, 64014638564, 251734985808, 992788252700, 3925688845948, 15560762343388, 61818928594952

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Formula

a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k,k) * binomial(2*n-4*k+1,n-3*k)/(2*n-4*k+1).

Prog

(PARI) a(n) = sum(k=0, n\4, binomial(n-3*k, k)*binomial(2*n-4*k+1, n-3*k)/(2*n-4*k+1));

Crossrefs

Cf. A006605, A049140.

Cf. A063021, A365267.

Sequence in context: A071739 A268407 A261003 * A366041 A372532 A218251

Adjacent sequences: A365265 A365266 A365267 * A365269 A365270 A365271

Keyword

nonn

Author

Seiichi Manyama, Aug 30 2023

Status

approved