A371819 - OEIS

A371819

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

1, 3, 10, 34, 118, 417, 1497, 5447, 20047, 74493, 279054, 1052467, 3992204, 15216662, 58239175, 223688159, 861769598, 3328779906, 12887832493, 49998248601, 194315972151, 756406944446, 2948649839743, 11509316352548, 44976030493706, 175942932935325

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

FORMULA

a(n) = [x^n] 1/(((1-x)^2+x^3) * (1-x)^n).

a(n) = binomial(1+2*n, n)*hypergeom([1, (1-n)/3, (2-n)/3, -n/3], [-1-2*n, 1+n/2, (3+n)/2], -27/4). - Stefano Spezia, Apr 07 2024

PROG

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

CROSSREFS

Cf. A001700, A120305, A371818, A371820.

Cf. A371773.

Sequence in context: A026016 A109263 A136439 * A178578 A188622 A047017

Adjacent sequences: A371816 A371817 A371818 * A371820 A371821 A371822

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Apr 06 2024

STATUS

approved