A371818 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n-2*k,n-3*k).

1, 2, 6, 19, 64, 224, 805, 2947, 10934, 40975, 154738, 587910, 2244681, 8605061, 33099767, 127687258, 493796454, 1913755319, 7431027611, 28902878561, 112585961052, 439148770623, 1715009647444, 6705019714554, 26240361155821, 102787164654287, 402972015656065

Offset

0,2

Links

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

Formula

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

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

Prog

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

Crossrefs

Cf. A120305, A371819, A371820.

Cf. A000984, A144904.

Sequence in context: A329802 A151283 A176950 * A119370 A192738 A192728

Adjacent sequences: A371815 A371816 A371817 * A371819 A371820 A371821

Keyword

nonn

Author

Seiichi Manyama, Apr 06 2024

Status

approved