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