OFFSET
0,6
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{k=0..floor(n/3)} k*A116633(n,k).
G.f.: (Sum_{i>=1} (x^(3i)/(1-x^(3i)))/(Product_{j>=1} (1-x^j)).
EXAMPLE
a(6)=5 because in the 11 partitions of 6, namely, [(6)],[5,1],[4,2],[4,1,1],[(3),(3)],[(3),2,1],[(3),1,1,1],[2,2,2],[2,2,1,1],[2,1,1,1,1] and [1,1,1,1,1,1], we have 5 multiples of 3 (shown between parentheses).
MAPLE
g:=sum(x^(3*i)/(1-x^(3*i)), i=1..50)/product(1-x^j, j=1..50): gser:=series(g, x=0, 60): seq(coeff(gser, x, n), n=0..52);
MATHEMATICA
With[{nmax = 50}, CoefficientList[Series[Sum[x^(3*k)/(1 - x^(3*k)), {k, 1, nmax}]/Product[(1 - x^j), {j, 1, nmax}], {x, 0, nmax}], x]] (* G. C. Greubel, Nov 19 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Feb 19 2006
STATUS
approved