login
A116635
Number of parts that are multiples of 3 in all partitions of n.
2
0, 0, 0, 1, 1, 2, 5, 7, 11, 19, 27, 40, 61, 85, 120, 170, 232, 316, 433, 576, 767, 1017, 1332, 1735, 2259, 2905, 3730, 4768, 6058, 7663, 9676, 12137, 15191, 18945, 23541, 29150, 36026, 44336, 54453, 66686, 81456, 99227, 120653, 146275, 177015, 213724
OFFSET
0,6
LINKS
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
Cf. A116633.
Sequence in context: A251964 A045351 A051645 * A340759 A252280 A184774
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Feb 19 2006
STATUS
approved