|
|
A339420
|
|
Number of compositions (ordered partitions) of n into an even number of cubes.
|
|
2
|
|
|
1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 4, 1, 6, 1, 8, 2, 10, 7, 12, 16, 14, 29, 16, 46, 22, 67, 40, 94, 78, 125, 144, 161, 246, 214, 394, 312, 602, 499, 878, 835, 1236, 1396, 1722, 2286, 2446, 3637, 3614, 5598, 5560, 8358, 8782, 12226, 14014, 17776, 22278, 26056, 34924
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,10
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1/2) * (1 / (1 - Sum_{k>=1} x^(k^3)) + 1 / Sum_{k>=0} x^(k^3)).
|
|
EXAMPLE
|
a(11) = 4 because we have [8, 1, 1, 1], [1, 8, 1, 1], [1, 1, 8, 1] and [1, 1, 1, 8].
|
|
MAPLE
|
b:= proc(n, t) option remember; local r, f, g;
if n=0 then t else r, f, g:=$0..2; while f<=n
do r, f, g:= r+b(n-f, 1-t), f+3*g*(g-1)+1, g+1 od; r fi
end:
a:= n-> b(n, 1):
|
|
MATHEMATICA
|
nmax = 57; CoefficientList[Series[(1/2) (1/(1 - Sum[x^(k^3), {k, 1, Floor[nmax^(1/3)] + 1}]) + 1/Sum[x^(k^3), {k, 0, Floor[nmax^(1/3)] + 1}]), {x, 0, nmax}], x]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|