|
|
A061569
|
|
Number of irreducible representations of the symmetric group S_n such that their degree is divisible by 3.
|
|
2
|
|
|
0, 0, 0, 2, 1, 2, 6, 4, 21, 33, 38, 50, 74, 81, 95, 150, 135, 331, 436, 519, 630, 840, 931, 1089, 1472, 1464, 2983, 3691, 4511, 5523, 6761, 8187, 9900, 12067, 14397, 17734, 21394, 25529, 30456, 36609, 43125, 50987, 61074, 70801, 87676, 104100, 121838, 142899
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
COMMENTS
|
The total number of irreducible representations of S_n is the partition function partition(n) (sequence A000041) and the number of irreducible representations of the symmetric group S_n with their degree not divisible by 3 is given in A060840 so a(n) = A000041(n) - A060840(n).
|
|
LINKS
|
|
|
EXAMPLE
|
a(3) = 0 because the degrees of the irreducible representations of S_3 are 1,1,2.
|
|
PROG
|
(Sage) def A061569(n) : dig = n.digits(3); return Partitions(n).cardinality() - prod([1, 3^m, 3^m*(3^m+3)//2][dig[m]] for m in range(len(dig))) # Eric M. Schmidt, Apr 30 2013
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Ola Veshta (olaveshta(AT)my-deja.com), May 18 2001
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|