A061569 Number of irreducible representations of the symmetric group S_n such that their degree is divisible by 3.

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

Offset: 1

Author

Ola Veshta (olaveshta(AT)my-deja.com), May 18 2001

Keywords

• nonn

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).

Examples

			a(3) = 0 because the degrees of the irreducible representations of S_3 are 1,1,2.
		

Links

• Eric M. Schmidt, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000041, A060840.

Programs

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

Extensions

More terms from Eric M. Schmidt, Apr 30 2013