A060368 Number of irreducible representations of the symmetric group S_n that have even degree.

0, 0, 1, 1, 3, 3, 7, 14, 22, 26, 40, 45, 69, 71, 112, 215, 281, 353, 458, 563, 728, 874, 1127, 1447, 1830, 2180, 2754, 3206, 4053, 4580, 5818, 8317, 10111, 12246, 14819, 17849, 21509, 25759, 30929, 37082, 44327, 52662, 62749, 74151, 88110, 103510, 122706

Offset: 1

Author

Avi Peretz (njk(AT)netvision.net.il), Apr 01 2001

Keywords

• nonn

Examples

			a(3) = 1 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

A059867, A000041.

Programs

Sage

def A060368(n) : dig = n.digits(2); return Partitions(n).cardinality() - prod(2^n for n in range(len(dig)) if dig[n]==1) # Eric M. Schmidt, Apr 29 2013

Formula

The total number of irreducible representations of S_n is the partition function p(n) (sequence A000041) and the number of irreducible representations of the symmetric group S_n that have odd degree is given in A059867 so a(n) = A000041(n) - A059867(n) for n >= 1

Extensions

More terms from Eric M. Schmidt, Apr 29 2013