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

1,5

Links

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

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

Example

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

Prog

(SageMath) 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

Crossrefs

A059867, A000041.

Sequence in context: A378959 A049772 A119470 * A218206 A218233 A218319

Adjacent sequences: A060365 A060366 A060367 * A060369 A060370 A060371

Keyword

nonn

Author

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

Extensions

More terms from Eric M. Schmidt, Apr 29 2013

Status

approved