cp's OEIS Frontend

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

%I A060368 #5 Dec 07 2019 12:18:22
%S A060368 0,0,1,1,3,3,7,14,22,26,40,45,69,71,112,215,281,353,458,563,728,874,
%T A060368 1127,1447,1830,2180,2754,3206,4053,4580,5818,8317,10111,12246,14819,
%U A060368 17849,21509,25759,30929,37082,44327,52662,62749,74151,88110,103510,122706
%N A060368 Number of irreducible representations of the symmetric group S_n that have even degree.
%H A060368 Eric M. Schmidt, <a href="/A060368/b060368.txt">Table of n, a(n) for n = 1..1000</a>
%F A060368 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
%e A060368 a(3) = 1 because the degrees of the irreducible representations of S_3 are 1,1,2.
%o A060368 (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
%Y A060368 A059867, A000041.
%K A060368 nonn
%O A060368 1,5
%A A060368 Avi Peretz (njk(AT)netvision.net.il), Apr 01 2001
%E A060368 More terms from _Eric M. Schmidt_, Apr 29 2013