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

%I A061569 #7 Dec 07 2019 12:18:22
%S A061569 0,0,0,2,1,2,6,4,21,33,38,50,74,81,95,150,135,331,436,519,630,840,931,
%T A061569 1089,1472,1464,2983,3691,4511,5523,6761,8187,9900,12067,14397,17734,
%U A061569 21394,25529,30456,36609,43125,50987,61074,70801,87676,104100,121838,142899
%N A061569 Number of irreducible representations of the symmetric group S_n such that their degree is divisible by 3.
%C A061569 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).
%H A061569 Eric M. Schmidt, <a href="/A061569/b061569.txt">Table of n, a(n) for n = 1..1000</a>
%e A061569 a(3) = 0 because the degrees of the irreducible representations of S_3 are 1,1,2.
%o A061569 (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
%Y A061569 Cf. A000041, A060840.
%K A061569 nonn
%O A061569 1,4
%A A061569 Ola Veshta (olaveshta(AT)my-deja.com), May 18 2001
%E A061569 More terms from _Eric M. Schmidt_, Apr 30 2013