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A060368
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Number of irreducible representations of the symmetric group S_n that have even degree.
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2
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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
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OFFSET
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1,5
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LINKS
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FORMULA
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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
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EXAMPLE
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a(3) = 1 because the degrees of the irreducible representations of S_3 are 1,1,2.
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Avi Peretz (njk(AT)netvision.net.il), Apr 01 2001
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EXTENSIONS
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STATUS
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approved
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