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A061721
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Number of zeros in the character table of the dihedral group with 2n elements.
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1
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0, 0, 1, 3, 2, 4, 3, 10, 4, 8, 5, 15, 6, 12, 7, 26, 8, 16, 9, 27, 10, 20, 11, 42, 12, 24, 13, 39, 14, 28, 15, 62, 16, 32, 17, 55, 18, 36, 19, 74, 20, 40, 21, 63, 22, 44, 23, 106, 24, 48, 25, 75, 26, 52, 27, 106, 28, 56, 29, 103, 30, 60, 31, 142, 32, 64, 33, 99
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OFFSET
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1,4
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LINKS
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FORMULA
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For odd n, a(n) = (n-1)/2.
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EXAMPLE
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a(3) = 1 because the group is isomorphic to S_3 and the table is : 1, 1, 1 1,-1, 1 2, 0,-1
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MATHEMATICA
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a[n_] := Count[FiniteGroupData[{"DihedralGroup", n}, "CharacterTable"], 0, 2]; Array[a, 100] (* Jean-François Alcover, Oct 08 2016 *)
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PROG
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(Sage)
if n % 2 == 1 : return (n - 1) // 2
if n % 4 == 2 : return n - 2
numzeros = n - 2
np = n // 4
for m in range(1, n // 2) :
t = lcm(m, np)
if (t // np) % 2 == 1 :
maxmul = m * n // 2
numzeros += (maxmul // t) - (maxmul // (2*t))
return numzeros
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 20 2001
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EXTENSIONS
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STATUS
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approved
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