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A061721
Number of zeros in the character table of the dihedral group with 2n elements.
1
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
OFFSET
1,4
LINKS
FORMULA
For odd n, a(n) = (n-1)/2.
For n = 2 (mod 4), a(n) = n - 2. - Eric M. Schmidt, Jul 04 2012
EXAMPLE
a(3) = 1 because the group is isomorphic to S_3 and the table is : 1, 1, 1 1,-1, 1 2, 0,-1
MATHEMATICA
a[n_] := Count[FiniteGroupData[{"DihedralGroup", n}, "CharacterTable"], 0, 2]; Array[a, 100] (* Jean-François Alcover, Oct 08 2016 *)
PROG
(Sage)
def A061721(n) :
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
# Eric M. Schmidt, Jul 04 2012
CROSSREFS
Cf. A060762.
Sequence in context: A245962 A325705 A243407 * A294209 A066257 A085591
KEYWORD
nonn
AUTHOR
Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 20 2001
EXTENSIONS
More terms from Eric M. Schmidt, Jul 04 2012
STATUS
approved