A061721 Number of zeros in the character table of the dihedral group with 2n elements.

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

Eric M. Schmidt, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A061718 A061719 A061720 * A061722 A061723 A061724

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