A063073 Square of determinant of character table of the dihedral group with 2n elements.

4, 256, 36, 4096, 500, 82944, 9604, 2097152, 236196, 64000000, 7086244, 2293235712, 250994068, 94450499584, 10251562500, 4398046511104, 474351505988, 228509902503936, 24524265031204, 13107200000000000

Offset

1,1

Comments

For any finite group G with order n we have that if A is the character table then |det(A)|^2 = product i (n/c(i)) where the product is over the conjugacy classes of G: c(i), so by this formula the square of the determinant is an integer (in the case of dihedral groups the characters are real).

Links

Harry J. Smith, Table of n, a(n) for n=1..200

Formula

a(n) = 4 * n^((n+1)/2) if n odd, a(n)= 64 * n^((n+2)/2) if n even. - Paul Boddington, Oct 22 2003

Prog

(PARI) { for (n=1, 200, if (n%2, a=4 * n^((n+1)/2), a=64 * n^((n+2)/2)); write("b063073.txt", n, " ", a) ) } \\ Harry J. Smith, Aug 16 2009

Crossrefs

Sequence in context: A087587 A346919 A203511 * A377383 A381268 A093760

Adjacent sequences: A063070 A063071 A063072 * A063074 A063075 A063076

Keyword

nonn

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Aug 03 2001

Extensions

Missing term included and more terms added by Harry J. Smith, Aug 16 2009

Status

approved