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A088437
Number of n X n orthogonal matrices over GF(2) modulo permutations of rows.
1
1, 1, 1, 2, 6, 32, 288, 4608, 130560, 6684672, 621674496, 106099113984, 33421220904960, 19556188689530880, 21359269286705627136, 43743783499173124374528, 168632285389312394463805440, 1227942828363775231508883701760, 16941927202935006869128068433182720, 444122456468619444070070837134825095168
OFFSET
1,4
COMMENTS
Also the number of distinct self-dual bases for GF(2^n) over GF(2). - Max Alekseyev, Feb 11 2008
LINKS
Max Alekseyev, PARI scripts
Joerg Arndt, Matters Computational (The Fxtbook), see p. 910.
Dieter Jungnickel, Alfred J. Menezes and Scott A. Vanstone, On the Number of Self-Dual Bases of GF(q^m) Over GF(q), Proc. Amer. Math. Soc. 109 (1990), 23-29.
FORMULA
a(n) = A003053(n) / n!.
PROG
(PARI)
/* based on http://home.gwu.edu/~maxal/gpscripts/nsdb.gp by Max Alekseyev */
sd(m, q) =
/* Number of distinct self-dual bases of GF(q^m) over GF(q) where q is a power of prime */
{
if ( q%2 && !(m%2), return(0) );
return ( (q%2 + 1) * prod(i=1, m-1, q^i - (i+1)%2) / m! );
}
vector(66, n, sd(n, 2)) /* Joerg Arndt, Jul 03 2011 */
CROSSREFS
Sequence in context: A326096 A346270 A133596 * A191691 A191712 A277475
KEYWORD
nonn
AUTHOR
Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 09 2003
EXTENSIONS
More terms from Max Alekseyev, Feb 11 2008
STATUS
approved