A088437 Number of n X n orthogonal matrices over GF(2) modulo permutations of rows.

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

Table of n, a(n) for n=1..20.

Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems

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 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

Cf. A053601, A135488.

Sequence in context: A326096 A346270 A133596 * A191691 A191712 A277475

Adjacent sequences: A088434 A088435 A088436 * A088438 A088439 A088440

Keyword

nonn

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 09 2003

Extensions

More terms from Max Alekseyev, Feb 11 2008

Status

approved