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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 (list; graph; refs; listen; history; text; internal format)
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 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)) /* show terms */ /* Joerg Arndt, Jul 03 2011 */

CROSSREFS

Cf. A053601, A135488.

Sequence in context: A012324 A121676 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

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Last modified September 26 10:59 EDT 2017. Contains 292518 sequences.