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A088437
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Number of n X n orthogonal matrices over GF(2) modulo permutations of rows.
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1
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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; internal format)
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OFFSET
| 1,4
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COMMENTS
| Also the number of distinct self-dual bases for GF(2^n) over GF(2). - Max Alekseyev, Feb 11 2008
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LINKS
| Max Alekseyev, PARI scripts
Joerg Arndt, 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.
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FORMULA
| a(n) = A003053(n) / n!.
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PROG
| (PARI)
/* based on http://www.cse.sc.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 */
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CROSSREFS
| Cf. A053601, A135488.
Sequence in context: A012324 A121676 A133596 * A191691 A191712 A005736
Adjacent sequences: A088434 A088435 A088436 * A088438 A088439 A088440
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KEYWORD
| nonn
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AUTHOR
| Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 09 2003
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EXTENSIONS
| More terms from Max Alekseyev, Feb 11 2008
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