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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 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 Cf. A053601, A135488. Sequence in context: A012324 A121676 A133596 * A191691 A191712 A277475 Adjacent sequences:  A088434 A088435 A088436 * A088438 A088439 A088440 KEYWORD nonn,changed 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 May 21 13:21 EDT 2018. Contains 304397 sequences. (Running on oeis4.)