cp's OEIS Frontend

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

%I A088437 #19 Feb 19 2021 04:52:39
%S A088437 1,1,1,2,6,32,288,4608,130560,6684672,621674496,106099113984,
%T A088437 33421220904960,19556188689530880,21359269286705627136,
%U A088437 43743783499173124374528,168632285389312394463805440,1227942828363775231508883701760,16941927202935006869128068433182720,444122456468619444070070837134825095168
%N A088437 Number of n X n orthogonal matrices over GF(2) modulo permutations of rows.
%C A088437 Also the number of distinct self-dual bases for GF(2^n) over GF(2). - _Max Alekseyev_, Feb 11 2008
%H A088437 Max Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI scripts</a>
%H A088437 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, see p. 910.
%H A088437 Dieter Jungnickel, Alfred J. Menezes and Scott A. Vanstone, <a href="https://doi.org/10.1090/S0002-9939-1990-1007501-X">On the Number of Self-Dual Bases of GF(q^m) Over GF(q)</a>, Proc. Amer. Math. Soc. 109 (1990), 23-29.
%F A088437 a(n) = A003053(n) / n!.
%o A088437 (PARI)
%o A088437 /* based on http://home.gwu.edu/~maxal/gpscripts/nsdb.gp by Max Alekseyev */
%o A088437 sd(m,q) =
%o A088437 /* Number of distinct self-dual bases of GF(q^m) over GF(q) where q is a power of prime */
%o A088437 {
%o A088437    if ( q%2 && !(m%2), return(0) );
%o A088437    return ( (q%2 + 1) * prod(i=1,m-1, q^i - (i+1)%2) / m! );
%o A088437 }
%o A088437 vector(66, n, sd(n,2)) /* _Joerg Arndt_, Jul 03 2011 */
%Y A088437 Cf. A053601, A135488.
%K A088437 nonn
%O A088437 1,4
%A A088437 Yuval Dekel (dekelyuval(AT)hotmail.com), Nov 09 2003
%E A088437 More terms from _Max Alekseyev_, Feb 11 2008