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
Keywords
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.
Programs
-
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 */
Formula
a(n) = A003053(n) / n!.
Extensions
More terms from Max Alekseyev, Feb 11 2008
Comments