A028666 a(n) = order of the orthogonal group O_n(2) if n is odd or O^(+)_n(2) if n is even.

1, 1, 12, 2880, 11612160, 758041804800, 794088208701849600, 13319336815141167562752000, 3575164027575627746190393606144000, 15354978274323252140217954794120612413440000, 1055182047088717407398960909148529544369642384916480000, 1160183823755957350394353874696058298158177597536388268425216000000

Offset

0,3

Comments

Pseudo-Galois numbers for d=4; order of group AGL(n,2^2).

References

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985, p. xii (but beware typos!).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..40

Formula

a(n) = p^n Product (p^n - p^k) for k=0 to n-1

Maple

f:=proc(n, eps) local m, d;
if n mod 2 = 0 then m:=n/2; d:=gcd(4, 2^m-eps);
2^(m*(m-1))*mul( 4^i-1, i=1..m)*(2^m-eps)/d;
else m:=(n-1)/2;
2^(m^2)*mul( 4^i-1, i=1..m);
fi; end;
[seq(f(n, +1), n=0..20)]

Mathematica

FoldList[ #1*4^#2 (4^#2-1)&, 1, Range[ 20 ] ]

Crossrefs

Bisections give A144546 and A144547.

Sequence in context: A092299 A006272 A111237 * A103658 A271515 A231042

Adjacent sequences: A028663 A028664 A028665 * A028667 A028668 A028669

Keyword

nonn

Author

Olivier Gérard

Extensions

Entry revised by N. J. A. Sloane, Dec 30 2008

Status

approved