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

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

Offset: 0

Author

Olivier Gérard

Keywords

• nonn

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 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xii (but beware typos!).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..39

Crossrefs

Bisections give A144546 and A144547.

Cf. A028668, A028670, A028671, A028672, A028674, A028676, A028677, A028678, A028680, A028682, A028683, A028684, A028686.

Cf. A100221.

Programs

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 ] ]
a[n_] := 4^n * Product[4^n - 4^k, {k, 0, n-1}]; Array[a, 10, 0] (* Amiram Eldar, Jul 14 2025 *)

PARI

a(n) = 4^n * prod(k = 0, n-1, 4^n - 4^k); \\ Amiram Eldar, Jul 14 2025

Formula

a(n) = 4^n * Product_{k=0..n-1} (4^n - 4^k).

a(n) ~ c * 4^(n^2+n), where c = A100221. - Amiram Eldar, Jul 14 2025

Extensions

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

Duplicate term 1 removed by Amiram Eldar, Jul 14 2025