A092299 a(n) = 4*3^(n^2+2n+1)*Product_{j=1..n} (9^j-1).

12, 2592, 50388480, 80225312993280, 10358730921842550374400, 108354149159204252828272715366400, 91807063616969429053277006948134413139968000, 6300752103463414524173850924959140409591369032708128768000, 35026261744325078751960598643637064012678383486922588643915999981076480000

Offset: 0

Author

N. J. A. Sloane, Feb 10 2004

Keywords

• nonn

Comments

The order of the p-Clifford group for an odd prime p is a*p^(n^2+2n+1)*Product_{j=1..n} (p^(2*j)-1), where a = gcd(p+1,4).

Links

• G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.

Crossrefs

Cf. A001309, A003956, A132037.

Cf. A092299 and A092301 (p=3), A092300 and A089989 (p=5), A090768 and A090769 (p=7), A090770 (p=2, although this is the wrong formula in that case).

Programs

Mathematica

a[n_] := 4*3^(n^2+2*n+1) * Product[9^j - 1, {j, 1, n}]; Array[a, 10, 0] (* Amiram Eldar, Jul 06 2025 *)

Formula

From Amiram Eldar, Jul 06 2025: (Start)

a(n) = 4 * A092301(n).

a(n) ~ c * 3^(2*n^2+3*n+1), where c = 4 * A132037. (End)