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A001309 Order of real Clifford group L_n connected with Barnes-Wall lattices in dimension 2^n. 12
2, 16, 2304, 5160960, 178362777600, 96253116206284800, 819651496316379542323200, 110857799304670627788849414144000, 238987988705420266773820308079698247680000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..8.

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

A. R. Calderbank, E. M. Rains, P. W. Shor and N. J. A. Sloane, Quantum error correction via codes over GF(4), IEEE Trans. Inform. Theory, 44 (1998), 1369-1387.

G. Nebe, E. M. Rains and N. J. A. Sloane, The invariants of the Clifford groups, Des. Codes Crypt. 24 (2001), 99-121.

Index entries for sequences related to Barnes-Wall lattices

Index entries for sequences related to groups

MAPLE

2^(n^2+n+2) * (2^n - 1) * product('2^(2*i)-1', 'i'=1..n-1);

MATHEMATICA

a[0] = 2; a[n_] := 2^(n^2+n+2) * (2^n-1) * Product[2^(2*i)-1, {i, 1, n-1}]; Table[a[n], {n, 0, 8}] (* Jean-Fran├žois Alcover, Jul 16 2015, after Maple *)

CROSSREFS

2^(2n+2) times order of Chevalley group D_n (2) (cf. A001308). Twice A014115. See also A014116, A003956 (for the complex group).

Sequence in context: A091479 A016031 A331691 * A132569 A165644 A203315

Adjacent sequences:  A001306 A001307 A001308 * A001310 A001311 A001312

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane, Peter Shor

STATUS

approved

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Last modified April 6 12:08 EDT 2020. Contains 333273 sequences. (Running on oeis4.)