A001309 Order of real Clifford group L_n connected with Barnes-Wall lattices in dimension 2^n.
2, 16, 2304, 5160960, 178362777600, 96253116206284800, 819651496316379542323200, 110857799304670627788849414144000, 238987988705420266773820308079698247680000
Offset: 0
Links
- A. R. Calderbank, E. M. Rains, P. W. Shor and N. J. A. Sloane, Quantum error correction via codes over GF(4), arXiv:quant-ph/9608006, 1996-1997; IEEE Trans. Inform. Theory, 44 (1998), 1369-1387.
- G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
- G. Nebe, E. M. Rains and N. J. A. Sloane, The invariants of the Clifford groups, arXiv:math/0001038 [math.CO], 2000; Des. Codes Crypt. 24 (2001), 99-121.
- Index entries for sequences related to Barnes-Wall lattices.
- Index entries for sequences related to groups.
Crossrefs
Programs
-
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-François Alcover, Jul 16 2015, after Maple *) -
Python
from math import prod def A001309(n): return 2 if n == 0 else ((1<
Formula
From Amiram Eldar, Jul 06 2025: (Start)
a(n) = 2^(n^2+n+2) * (2^n-1) * Product_{k=1..n-1} (2^(2*k)-1).
a(n) ~ c * 2^(2*n^2+n+2), where c = A100221. (End)