A014116 Order of automorphism group of Barnes-Wall lattice in dimension 2^n.

2, 8, 1152, 696729600, 89181388800, 48126558103142400, 409825748158189771161600, 55428899652335313894424707072000

Offset

0,1

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 129.

Links

Table of n, a(n) for n=0..7.

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. E. Wall, On the Clifford collineation, transform and similarity groups. IV. An application to quadratic forms, Nagoya Math. J., 21 (1962), pp. 199-222.

Index entries for sequences related to Barnes-Wall lattices

Maple

2^(n^2+n+1) * (2^n - 1) * product('2^(2*i)-1', 'i'=1..n-1); # except for n=3.

Prog

(Python)
from math import prod
def A014116(n): return 2+696729598*(n//3) if n == 0 or n == 3 else ((1<<n)-1)*prod((1<<i)-1 for i in range(2, 2*n-1, 2)) << n*(n+1)+1 # Chai Wah Wu, Jun 20 2022

Crossrefs

Agrees with A014115 except at n=3. Equals half of A001309. Cf. A003956.

Sequence in context: A103085 A084148 A014115 * A027668 A121015 A216619

Adjacent sequences: A014113 A014114 A014115 * A014117 A014118 A014119

Keyword

nonn

Author

N. J. A. Sloane

Status

approved