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A014116 Order of automorphism group of Barnes-Wall lattice in dimension 2^n. 4
2, 8, 1152, 696729600, 89181388800, 48126558103142400, 409825748158189771161600, 55428899652335313894424707072000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 129.
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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified February 24 13:52 EST 2024. Contains 370303 sequences. (Running on oeis4.)