cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A014116 #15 Jun 21 2022 05:07:23
%S A014116 2,8,1152,696729600,89181388800,48126558103142400,
%T A014116 409825748158189771161600,55428899652335313894424707072000
%N A014116 Order of automorphism group of Barnes-Wall lattice in dimension 2^n.
%D A014116 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 129.
%H A014116 A. R. Calderbank, E. M. Rains, P. W. Shor and N. J. A. Sloane, <a href="https://arxiv.org/abs/quant-ph/9608006">Quantum error correction via codes over GF(4)</a>, arXiv:quant-ph/9608006, 1996-1997; IEEE Trans. Inform. Theory, 44 (1998), 1369-1387.
%H A014116 G. E. Wall, <a href="https://doi.org/10.1017/S0027763000023837">On the Clifford collineation, transform and similarity groups. IV. An application to quadratic forms</a>, Nagoya Math. J., 21 (1962), pp. 199-222.
%H A014116 <a href="/index/Ba#BW">Index entries for sequences related to Barnes-Wall lattices</a>
%p A014116 2^(n^2+n+1) * (2^n - 1) * product('2^(2*i)-1','i'=1..n-1); # except for n=3.
%o A014116 (Python)
%o A014116 from math import prod
%o A014116 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
%Y A014116 Agrees with A014115 except at n=3. Equals half of A001309. Cf. A003956.
%K A014116 nonn
%O A014116 0,1
%A A014116 _N. J. A. Sloane_