A054908 Number of n-dimensional odd unimodular lattices (or quadratic forms) containing no vectors of norm 1.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 4, 3, 12, 12, 28, 49, 156, 368, 1901, 14493, 357003

Offset: 0

Author

N. J. A. Sloane, May 23 2000

Keywords

• nonn
• nice
• more
• hard

References

• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 49.

Links

• Bill Allombert and Gaëtan Chenevier, Unimodular Hunting II, arXiv:2410.19569 [math.NT], 2024.
• Gaëtan Chenevier, Unimodular Hunting, arXiv:2410.18788 [math.NT], 2024.

Crossrefs

Cf. A005134, A054907, A054909, A054911.

Formula

If 8 divides n, then a(n) = A054907(n) - A054909(n/8), otherwise a(n) = A054907(n). - Robin Visser, Jan 24 2025

Extensions

a(26)-a(28) added from Bill Allombert's and Gaëtan Chenevier's computations by Robin Visser, Jan 24 2025