A054907 Number of n-dimensional unimodular lattices (or quadratic forms) containing no vectors of norm 1.

1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 3, 1, 4, 3, 12, 12, 28, 49, 180, 368, 1901, 14493, 357003

Offset: 0

Author

N. J. A. Sloane, May 23 2000

Keywords

• nonn
• nice
• hard

References

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

Links

• Gaëtan Chenevier, Statistics for Kneser p-neighbors, arXiv:2104.06846 [math.NT], 2021.
• Gaëtan Chenevier, Publications, in particular The rank n unimodular lattices with no norm 1 vector, for 1<=n<=27 and The rank 28 unimodular lattices with no norm 1 vector.
• Gaëtan Chenevier, Unimodular hunting, Modular Forms Workshop, Oberwolfach online, Feb 2021.

Crossrefs

Cf. A005134 (cumulative sums), A054908, A054909, A054911.

Formula

If 8|n then a(n) = A054908(n) + A054909(n/8), otherwise a(n) = A054908(n). - Andrey Zabolotskiy, Nov 05 2021

Extensions

a(26)-a(28) added from Gaëtan Chenevier's page by Andrey Zabolotskiy, Nov 05 2021