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

0,17

References

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

Links

Table of n, a(n) for n=0..28.

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.

Formula

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

Crossrefs

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

Sequence in context: A337588 A364272 A316402 * A245539 A373987 A089554

Adjacent sequences: A054904 A054905 A054906 * A054908 A054909 A054910

Keyword

nonn,nice,hard

Author

N. J. A. Sloane, May 23 2000

Extensions

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

Status

approved