A018843 Number of n-dimensional unimodular lattices without roots.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 3, 38, 10092

Offset: 0

Author

N. J. A. Sloane, Roland Bacher

Keywords

• nonn
• hard

Comments

The paper by Oliver King (king(AT)math.berkeley.edu) shows that a(29) >= 8900 and a(30) >= 82000000.

Links

• R. Bacher and B. B. Venkov, Réseaux entiers unimodulaires sans racine en dimension 27 et 28, in Réseaux euclidiens, designs sphériques et formes modulaires, pp. 212-267, Enseignement Math., Geneva, 2001.
• Gaëtan Chenevier, Publications
• J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, Preface to 3rd ed.
• O. King, A mass formula for unimodular lattices with no roots, arXiv:math/0012231 [math.NT], 2000-2001.

Crossrefs

Cf. A005134.

Extensions

a(29) added from Gaëtan Chenevier's page by Andrey Zabolotskiy, Nov 02 2021