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

0,25

Comments

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

Links

Table of n, a(n) for n=0..29.

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.

Sequence in context: A271699 A216701 A278326 * A152836 A152837 A182036

Adjacent sequences: A018840 A018841 A018842 * A018844 A018845 A018846

Keyword

nonn,hard

Author

N. J. A. Sloane, Roland Bacher

Extensions

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

Status

approved