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A018843 Number of n-dimensional unimodular lattices without roots. 0
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 (list; graph; refs; listen; history; text; internal format)
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..28.

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.

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

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

STATUS

approved

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Last modified April 20 20:26 EDT 2021. Contains 343137 sequences. (Running on oeis4.)