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Number of n-dimensional unimodular lattices without roots.
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%I #22 Nov 02 2021 07:05:30

%S 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

%N Number of n-dimensional unimodular lattices without roots.

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

%H R. Bacher and B. B. Venkov, <a href="https://www-fourier.univ-grenoble-alpes.fr/?q=fr/content/reseaux-entiers-unimodulaires-sans-racine-en-dimension-27-et-28">Réseaux entiers unimodulaires sans racine en dimension 27 et 28</a>, in Réseaux euclidiens, designs sphériques et formes modulaires, pp. 212-267, Enseignement Math., Geneva, 2001.

%H Gaëtan Chenevier, <a href="http://gaetan.chenevier.perso.math.cnrs.fr/pub.html">Publications</a>

%H J. H. Conway and N. J. A. Sloane, <a href="https://www.researchgate.net/publication/46957856_Sphere_Packings_Lattices_and_Groups">Sphere Packings, Lattices and Groups</a>, Springer-Verlag, Preface to 3rd ed.

%H O. King, <a href="http://arXiv.org/abs/math/0012231">A mass formula for unimodular lattices with no roots</a>, arXiv:math/0012231 [math.NT], 2000-2001.

%Y Cf. A005134.

%K nonn,hard

%O 0,25

%A _N. J. A. Sloane_, _Roland Bacher_

%E a(29) added from Gaëtan Chenevier's page by _Andrey Zabolotskiy_, Nov 02 2021