%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