cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A054909 Number of 8n-dimensional even unimodular lattices (or quadratic forms).

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%I A054909 #24 Jan 25 2025 09:14:51
%S A054909 1,1,2,24
%N A054909 Number of 8n-dimensional even unimodular lattices (or quadratic forms).
%C A054909 King shows that a(4) >= 1162109024. - _Charles R Greathouse IV_, Nov 05 2013
%D A054909 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 49.
%H A054909 Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Minkowski-Siegel mass constants</a> [Broken link]
%H A054909 Steven R. Finch, <a href="https://oeis.org/A241121/a241121.pdf">Minkowski-Siegel mass constants</a>
%H A054909 Oliver 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; Mathematics of Computation 72:242 (2003), pp. 839-863.
%F A054909 a(n) = A005134(8*n) - A054911(8*n). - _Robin Visser_, Jan 24 2025
%Y A054909 Cf. A005134, A054907, A054908, A054911.
%K A054909 nonn,nice,hard
%O A054909 0,3
%A A054909 _N. J. A. Sloane_, May 23 2000
%E A054909 The classical mass formula shows that the next term is at least 8*10^7.
%E A054909 Oliver King and Richard Borcherds (reb(AT)math.berkeley.edu) have recently improved this estimate and have shown that a(4), the number in dimension 32, is at least 10^9 (Jul 22 2000)