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.

A005134 Number of n-dimensional unimodular lattices (or quadratic forms).

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%I A005134 M0219 #24 Feb 10 2025 02:08:00
%S A005134 1,1,1,1,1,1,1,1,2,2,2,2,3,3,4,5,8,9,13,16,28,40,68,117,297,665,2566,
%T A005134 17059,374062
%N A005134 Number of n-dimensional unimodular lattices (or quadratic forms).
%C A005134 King gives the lower bounds a(29) >= 37938009 and a(30) >= 20169641025. - _Robin Visser_, Feb 08 2025
%D A005134 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 49.
%D A005134 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005134 Bill Allombert and Gaëtan Chenevier, <a href="https://arxiv.org/abs/2410.19569">Unimodular Hunting II</a>, arXiv:2410.19569 [math.NT], 2024.
%H A005134 Gaëtan Chenevier, <a href="https://arxiv.org/abs/2410.18788">Unimodular Hunting</a>, arXiv:2410.18788 [math.NT], 2024.
%H A005134 Oliver D. King, <a href="https://doi.org/10.1090/S0025-5718-02-01455-2">A mass formula for unimodular lattices with no roots</a>, Math. Comp., 72 (2003), no. 242, 839-863.  See page 854.
%F A005134 If 8 divides n, then a(n) = A054911(n) + A054909(n/8), otherwise a(n) = A054911(n). - _Robin Visser_, Jan 24 2025
%F A005134 a(n) >= 2*A241121(n)/A241122(n). - _Robin Visser_, Feb 08 2025
%Y A005134 Cf. A054907, A054908, A054909, A054911.
%K A005134 nonn,nice,hard
%O A005134 0,9
%A A005134 _N. J. A. Sloane_
%E A005134 a(26)-a(28) added from Bill Allombert's and Gaëtan Chenevier's computations by _Robin Visser_, Jan 24 2025