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.

A353294 A generator matrix for the Leech lattice, multiplied by sqrt(8), read by rows.

This page as a plain text file.
%I A353294 #16 Jun 04 2022 14:15:27
%S A353294 8,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,4,0,0,0,0,0,0,0,0,
%T A353294 0,0,0,0,0,0,0,0,0,0,0,0,0,0,4,0,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%U A353294 0,0,0,0
%N A353294 A generator matrix for the Leech lattice, multiplied by sqrt(8), read by rows.
%C A353294 There are infinitely many such matrices, this just happens to be a concrete example that we gave in the Sphere-Packing book. It is not unique in any way. - _N. J. A. Sloane_, Jun 04 2022
%H A353294 Paolo Xausa, <a href="/A353294/b353294.txt">Table of n, a(n) for n = 1..576 (rows 1..24 of the matrix, flattened)</a>
%H A353294 J. H. Conway and N. J. A. Sloane, <a href="https://doi.org/10.1007/978-1-4757-6568-7">Sphere Packings, Lattices and Groups</a>, 3rd edition, Springer, New York, NY, 1999, pp. 131-133.
%H A353294 Wikipedia, <a href="https://en.wikipedia.org/wiki/Leech_lattice">Leech lattice</a>.
%H A353294 Wikipedia, <a href="https://en.wikipedia.org/wiki/Miracle_Octad_Generator">Miracle Octad Generator</a>.
%F A353294 det(A/sqrt(8)) = 1, where A is the present matrix.
%e A353294 As depicted by Conway and Sloane (1999), p. 133, the full 24 X 24 matrix is given below, in standard MOG (Miracle Octad Generator) coordinates.
%e A353294 .
%e A353294    8 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e A353294    4 4 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e A353294    4 0 4 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e A353294    4 0 0 4 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e A353294    --------|---------|---------|---------|---------|--------
%e A353294    4 0 0 0 | 4 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e A353294    4 0 0 0 | 0 4 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e A353294    4 0 0 0 | 0 0 4 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e A353294    2 2 2 2 | 2 2 2 2 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e A353294    --------|---------|---------|---------|---------|--------
%e A353294    4 0 0 0 | 0 0 0 0 | 4 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e A353294    4 0 0 0 | 0 0 0 0 | 0 4 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e A353294    4 0 0 0 | 0 0 0 0 | 0 0 4 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e A353294    2 2 2 2 | 0 0 0 0 | 2 2 2 2 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0
%e A353294    --------|---------|---------|---------|---------|--------
%e A353294    4 0 0 0 | 0 0 0 0 | 0 0 0 0 | 4 0 0 0 | 0 0 0 0 | 0 0 0 0
%e A353294    2 2 0 0 | 2 2 0 0 | 2 2 0 0 | 2 2 0 0 | 0 0 0 0 | 0 0 0 0
%e A353294    2 0 2 0 | 2 0 2 0 | 2 0 2 0 | 2 0 2 0 | 0 0 0 0 | 0 0 0 0
%e A353294    2 0 0 2 | 2 0 0 2 | 2 0 0 2 | 2 0 0 2 | 0 0 0 0 | 0 0 0 0
%e A353294    --------|---------|---------|---------|---------|--------
%e A353294    4 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 0 0 | 4 0 0 0 | 0 0 0 0
%e A353294    2 0 2 0 | 2 0 0 2 | 2 2 0 0 | 0 0 0 0 | 2 2 0 0 | 0 0 0 0
%e A353294    2 0 0 2 | 2 2 0 0 | 2 0 2 0 | 0 0 0 0 | 2 0 2 0 | 0 0 0 0
%e A353294    2 2 0 0 | 2 0 2 0 | 2 0 0 2 | 0 0 0 0 | 2 0 0 2 | 0 0 0 0
%e A353294    --------|---------|---------|---------|---------|--------
%e A353294    0 2 2 2 | 2 0 0 0 | 2 0 0 0 | 2 0 0 0 | 2 0 0 0 | 2 0 0 0
%e A353294    0 0 0 0 | 0 0 0 0 | 2 2 0 0 | 2 2 0 0 | 2 2 0 0 | 2 2 0 0
%e A353294    0 0 0 0 | 0 0 0 0 | 2 0 2 0 | 2 0 2 0 | 2 0 2 0 | 2 0 2 0
%e A353294   -3 1 1 1 | 1 1 1 1 | 1 1 1 1 | 1 1 1 1 | 1 1 1 1 | 1 1 1 1
%Y A353294 Cf. A008408, A260646, A351831.
%K A353294 sign,tabf,fini,full
%O A353294 1,1
%A A353294 _Paolo Xausa_, Apr 12 2022