%I #17 Feb 21 2022 07:23:58
%S 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,70
%N Vector in the 26-dimensional even Lorentzian unimodular lattice II_25,1 used to construct the Leech lattice.
%C As noted by Conway and Sloane (1999), the only nontrivial solution of 0^2 + 1^2 + ... + m^2 = n^2 in positive integers is m = 24, n = 70, allowing them to use the vector (0, 1, 2, 3, ..., 23, 24 | 70) to construct the Leech lattice.
%H Richard E. Borcherds, <a href="https://www.youtube.com/watch?v=ycpmMnO3-Uk">How to construct the Leech lattice</a>, YouTube video, 2022.
%H J. H. Conway and N. J. A. Sloane, <a href="https://doi.org/10.1090/S0273-0979-1982-14985-0">Lorentzian forms for the Leech lattice</a>, Bulletin (New Series) of the American Mathematical Society, Volume 6, Number 2, March 1982.
%H 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. 524-528.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/II25,1">II_25,1</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Leech_lattice">Leech lattice</a>.
%t Append[Range[0,24],70]
%Y Cf. A008408, A260646, A351830.
%K nonn,easy,fini,full
%O 1,3
%A _Paolo Xausa_, Feb 21 2022