A351831 Vector in the 26-dimensional even Lorentzian unimodular lattice II_25,1 used to construct the Leech lattice.

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

Offset

1,3

Comments

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.

Links

Table of n, a(n) for n=1..26.

Richard E. Borcherds, How to construct the Leech lattice, YouTube video, 2022.

J. H. Conway and N. J. A. Sloane, Lorentzian forms for the Leech lattice, Bulletin (New Series) of the American Mathematical Society, Volume 6, Number 2, March 1982.

J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, 3rd edition, Springer, New York, NY, 1999, pp. 524-528.

Wikipedia, II_25,1.

Wikipedia, Leech lattice.

Mathematica

Append[Range[0, 24], 70]

Crossrefs

Cf. A008408, A260646, A351830.

Sequence in context: A090273 A135381 A135382 * A328617 A230308 A357875

Adjacent sequences: A351828 A351829 A351830 * A351832 A351833 A351834

Keyword

nonn,easy,fini,full

Author

Paolo Xausa, Feb 21 2022

Status

approved