A323273 Number of orbits of the Conway group Co_0 acting on vectors of norm 2n in the Leech lattice.

1, 0, 1, 1, 1, 1, 2, 1, 3, 2, 3, 2, 6, 3, 5, 5, 7

Offset

0,7

References

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. 181. There is a typo in the table: the second line for vectors of type 11 should read u_3 + 2 v_4 (w_3).

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, 3rd. ed., 1993. Tables 4.13 and 4.14.

Links

Table of n, a(n) for n=0..16.

Example

a(2) = 1 since the group acts transitively on the 196560 minimal vectors (which have norm 4).

Crossrefs

A008408 gives the total number of vectors of norm 2n in the Leech lattice.

Sequence in context: A023022 A177501 A330926 * A100677 A188637 A083290

Adjacent sequences: A323270 A323271 A323272 * A323274 A323275 A323276

Keyword

nonn,more

Author

N. J. A. Sloane, Jan 11 2019

Status

approved