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

Author

N. J. A. Sloane, Jan 11 2019

Keywords

• nonn
• more

Examples

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

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.

Crossrefs

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