%I #13 Jun 14 2024 22:31:10
%S 1,0,1,1,1,1,2,1,3,2,3,2,6,3,5,5,7
%N Number of orbits of the Conway group Co_0 acting on vectors of norm 2n in the Leech lattice.
%D 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).
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, 3rd. ed., 1993. Tables 4.13 and 4.14.
%e a(2) = 1 since the group acts transitively on the 196560 minimal vectors (which have norm 4).
%Y A008408 gives the total number of vectors of norm 2n in the Leech lattice.
%K nonn,more
%O 0,7
%A _N. J. A. Sloane_, Jan 11 2019