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