A153054 Number of points in sporadic known universal optima arising in energy-minimizing point configurations on spheres.

12, 120, 16, 27, 56, 240, 112, 162, 100, 275, 891, 552, 4600, 196560

Offset

1,1

Comments

From the second column of Table 1, p. 3, of Ballinger et al. This is an unsorted list of, in a sense, the sporadic solutions, which exclude infinite subsequences corresponding to the n points of the n-gon on the 2-sphere (circle), the n+1 points of the simplex on the n-sphere, the 2n points of the cross polytope on the n-sphere and the (q+1)*(1+q^3) points on isotropic subspaces of the q*(1+q^3)/(q+1)-sphere where q is a prime power.

Links

Table of n, a(n) for n=1..14.

B. Ballinger, G. Blekherman, H. Cohn, N. Giansiracusa, E. Kelly and A. Schurmann, Experimental study of energy-minimizing point configurations on spheres, arXiv:math/0611451 [math.MG], 2006-2008.

Example

120 is in the sequence because of the 120 points which are vertices of the regular 600-cell in dimension 4.
196560 is in the sequence because of the Leech lattice minimal vectors in 24 dimensions.

Crossrefs

Cf. A154255.

Sequence in context: A077251 A289542 A075622 * A075366 A276668 A076633

Adjacent sequences: A153051 A153052 A153053 * A153055 A153056 A153057

Keyword

nonn,more

Author

Jonathan Vos Post, Dec 17 2008

Status

approved