A154255 Floor of harmonic energy of the conjectural minimal-energy configurations of n points on the unit sphere in R^4, under the harmonic potential function.

0, 1, 2, 4, 6, 9, 13, 17, 22, 28, 34, 41, 49, 57, 66, 76, 87, 98, 110, 123, 137, 152, 167, 182, 199, 217, 235, 254, 274, 294, 315, 337, 360, 384, 409, 434, 460, 487, 514, 543, 572, 601, 632, 664, 697, 730, 764, 799, 835, 871, 909, 947, 985, 1025, 1066, 1108

Offset: 2

Author

Jonathan Vos Post, Jan 05 2009

Keywords

• nonn

Comments

Floor of the right-hand column of the subtable for k=4 given by Ballinger et al., in the table of data related to their paper. This table shows the conjectural minimal-energy configurations of n points on the unit sphere in R^k (for k from 2 to 64), under the harmonic potential function: the potential energy between two points at distance r is 1/r^(k-2). In each entry in the table, the column for n links to coordinates for the configuration (given as a plain text file in which each line lists the coordinates for one point).

Examples

			a(7) = 9 because the harmonic energy given for 7 points on the 3-dimensional hypersurface of the 4-dimensional hypersphere is 9.500000000000 and floor(9.5) = 9. The coordinates of the 7 points are: (-0.774303376406259, -0.485591416628164, -0.399742015818543, +0.069725018266390); (-0.041986168871976, -0.225694667224730, +0.501037029764170, +0.834422539014180); (+0.041986168871976, +0.225694667224730, -0.501037029764170, -0.834422539014180); (+0.487341518427503, -0.842251530902810, +0.039549697743334, -0.227038376749526); (+0.104024891455872, +0.475037164815855, -0.683629522540632, +0.544214286758604); (+0.774303376406259, +0.485591416628164, +0.399742015818543, -0.069725018266390); (-0.591366409883375, +0.367214366086955, +0.644079824797298, -0.317175910009077).
		

Links

• B. Ballinger, G. Blekherman, H. Cohn, N. Giansiracusa, E. Kelly and A. Schurmann, This table shows the conjectural minimal-energy configurations of N points on the unit sphere in R^n...
• 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.

Crossrefs

Cf. A153054.