

A154255


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


4



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
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OFFSET

2,3


COMMENTS

Floor of the righthand 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 minimalenergy 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^(k2). 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).


LINKS

Table of n, a(n) for n=2..57.
B. Ballinger, G. Blekherman, H. Cohn, N. Giansiracusa, E. Kelly and A. Schurmann, This table shows the conjectural minimalenergy 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 energyminimizing point configurations on spheres, arXiv:math/0611451 [math.MG], 20062008.


EXAMPLE

a(7) = 9 because the harmonic energy given for 7 points on the 3dimensional hypersurface of the 4dimensional 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).


CROSSREFS

Cf. A153054.
Sequence in context: A255977 A022331 A087483 * A232739 A006697 A294860
Adjacent sequences: A154252 A154253 A154254 * A154256 A154257 A154258


KEYWORD

nonn


AUTHOR

Jonathan Vos Post, Jan 05 2009


STATUS

approved



