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 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. 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS Floor of the right-hand column of the sub-table 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). 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. EXAMPLE 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). 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

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Last modified May 26 17:02 EDT 2020. Contains 334630 sequences. (Running on oeis4.)