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Search: id:A154255
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| A154255 |
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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. |
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4
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| 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; listen)
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OFFSET
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2,3
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COMMENT
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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).
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LINKS
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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, Oct 07, 2008.
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EXAMPLE
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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).
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CROSSREFS
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Cf. A153054.
Sequence in context: A025697 A022331 A087483 this_sequence A006697 A079717 A114830
Adjacent sequences: A154252 A154253 A154254 this_sequence A154256 A154257 A154258
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 05 2009
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