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Search: id:A109130
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| A109130 |
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Magic constant of smallest order-n perfect magic cube. |
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+0
1
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| 1, 0, 0, 0, 315, 651, 1204, 2052, 3285, 5005, 7326, 10374, 14287, 19215, 25320, 32776, 41769, 52497, 65170, 80010, 97251, 117139, 139932, 165900, 195325, 228501, 265734, 307342, 353655, 405015, 461776, 524304, 592977, 668185, 750330, 839826
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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A perfect magic cube is one such that each square extracted from it is magic. (The sum of columns, rows, diagonals of each face and diagonals of opposite vertices all sum up to the same constant).
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REFERENCES
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C. Boyer, "Le plus petit cube magique parfait", La Recherche pp. 48-50 March 2004 Paris.
N. Revoy, "Cube magique", Science et Vie, pp. 66-69 March 2004, Paris.
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LINKS
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C. Boyer, Perfect magic cubes
I. Peterson, Perfect Magic Cubes
W. Trump, The Successful Search for the Smallest Perfect Magic Cube
Eric Weisstein, Mathworld Headline News, Perfect Magic Cube of Order 5 Discovered
Wikipedia, Perfect magic cube
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FORMULA
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a(n)=(n^4 + n)/2 for n=1 and n>=5.
a(n) = A027441(n) or 0. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 12 2008
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EXAMPLE
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a(5)=315 implies each of the 109 {=A056107(5+1)} lines crossing 5 cells of the side 5 perfect magic cube numbered 1 through 5^3 adds up to 315.
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CROSSREFS
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Sequence in context: A076648 A076773 A114807 this_sequence A087415 A088010 A048905
Adjacent sequences: A109127 A109128 A109129 this_sequence A109131 A109132 A109133
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KEYWORD
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nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 17 2005; revised Aug 23 2005
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 12 2008
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