A109130 Magic constant of smallest order-n perfect magic cube.

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

Offset

1,5

Comments

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).

References

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.

Links

Table of n, a(n) for n=1..36.

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

Formula

a(n)=(n^4 + n)/2 for n=1 and n>=5.

a(n) = A027441(n) or 0. - R. J. Mathar, Feb 12 2008

Example

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.

Crossrefs

Sequence in context: A349937 A076773 A114807 * A284981 A341358 A087415

Adjacent sequences: A109127 A109128 A109129 * A109131 A109132 A109133

Keyword

nonn

Author

Lekraj Beedassy, Aug 17 2005; revised Aug 23 2005

Extensions

More terms from R. J. Mathar, Feb 12 2008

Status

approved