A126276 Moment of inertia of all magic cubes of order n.

18, 504, 5200, 31500, 136710, 471968, 1378944, 3547800, 8258250, 17728920, 35603568, 67606084, 122399550, 212688000, 356602880, 579419568, 915652674, 1411582200, 2128266000, 3145097340, 4563969718, 6514114464, 9157680000, 12696125000, 17377501050

Offset

2,1

Links

Table of n, a(n) for n=2..26.

Peter Loly, The invariance of the moment of inertia of magic squares, Mathematical Gazette 88 (March 2004):151-153. [Wayback Machine link]

Ivars Peterson, Magic Square Physics, Science News online, Jul 01, 2006; Vol. 170, No. 1.

Adam Rogers and Peter Loly, Rotational sorcery: The inertial properties of magic squares and cubes. Canadian Undergraduate Physics Journal 3(No. 2):25, 2005. [Wayback Machine link]

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Index entries for sequences related to moment of inertia.

Formula

a(n) = (n^3)*(n^3 + 1)*(n^2 - 1)/12.

G.f.: -2*x^2*(7*x^5+171*x^4+666*x^3+656*x^2+171*x+9) / (x-1)^9. - Colin Barker, May 08 2013

Crossrefs

Sequence in context: A116176 A035023 A180791 * A035277 A011906 A255859

Adjacent sequences: A126273 A126274 A126275 * A126277 A126278 A126279

Keyword

easy,nonn

Author

Jonathan Vos Post, Dec 23 2006

Extensions

More terms from Colin Barker, May 08 2013

Status

approved