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
Links
- 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
Extensions
More terms from Colin Barker, May 08 2013