A126275 Moment of inertia of all magic squares of order n.

5, 60, 340, 1300, 3885, 9800, 21840, 44280, 83325, 147620, 248820, 402220, 627445, 949200, 1398080, 2011440, 2834325, 3920460, 5333300, 7147140, 9448285, 12336280, 15925200, 20345000, 25742925, 32284980, 40157460, 49568540, 60749925, 73958560, 89478400

Offset

2,1

Links

Michael De Vlieger, Table of n, a(n) for n = 2..10000

Peter Loly, The Invariance of the Moment of Inertia of Magic Squares, Mathematical Gazette, Vol. 88, No. 511 (March 2004), 151-153, JSTOR:3621372.

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

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Index entries for sequences related to moment of inertia.

Formula

a(n) = (n^2 * (n^4 - 1))/12.

G.f.: -5*x^2*(x+1)*(x^2+4*x+1) / (x-1)^7. - Colin Barker, Dec 10 2012

a(n) = Sum_{i=0..n^2-1} (k+i)^2 - (k*n + A027480(n-1))^2. - Charlie Marion, May 08 2021

Mathematica

Array[(#^2*(#^4 - 1))/12 &, 31, 2] (* or *)
Drop[CoefficientList[Series[-5 x^2*(x + 1) (x^2 + 4 x + 1)/(x - 1)^7, {x, 0, 32}], x], 2] (* Michael De Vlieger, Apr 13 2021 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {5, 60, 340, 1300, 3885, 9800, 21840}, 40] (* Harvey P. Dale, Apr 03 2023 *)

Prog

(PARI) a(n) = (n^2 * (n^4 - 1))/12 \\ Felix Fröhlich, May 31 2021
(PARI) Vec(-5*x^2*(x+1)*(x^2+4*x+1)/(x-1)^7 + O(x^30)) \\ Felix Fröhlich, May 31 2021

Crossrefs

Cf. A027480.

Sequence in context: A091457 A289724 A100906 * A059602 A290747 A212700

Adjacent sequences: A126272 A126273 A126274 * A126276 A126277 A126278

Keyword

easy,nonn

Author

Jonathan Vos Post, Dec 23 2006

Extensions

More terms from Colin Barker, Dec 10 2012

Status

approved