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A126275 Moment of inertia of all magic squares of order n. 4
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 (list; graph; refs; listen; history; text; internal format)
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).

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 *)

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

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Last modified October 24 05:38 EDT 2021. Contains 348217 sequences. (Running on oeis4.)