A125116 Number of 8 X 8 pandiagonal Franklin squares with magic sum 4n.

1, 32, 417, 3072, 15585, 60960, 197057, 550912, 1374273, 3127840, 6602849, 13089792, 24605217, 44188704, 76283265, 127213568, 205777537, 323968032, 497842465, 748559360, 1103602017, 1598210592, 2277045057, 3196102656

Offset: 0

Author

R. J. Mathar, Jan 25 2007

Keywords

• easy
• nonn

Links

• M. M. Ahmed, Algebraic Combinatorics of Magic Squares, arXiv:math/0405476 [math.CO], 2004.
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A145217.

Programs

Maple

a := proc(n) local s ; s :=4*n ; s^8/2293760+s^7/71680+s^6/3840+s^5/320+s^4/40+2*s^3/15+197*s^2/420+106*s/105+1 ; end: for n from 0 to 30 do printf("%d ",a(n)) ; od;

Mathematica

CoefficientList[((1 + x)^3*(1 + 10*x + x^2)^2)/(1 - x)^9 + O[x]^24, x] (* Jean-François Alcover, Dec 06 2017 *)

Formula

a(n) = s^8/2293760 + s^7/71680 + s^6/3840 + s^5/320 + s^4/40 + 2*s^3/15 + 197*s^2/420 + 106*s/105 + 1 where s=4*n [Ahmed].

G.f.: -(x+1)^3*(x^2+10*x+1)^2 / (x-1)^9. - Colin Barker, Dec 10 2012

a(n) = A145217(n+1) - A145217(n-1). - Peter Bala, Dec 12 2024