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

0,2

Links

Table of n, a(n) for n=0..23.

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).

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

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 *)

Crossrefs

Cf. A145217.

Sequence in context: A275232 A061594 A145403 * A145217 A125444 A022692

Adjacent sequences: A125113 A125114 A125115 * A125117 A125118 A125119

Keyword

easy,nonn,changed

Author

R. J. Mathar, Jan 25 2007

Status

approved