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A125116 Number of 8 X 8 pandiagonal Franklin squares with magic sum 4n. 0
1, 32, 417, 3072, 15585, 60960, 197057, 550912, 1374273, 3127840, 6602849, 13089792, 24605217, 44188704, 76283265, 127213568, 205777537, 323968032, 497842465, 748559360, 1103602017, 1598210592, 2277045057, 3196102656 (list; graph; refs; listen; history; text; internal format)
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+2s^3/15+197s^2/420+106s/105+1 where s=4n [Ahmed].

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

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-Fran├žois Alcover, Dec 06 2017 *)

CROSSREFS

Sequence in context: A275232 A061594 A145403 * A145217 A125444 A022692

Adjacent sequences:  A125113 A125114 A125115 * A125117 A125118 A125119

KEYWORD

easy,nonn

AUTHOR

R. J. Mathar, Jan 25 2007

STATUS

approved

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Last modified July 4 09:40 EDT 2020. Contains 335446 sequences. (Running on oeis4.)