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
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
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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;
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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