Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #22 Dec 14 2024 10:51:38
%S 1,32,417,3072,15585,60960,197057,550912,1374273,3127840,6602849,
%T 13089792,24605217,44188704,76283265,127213568,205777537,323968032,
%U 497842465,748559360,1103602017,1598210592,2277045057,3196102656
%N Number of 8 X 8 pandiagonal Franklin squares with magic sum 4n.
%H M. M. Ahmed, <a href="https://arxiv.org/abs/math/0405476">Algebraic Combinatorics of Magic Squares</a>, arXiv:math/0405476 [math.CO], 2004.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F 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].
%F G.f.: -(x+1)^3*(x^2+10*x+1)^2 / (x-1)^9. - _Colin Barker_, Dec 10 2012
%F a(n) = A145217(n+1) - A145217(n-1). - _Peter Bala_, Dec 12 2024
%p 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;
%t CoefficientList[((1 + x)^3*(1 + 10*x + x^2)^2)/(1 - x)^9 + O[x]^24, x] (* _Jean-François Alcover_, Dec 06 2017 *)
%Y Cf. A145217.
%K easy,nonn,changed
%O 0,2
%A _R. J. Mathar_, Jan 25 2007