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%I #3 Mar 30 2012 17:39:15
%S 1,0,34,64,483,1152,4228,9792,25957,54848,120934,233664,455751,816832,
%T 1458184,2456192,4100169,6560960,10388394,15928576,24163115,35742464,
%U 52332172,75080960,106697901,149112576,206572782,282188608,382414991
%N Number of 8 X 8 Franklin squares with magic sum 2n.
%H M. M. Ahmed, <a href="http://arXiv.org/abs/math.CO/0405476">Algebraic Combinatorics of Magic Squares</a>, math.CO/0405476.
%p a := proc(n) local s,s6,s3a,s3b ; s :=2*n ; s6 := 23*s^9/627056640+23*s^8/17418240+167*s^7/6531840+5*s^6/15552 ; s3a := 2419*s^5/933120+1013*s^4/77760+701*s^3/22680 ; s3b := 581*s^5/186624+1823*s^4/77760+6127*s^3/45360 ; if s<>2 and s mod 12 = 2 then s6+s3a -359*s^2/10206 -177967*s/816480+241/17496 ; elif s mod 12 = 4 then s6+s3b +10741*s^2/20412 +113443*s/102060+3211/2187 ; elif s mod 12 = 6 then s6+s3a -5*s^2/378 -3967*s/10080-13/8 ; elif s mod 12 = 8 then s6+s3b +11189*s^2/20412 +167203*s/102060+5771/2187 ; elif s mod 12 = 10 then s6+s3a -583*s^2/10206 -608047*s/816480-20239/17496 ; elif s mod 12 = 0 then s6+s3b +431*s^2/756 +1843*s/1260+1 ; else 0 fi ; end: for n from 0 to 30 do printf("%d ",a(n)) ; od;
%K easy,nonn
%O 0,3
%A _R. J. Mathar_, Jan 25 2007
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