A125192 Number of 8 X 8 Franklin squares with magic sum 2n.

1, 0, 34, 64, 483, 1152, 4228, 9792, 25957, 54848, 120934, 233664, 455751, 816832, 1458184, 2456192, 4100169, 6560960, 10388394, 15928576, 24163115, 35742464, 52332172, 75080960, 106697901, 149112576, 206572782, 282188608, 382414991

Offset

0,3

Links

Table of n, a(n) for n=0..28.

M. M. Ahmed, Algebraic Combinatorics of Magic Squares, math.CO/0405476.

Maple

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;

Crossrefs

Sequence in context: A303239 A280931 A115159 * A039381 A043204 A043984

Adjacent sequences: A125189 A125190 A125191 * A125193 A125194 A125195

Keyword

easy,nonn

Author

R. J. Mathar, Jan 25 2007

Status

approved