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A051235 Number of essentially different most-perfect pandiagonal magic squares of order 4n. 1
1, 48, 368640, 22295347200, 932242784256000, 144982397807493120000, 221340898613898982195200000, 21421302878528360015430942720000, 59225618198555209770663470432256000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

K. Ollerenshaw and D. S. Bree, Most-perfect Pan-diagonal Magic Squares: Their Construction and Enumeration, Inst. Math. Applic., Southend-on-Sea, England, 1998.

I. Stewart, Most-perfect magic squares, Sci. Amer., Nov. 1999, pp. 122-123.

LINKS

Table of n, a(n) for n=0..8.

Index entries for sequences related to magic squares

FORMULA

Let N = 4n = Product{g}[(p_g)^(s_g)] (p_g prime) and let W_v(n) = Sum{0 <= i <= v-1}[(-1)^{v+i}BINOM(v+1, i+1)*Product{g}BINOM(s_g+i, i)] then a(n) = 2^(N-2)*(2n)!^2*Sum{0 <= v < Sum{g}s_g}[W_v(N)(W_v(N)+W_{v+1}(N))].

CROSSREFS

Sequence in context: A037947 A146204 A079234 * A165643 A165047 A115480

Adjacent sequences:  A051232 A051233 A051234 * A051236 A051237 A051238

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Formula and more terms from Floor van Lamoen (fvlamoen(AT)hotmail.com), Aug 16 2001

STATUS

approved

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Last modified December 19 05:27 EST 2014. Contains 252177 sequences.