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A051235
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Number of essentially different most-perfect pandiagonal magic squares of order 4n.
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1
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1, 48, 368640, 22295347200, 932242784256000, 144982397807493120000, 221340898613898982195200000, 21421302878528360015430942720000, 59225618198555209770663470432256000000
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OFFSET
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0,2
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=0..8.
Index entries for sequences related to magic squares
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FORMULA
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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))].
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CROSSREFS
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Sequence in context: A037947 A146204 A079234 * A165643 A165047 A115480
Adjacent sequences: A051232 A051233 A051234 * A051236 A051237 A051238
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Formula and more terms from Floor van Lamoen (fvlamoen(AT)hotmail.com), Aug 16 2001
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STATUS
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approved
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