

A051235


Number of essentially different mostperfect 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, Mostperfect Pandiagonal Magic Squares: Their Construction and Enumeration, Inst. Math. Applic., SouthendonSea, England, 1998.
I. Stewart, Mostperfect magic squares, Sci. Amer., Nov. 1999, pp. 122123.


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 <= v1}[(1)^{v+i}BINOM(v+1, i+1)*Product{g}BINOM(s_g+i, i)] then a(n) = 2^(N2)*(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



