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%I #27 Feb 25 2023 09:38:56
%S 16,3,2,13,5,10,11,8,9,6,7,12,4,15,14,1
%N Entries in Durer's magic square.
%C 4 X 4 magic square included in Albrecht Durer's 1514 engraving "Melancolia". 15 and 14 appear in the bottom row, giving the date.
%C A006003(4) = 34 is the magic constant, occurring 23 times as sum of exactly 4 distinct numbers 1..16 with regular patterns in the 4 X 4 square(see also link): - _Reinhard Zumkeller_, Jun 20 2013
%C sum(T(k,i): i = 1..4) = sum(T(i,k): i = 1..4) = 34, for k = 1..4;
%C sum(T(k,k): k = 1..4) = sum(T(k,5-k): k = 1..4) = 34;
%C T(1,1) + T(1,2) + T(2,1) + T(2,2) = 16 + 3 + 5 + 10 = 34;
%C T(1,3) + T(1,4) + T(2,3) + T(2,4) = 2 + 13 + 11 + 8 = 34;
%C T(3,1) + T(3,2) + T(4,1) + T(4,2) = 9 + 6 + 4 + 15 = 34;
%C T(3,3) + T(3,4) + T(4,3) + T(4,4) = 7 + 12 + 14 + 1 = 34;
%C T(1,1) + T(1,4) + T(4,1) + T(4,4) = 16 + 13 + 4 + 1 = 34;
%C T(2,2) + T(2,3) + T(3,2) + T(3,3) = 10 + 11 + 6 + 7 = 34;
%C T(1,2) + T(2,4) + T(4,3) + T(3,1) = 3 + 8 + 14 + 9 = 34;
%C T(1,3) + T(3,4) + T(4,2) + T(2,1) = 2 + 12 + 15 + 5 = 34;
%C T(1,2) + T(2,3) + T(4,2) + T(2,1) = 3 + 11 + 15 + 5 = 34;
%C T(1,3) + T(2,4) + T(4,3) + T(2,2) = 2 + 8 + 14 + 10 = 34;
%C T(1,2) + T(3,3) + T(4,2) + T(3,1) = 3 + 7 + 15 + 9 = 34;
%C T(1,3) + T(3,4) + T(4,3) + T(3,2) = 2 + 12 + 14 + 6 = 34;
%C T(1,2) + T(1,3) + T(4,2) + T(4,3) = 3 + 2 + 15 + 14 = 34;
%C T(4,2)*100 + T(4,3) = 1514, the year of the engraving and the pair (T(4,4),T(4,1)) = (1,4) corresponds to Albrecht Dürer's coded initials.
%C The square has its magic constant (34) equal to one of its eigenvalues (34, 8, -8, 0) like any other normal magic square of order n > 2. - _Michal Paulovic_, Mar 14 2021
%D Hossin Behforooz, "Permutation-free magic squares", J. Recreational Mathematics, vol. 33, (2004-2005), pp. 103-106.
%H History 291, Princeton University, <a href="http://www.princeton.edu/~his291/Durer_Melancolia.html">Durer's Melancolia</a>
%H Laurence Eaves and Brady Haran, <a href="http://www.youtube.com/watch?v=gGvyeuDT2Do">Magic square - Sixty Symbols</a>
%H A. Skalli, <a href="https://sites.google.com/site/aliskalligvaen/home-page/-magic-cube-with-duerer-s-square">Magic cube with Dürer's square</a>
%H Torsten "Kermit", <a href="https://web.archive.org/web/20150912040302/http://www.heim2.tu-clausthal.de/~kermit/faust-duerer.shtml">Die Rolle Dürers in Thomas Manns Doktor Faustus</a> (in German).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DuerersMagicSquare.html">Dürer's Magic Square</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GnomonMagicSquare.html">Gnomon Magic Square</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Magic_square#Albrecht_D.C3.BCrer.27s_magic_square">Albrecht Dürer's magic square</a>
%H Reinhard Zumkeller, <a href="/A080992/a080992.txt">The 23 sums in Albrecht Dürer's magic square</a>
%H <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a>
%e . 1 2 3 4
%e . +----+----+----+----+
%e . 1 | 16 | 3 | 2 | 13 |
%e . +----+----+----+----+
%e . 2 | 5 | 10 | 11 | 8 |
%e . +----+----+----+----+
%e . 3 | 9 | 6 | 7 | 12 |
%e . +----+----+----+----+
%e . 4 | 4 | 15 | 14 | 1 |
%e . +----+----+----+----+
%e . D ^^ ^^ A
%K fini,full,nonn
%O 1,1
%A _David W. Wilson_, Feb 26 2003
%E Extended by _Reinhard Zumkeller_, Jun 20 2013
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