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 A080992 Entries in Durer's magic square. 4
 16, 3, 2, 13, 5, 10, 11, 8, 9, 6, 7, 12, 4, 15, 14, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 4 X 4 magic square included in Albrecht Durer's 1514 engraving "Melancolia". 15 and 14 appear in the bottom row, giving the date. 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 sum(T(k,i): i = 1..4) = sum(T(i,k): i = 1..4) = 34, for k = 1..4; sum(T(k,k): k = 1..4) = sum(T(k,5-k): k = 1..4) = 34; T(1,1) + T(1,2) + T(2,1) + T(2,2) = 16 + 3 + 5 + 10 = 34; T(1,3) + T(1,4) + T(2,3) + T(2,4) = 2 + 13 + 11 + 8 = 34; T(3,1) + T(3,2) + T(4,1) + T(4,2) = 9 + 6 + 4 + 15 = 34; T(3,3) + T(3,4) + T(4,3) + T(4,4) = 7 + 12 + 14 + 1 = 34; T(1,1) + T(1,4) + T(4,1) + T(4,4) = 16 + 13 + 4 + 1 = 34; T(2,2) + T(2,3) + T(3,2) + T(3,3) = 10 + 11 + 6 + 7 = 34; T(1,2) + T(2,4) + T(4,3) + T(3,1) = 3 + 8 + 14 + 9 = 34; T(1,3) + T(3,4) + T(4,2) + T(2,1) = 2 + 12 + 15 + 5 = 34; T(1,2) + T(2,3) + T(4,2) + T(2,1) = 3 + 11 + 15 + 5 = 34; T(1,3) + T(2,4) + T(4,3) + T(2,2) = 2 + 8 + 14 + 10 = 34; T(1,2) + T(3,3) + T(4,2) + T(3,1) = 3 + 7 + 15 + 9 = 34; T(1,3) + T(3,4) + T(4,3) + T(3,2) = 2 + 12 + 14 + 6 = 34; T(1,2) + T(1,3) + T(4,2) + T(4,3) = 3 + 2 + 15 + 14 = 34; 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. 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 REFERENCES Hossin Behforooz, "Permutation-free magic squares", J. Recreational Mathematics, vol. 33, (2004-2005), pp. 103-106. LINKS History 291, Princeton University, Durer's Melancolia Laurence Eaves and Brady Haran, Magic square - Sixty Symbols A. Skalli, Magic cube with Dürer's square Torsten "Kermit", Die Rolle Dürers in Thomas Manns Doktor Faustus (in German). Eric Weisstein's World of Mathematics, Dürer' Magic Square Eric Weisstein's World of Mathematics, Gnomon Magic Square Wikipedia, Albrecht Dürer's magic square Reinhard Zumkeller, The 23 sums in Albrecht Dürer's magic square EXAMPLE .          1    2    3    4 .       +----+----+----+----+ .    1  | 16 |  3 |  2 | 13 | .       +----+----+----+----+ .    2  |  5 | 10 | 11 |  8 | .       +----+----+----+----+ .    3  |  9 |  6 |  7 | 12 | .       +----+----+----+----+ .    4  |  4 | 15 | 14 |  1 | .       +----+----+----+----+ .          D   ^^   ^^    A CROSSREFS Sequence in context: A031323 A095838 A040248 * A040249 A099143 A070709 Adjacent sequences:  A080989 A080990 A080991 * A080993 A080994 A080995 KEYWORD fini,full,nonn,changed AUTHOR David W. Wilson, Feb 26 2003 EXTENSIONS Extended by Reinhard Zumkeller, Jun 20 2013 STATUS approved

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Last modified April 22 22:19 EDT 2021. Contains 343197 sequences. (Running on oeis4.)