A088745 - OEIS

%I #10 Mar 04 2015 21:27:41

%S 1,3,4,8,2,6,11,7,9,15,24,16,5,12,17,26,18,13,14,25,35,48,36,22,10,23,

%T 27,37

%N Infinite array read by antidiagonals: for n>=1 let T_n = upper left n X n matrix. Then T_1 = (1), T_n has elements 1..n^2, contains T_{n-1} as n-1 X n-1 upper left submatrix and abs(det(T_n)) is a maximized.

%C Matrices with elements 1..n^2 that are to have maximum absolute determinant under the following construction. Start with a(1,1)=1, build successive n X n matrices by fixing previous (n-1) X (n-1) matrix and adding matrix elements (n-1)^2+1..n^2 on lower and right border of matrix. Determinants of upper left n X n matrices are: {1, -10, 205, -6300, 276363, -15615642, ...}.

%C The definition is incomplete since it does not say what to do if there are several possibilities for the new border. - _N. J. A. Sloane_, Oct 18 2003

%C Terms computed by Hugo Pfoertner (see link). If we start with either 2 X 2 matrices [1,3][4,2] or [1,4][3,2], initially there seems to be a unique solution for the subsequent enhanced matrices.

%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a088745.txt">Construction of maximal determinants.</a> FORTRAN program.

%e The 7 X 7 subarray is:

%e [ 1, 3, 8, 11, 24, 26, 48]

%e [ 4, 2, 7, 16, 18, 36, 39]

%e [ 6, 9, 5, 13, 22, 30, 40]

%e [15, 12, 14, 10, 21, 34, 42]

%e [17, 25, 23, 20, 19, 31, 47]

%e [35, 27, 29, 33, 32, 28, 45]

%e [37, 43, 46, 41, 49, 44, 38]

%Y Cf. A088746 (determinants), A085000, A088217.

%K nonn,tabl

%O 1,2

%A _Paul D. Hanna_, Oct 14 2003