OFFSET
1,2
COMMENTS
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, ...}.
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
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.
LINKS
Hugo Pfoertner, Construction of maximal determinants. FORTRAN program.
EXAMPLE
The 7 X 7 subarray is:
[ 1, 3, 8, 11, 24, 26, 48]
[ 4, 2, 7, 16, 18, 36, 39]
[ 6, 9, 5, 13, 22, 30, 40]
[15, 12, 14, 10, 21, 34, 42]
[17, 25, 23, 20, 19, 31, 47]
[35, 27, 29, 33, 32, 28, 45]
[37, 43, 46, 41, 49, 44, 38]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Oct 14 2003
STATUS
approved