

A088745


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_{n1} as n1 X n1 upper left submatrix and abs(det(T_n)) is a maximized.


2



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, 27, 37
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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 (n1) X (n1) matrix and adding matrix elements (n1)^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



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



AUTHOR



STATUS

approved



