

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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



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

Table of n, a(n) for n=1..28.
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

Cf. A088746 (determinants), A085000, A088217.
Sequence in context: A016609 A346411 A199618 * A213922 A306568 A154743
Adjacent sequences: A088742 A088743 A088744 * A088746 A088747 A088748


KEYWORD

nonn,tabl


AUTHOR

Paul D. Hanna, Oct 14 2003


STATUS

approved



