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_{n-1} as n-1 X n-1 upper left submatrix and abs(det(T_n)) is a maximized.

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

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

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