A099815 Maximum determinant that can be formed from the optimal set of nonnegative 3 X 3 matrix elements <=n, which maximize the number of different determinants given in A099834.

2, 7, 28, 62, 123, 202, 331, 456, 724, 937, 1391, 1526, 2084, 2424, 3107, 3771, 4694, 5704, 7119, 8062, 9632, 10987, 12332, 14506, 16626, 19296, 22492, 21669, 25179, 27430, 32044, 32555, 39916, 41032

Offset

1,1

Comments

If more than one set of optimal matrix elements exists then the set producing the smallest maximum is selected. This occurs for n=2, where 3 different sets of matrix elements allow the construction of 15 different determinants. {2 2 2 1 1 1 1 0 0} produces the smallest maximum a(2)=7. Other examples are n=5 and n=41 (a(41)=77902).

Links

Table of n, a(n) for n=1..34.

Hugo Pfoertner, Elements of 3 X 3 matrices with maximal number of different determinants.

Index entries for sequences related to maximal determinants

Example

a(3)=28 because the largest determinant (of A099834(3)=53 possible different determinants) of a matrix using the elements of the optimal set {3 3 3 2 2 1 1 0 0} is det((3,2,0),(0,3,1),(2,1,3))=28.

Crossrefs

Cf. A099834.

Sequence in context: A077622 A137108 A294128 * A123363 A102961 A155581

Adjacent sequences: A099812 A099813 A099814 * A099816 A099817 A099818

Keyword

more,nonn

Author

Hugo Pfoertner, Nov 19 2004

Status

approved