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

Author

Hugo Pfoertner, Nov 19 2004

Keywords

• more
• nonn

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).

Examples

			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.
		

Links

• Hugo Pfoertner, Elements of 3 X 3 matrices with maximal number of different determinants.
• Index entries for sequences related to maximal determinants

Crossrefs

Cf. A099834.