A099834 Maximum number of different determinants that can be produced by permuting the elements of a 3 X 3 integer matrix with nonnegative entries <= n.

5, 15, 53, 109, 209, 351, 573, 811, 1193, 1509, 1971, 2501, 3183, 3769, 4511, 5025, 5641, 6165, 6600, 6964, 7354, 7696, 7960, 8110, 8404, 8606, 8704, 8846, 8962, 9125, 9210, 9284, 9362, 9420

Offset

1,1

Comments

For large values of n it is always possible to find a matrix that produces A088021(3)=10080 different determinants. Examples are given in the link. Currently (October 2004) the smallest known n for which a(n)=10080 is 100. The elements of the corresponding matrix are given in A098072.

Links

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

Hugo Pfoertner, List of 3 X 3 integer matrices that give 10080 different determinants.

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

Example

a(10)=1509: A corresponding set of matrix elements is {10,9,9,8,7,5,2,1,0}.

Crossrefs

Cf. A033431, A088021, A088217, A089472, A099815.

Cf. A099815 largest determinant that can be produced by the optimal set of matrix elements.

Sequence in context: A149578 A149579 A149580 * A034537 A318493 A335025

Adjacent sequences: A099831 A099832 A099833 * A099835 A099836 A099837

Keyword

nonn,hard

Author

Hugo Pfoertner, Oct 29 2004

Status

approved