

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.


3



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
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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 A149581
Adjacent sequences: A099831 A099832 A099833 * A099835 A099836 A099837


KEYWORD

nonn,hard


AUTHOR

Hugo Pfoertner, Oct 29 2004


STATUS

approved



