

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.


1



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
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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



