%I
%S 2,7,28,62,123,202,331,456,724,937,1391,1526,2084,2424,3107,3771,4694,
%T 5704,7119,8062,9632,10987,12332,14506,16626,19296,22492,21669,25179,
%U 27430,32044,32555,39916,41032
%N 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.
%C 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).
%H Hugo Pfoertner, <a href="http://www.randomwalk.de/sequences/a099834.txt">Elements of 3 X 3 matrices with maximal number of different determinants.</a>
%H <a href="/index/De#determinants">Index entries for sequences related to maximal determinants</a>
%e 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.
%Y Cf. A099834.
%K more,nonn
%O 1,1
%A _Hugo Pfoertner_, Nov 19 2004
