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Search: id:A099815
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| A099815 |
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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. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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).
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LINKS
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Hugo Pfoertner, Elements of 3 X 3 matrices with maximal number of different determinants.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A099834.
Sequence in context: A058800 A077622 A137108 this_sequence A123363 A102961 A048504
Adjacent sequences: A099812 A099813 A099814 this_sequence A099816 A099817 A099818
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KEYWORD
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more,nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Nov 19 2004
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