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Search: id:A099834
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| A099834 |
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Maximum number of different determinants that can be produced by permuting the elements of a 3 X 3 integer matrix with nonnegative entries <= n. |
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+0
3
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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LINKS
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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.
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EXAMPLE
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a(10)=1509: A corresponding set of matrix elements is {10,9,9,8,7,5,2,1,0}.
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CROSSREFS
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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 this_sequence A034537 A149581 A149582
Adjacent sequences: A099831 A099832 A099833 this_sequence A099835 A099836 A099837
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KEYWORD
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nonn,hard
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Oct 29 2004
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