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Search: id:A097693
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| A097693 |
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Largest achievable determinant of a 3 X 3 matrix whose elements are 9 distinct integers chosen from the range -n...n. |
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+0
6
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| 86, 216, 438, 776, 1254, 1896, 2726, 3768, 5046, 6584, 8406, 10536, 12998, 15816, 19014, 22616, 26646, 31128, 36086, 41544, 47526, 54056, 61158, 68856, 77174, 86136, 95766, 106088, 117126, 128904, 141446, 154776, 168918, 183896, 199734
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OFFSET
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4,1
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FORMULA
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An optimal choice and arrangement is of the following form: det((-n, 1-n, n-4), (n-3, 3-n, n), (2-n, n-1, n-2))=2*(2*n^3-7*n^2+6*n+3). There are 35 other equivalent arrangements corresponding to permutations of rows and columns.
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EXAMPLE
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Example:a(5)=216 because no larger determinant of a 3 X 3 integer matrix b(j,k) with distinct elements -5<=b(j,k)<=5,j=1..3,k=1..3 can be built than
det((-5,-4,1),(2,-2,5),(-3,4,3))=216.
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CROSSREFS
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Other maximal 3 X 3 determinants: Cf. A097399: 3 X 3 matrix filled with consecutive integers, A097401: 3 X 3 matrix filled with integers from 0...n, A097694, A097695, A097696: corresponding sequences for 4 X 4 matrices.
Sequence in context: A063353 A044418 A044799 this_sequence A113690 A043379 A162028
Adjacent sequences: A097690 A097691 A097692 this_sequence A097694 A097695 A097696
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KEYWORD
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nonn
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AUTHOR
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Hugo Pfoertner (hugo(AT)pfoertner.org), Aug 24 2004
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