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A097401
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Largest achievable determinant of a 3 X 3 matrix whose elements are 9 distinct nonnegative integers chosen from the range 0..n.
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5
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332, 528, 796, 1148, 1596, 2152, 2828, 3636, 4588, 5696, 6972, 8428, 10076, 11928, 13996, 16292, 18828, 21616, 24668, 27996, 31612, 35528, 39756, 44308, 49196, 54432, 60028, 65996, 72348, 79096, 86252, 93828, 101836, 110288, 119196, 128572
(list; graph; refs; listen; history; internal format)
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OFFSET
| 8,1
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FORMULA
| An optimal choice and arrangement is of the following form: det((n, n-5, 1), (2, n-1, n-3), (n-4, 0, n-2))=2*(n^3-9*n^2+34*n-42). There are 35 other equivalent arrangements corresponding to permutations of rows and columns.
2n^3 - 24n^2 + 110n - 172.
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EXAMPLE
| a(10)=796 because no larger determinant of a 3 X 3 matrix b(j,k) with distinct elements 0<=b(j,k)<=10,j=1..3,k=1..3 can be built than det((10,5,1),(2,9,7),(6,0,8))=796.
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CROSSREFS
| Other maximal 3 X 3 determinants: Cf. a(8)=A097399(4)=332: 3 X 3 matrix filled with consecutive integers, A097693: 3 X 3 matrix filled with integers from -n...n, A097694, A097695, A097696: corresponding sequences for 4 X 4 matrices.
Sequence in context: A002228 A199820 A133141 * A114084 A095199 A111690
Adjacent sequences: A097398 A097399 A097400 * A097402 A097403 A097404
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KEYWORD
| nonn
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AUTHOR
| Hugo Pfoertner (hugo(AT)pfoertner.org), Aug 24 2004
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