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Search: id:A097696
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| A097696 |
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Largest achievable determinant of a 4 X 4 matrix whose elements are the 16 consecutive integers n-15,...,n. |
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+0
5
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| 7343, 8784, 12065, 16800, 21600, 26400, 31200, 36000, 40800, 45600, 50400, 55200, 60000, 64800, 69600, 74400, 79200, 84000, 88800, 93600, 98400, 103200, 108000, 112800, 117600, 122400, 127200, 132000, 136800, 141600, 146400, 151200, 156000
(list; graph; listen)
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OFFSET
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8,1
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FORMULA
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For n>10 an arrangement maximizing the determinant is of the following form: det((n, n-9, n-13, n-8), (n-12, n-1, n-11, n-5), (n-7, n-6, n-2, n-15), (n-10, n-14, n-4, n-3)) =2400*(2*n-15). a(n)=a(15-n) for n<8.
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CROSSREFS
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Other maximal 4 X 4 determinants: Cf. A097694: 4 X 4 matrix filled with integers from 0...n, A097695: 4 X 4 matrix filled with integers from -n...n. A097399, A097401, A097693: corresponding sequences for 3 X 3 matrices. a(16)=A085000(4).
Sequence in context: A116248 A140078 A117799 this_sequence A128478 A043589 A043806
Adjacent sequences: A097693 A097694 A097695 this_sequence A097697 A097698 A097699
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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 25 2004
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