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A097693 Largest achievable determinant of a 3 X 3 matrix whose elements are 9 distinct integers chosen from the range -n...n. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

LINKS

Table of n, a(n) for n=4..38.

FORMULA

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.

G.f.: 2*x^4*(43-64*x+45*x^2-12*x^3)/(1-x)^4. [Colin Barker, Mar 29 2012]

EXAMPLE

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.

CROSSREFS

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: A202777 A202770 A184095 * A184087 A304518 A306112

Adjacent sequences:  A097690 A097691 A097692 * A097694 A097695 A097696

KEYWORD

nonn,easy

AUTHOR

Hugo Pfoertner, Aug 24 2004

STATUS

approved

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Last modified May 18 23:31 EDT 2022. Contains 353826 sequences. (Running on oeis4.)