

A097694


Largest achievable determinant of a 4 X 4 matrix whose elements are 16 distinct nonnegative integers chosen from the range 0...n.


4



36000, 50736, 69828, 94092, 124699, 162604, 208697, 264094, 329983, 407624, 498349, 603562
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OFFSET

15,1


LINKS

Table of n, a(n) for n=15..26.


FORMULA

For n<=18 an optimal choice and arrangement is of the following form det((n, 6, 2, n8), (3, n1, 4, n5), (n7, n6, n2, 0), (5, 1, n4, n3))= 3*n^462*n^3+543*n^22128*n+3120. For n>18 up to the limit investigated (n<=26) one choice maximizing the determinant is det((n, 6, 2, n8), (3, n1, 4, n5), (n7, n6, n3, 0), (5, 1, n2, n4))= 3*n^460*n^3+491*n^21821*n+2624. In both cases there are 575 other equivalent arrangements corresponding to permutations of rows and columns.


EXAMPLE

a(18)=94092 because no 4 X 4 matrix b(j,k) with distinct elements 0<=b(j,k)<=18,j=1..4,k=1..4 can be built that has a larger determinant than
det((18,6,2,10),(3,17,4,13),(11,12,16,0),(5,1,14,15)=94092.


CROSSREFS

Other maximal 4 X 4 determinants: Cf. A097696: 4 X 4 matrix filled with consecutive integers, A097695: 4 X 4 matrix filled with integers from n...n, A097399, A097401, A097693: corresponding sequences for 3 X 3 matrices, A085000: n X n matrix filled with consecutive integers 1...n^2.
Sequence in context: A236201 A034605 A031827 * A209956 A256365 A011766
Adjacent sequences: A097691 A097692 A097693 * A097695 A097696 A097697


KEYWORD

more,nonn


AUTHOR

Hugo Pfoertner, Aug 24 2004


STATUS

approved



