A088217 - OEIS

A088217

Number of distinct values that can be assumed by the determinant of an n X n matrix whose entries are all permutations of the numbers 1..n^2.

1, 6, 777, 79455, 13602389, 3722956267

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OFFSET

1,2

COMMENTS

a(5) = 1 + 2*(A085000(5) - (number of terms of A088238)).

LINKS

EXAMPLE

a(2)=6 because the determinants of the 24 2 X 2 matrices whose entries are all permutations of 1,2,3,4 can only assume the values -10,-5,-2,2,5,10.

MATHEMATICA

f[n_] := (p = Permutations[ Table[i, {i, n^2}]]; Length[ Union[ Table[ Det[ Partition[ p[[i]], n]], {i, 1, (n^2)!}]]]) (* Robert G. Wilson v *)

PROG

See link given in A088238.

CROSSREFS

KEYWORD

nonn,more,hard

AUTHOR

EXTENSIONS

Minor edits and a(6) from Hugo Pfoertner, Sep 08 2019

STATUS

approved