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

Offset: 1

Author

Hugo Pfoertner, Sep 23 2003

Keywords

• nonn
• more
• hard

Comments

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

Examples

			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.
		

Crossrefs

Cf. A085000, A088214, A088215, A088216, A088238, A325900.

Programs

Fortran

C See link given in A088238.

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 *)

Extensions

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