A350711 The number of different values taken by the determinant of a square n X n matrix whose elements are 1 or i = sqrt(-1).

1, 2, 7, 11, 27, 63, 177

Offset: 0

Author

Vladimir Reshetnikov, Mar 27 2022

Keywords

• nonn
• hard
• more

Examples

			For n = 2 there are 2^(2*2) = A002416(2) = 16 square 2 X 2 matrices whose elements are 1 or i. Their determinants take 7 distinct values: 0, 2, -2, 1 + i, 1 - i, -1 + i, -1 - i. So a(2) = 7.
		

Crossrefs

Cf. A002416, A089472.

Programs

Mathematica

Join[{1, 2}, Table[With[{d = Union[Det /@ DeleteCases[Subsets[Tuples[{1, I}, n], {n}], {{, 1}, , {I, } | {, I}}]]}, Length[Union[d, -d, {0}]]], {n, 2, 6}]]