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The number of different values taken by the determinant of a square n X n matrix whose elements are 1 or i = sqrt(-1).
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%I #16 Mar 27 2022 22:58:07

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

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

%e 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.

%t 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}]]

%Y Cf. A002416, A089472.

%K nonn,hard,more

%O 0,2

%A _Vladimir Reshetnikov_, Mar 27 2022