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%I #20 Apr 25 2022 08:02:22
%S 1,3,5,9,25,67
%N Number of different values taken by the determinant of a real (-1,0,1) matrix of order n.
%C Every term in this sequence is odd, since 0 is a possible determinant, and if d is a possible determinant then so is -d.
%C a(n) >= 1 + 2^n, since every integer determinant between -2^(n-1) and 2^(n-1) is possible (see MathOverflow link).
%H MathOverflow, <a href="https://mathoverflow.net/questions/420554/possible-values-of-the-determinant-for-matrices-with-elements-1-0-1">Possible values of the determinant for matrices with elements {1,0,-1}</a>
%H Steven E. Thornton, <a href="http://www.bohemianmatrices.com/cpdb/unstructured/unstructured_n1_0_1">Properties of the Bohemian family of n x n matrices with population {-1, 0, 1}</a>, Characteristic Polynomial Database.
%e For n = 2, the possible determinants of a 2x2 matrix with entries from {-1,0,1} are -2, -1, 0, 1, and 2. Since there are 5 numbers in this list, a(2) = 5.
%e The possible nonnegative determinants for small values of n are as follows (all the negatives of these numbers are also possible determinants):
%e n = 1: 0, 1
%e n = 2: 0, 1, 2
%e n = 3: 0, 1, 2, 3, 4
%e n = 4: 0 through 10, 12, 16
%e n = 5: 0 through 28, 30, 32, 36, 40, 48
%Y Number of matrices having maximum determinant is in A051753.
%K nonn,more,hard
%O 0,2
%A _Steven E. Thornton_, Mar 12 2019
%E Edited and expanded by _Nathaniel Johnston_, Apr 19 2022
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