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A306838 Number of different values taken by the determinant of a real (-1,0,1) matrix of order n.

%I A306838 #24 May 31 2024 05:53:10
%S A306838 1,3,5,9,25,67,233
%N A306838 Number of different values taken by the determinant of a real (-1,0,1) matrix of order n.
%C A306838 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 A306838 a(n) >= 1 + 2^n, since every integer determinant between -2^(n-1) and 2^(n-1) is possible (see MathOverflow link).
%H A306838 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 A306838 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.
%H A306838 Minfeng Wang, <a href="/A306838/a306838.cpp.txt">C++ program to calculate A306838</a>
%e A306838 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 A306838 The possible nonnegative determinants for small values of n are as follows (all the negatives of these numbers are also possible determinants):
%e A306838 n = 1: 0, 1
%e A306838 n = 2: 0, 1, 2
%e A306838 n = 3: 0, 1, 2, 3, 4
%e A306838 n = 4: 0 through 10, 12, 16
%e A306838 n = 5: 0 through 28, 30, 32, 36, 40, 48
%e A306838 n = 6: 0 through 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 112, 114, 116, 120, 125, 128, 130, 132, 136, 144, 160
%Y A306838 Number of matrices having maximum determinant is in A051753.
%K A306838 nonn,more,hard
%O A306838 0,2
%A A306838 _Steven E. Thornton_, Mar 12 2019
%E A306838 Edited and expanded by _Nathaniel Johnston_, Apr 19 2022
%E A306838 a(6) from _Minfeng Wang_, May 31 2024