OFFSET
0,2
COMMENTS
Every term in this sequence is odd, since 0 is a possible determinant, and if d is a possible determinant then so is -d.
a(n) >= 1 + 2^n, since every integer determinant between -2^(n-1) and 2^(n-1) is possible (see MathOverflow link).
LINKS
Steven E. Thornton, Properties of the Bohemian family of n x n matrices with population {-1, 0, 1}, Characteristic Polynomial Database.
Minfeng Wang, C++ program to calculate A306838
EXAMPLE
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.
The possible nonnegative determinants for small values of n are as follows (all the negatives of these numbers are also possible determinants):
n = 1: 0, 1
n = 2: 0, 1, 2
n = 3: 0, 1, 2, 3, 4
n = 4: 0 through 10, 12, 16
n = 5: 0 through 28, 30, 32, 36, 40, 48
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
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Steven E. Thornton, Mar 12 2019
EXTENSIONS
Edited and expanded by Nathaniel Johnston, Apr 19 2022
a(6) from Minfeng Wang, May 31 2024
STATUS
approved