A262719 a(n) is the smallest nonnegative k such that there is no 3 X 3 matrix with entries in {1,...,n} whose determinant is k.

1, 6, 21, 55, 110, 203, 357, 544, 808, 1177, 1670, 2215, 2865, 3599, 4558, 5621, 6637, 8041, 9769, 11413, 13394, 15593, 17683, 20317, 23249, 26063, 29506, 33287, 37461, 41692, 46306, 50707, 55667, 61723, 67547, 73939, 80767, 87941, 94913, 101613, 111422

Offset: 1

Author

Christian Perfect, Sep 28 2015

Keywords

• nonn

Examples

			For n=1, the only matrix is the matrix of all 1s, which has determinant 0. Hence, a(1)=1.
		

Links

• Hiroaki Yamanouchi, Table of n, a(n) for n = 1..50

Programs

Python

from itertools import product, groupby, count
def det(m):
    a, b, c, d, e, f, g, h, i = m
    return abs(a*(e*i-f*h)-b*(d*i-f*g)+c*(d*h-e*g))
def a262719(n):
    s = list(product(range(1, n+1), repeat=9))
    i = 0
    for k, ms in groupby(sorted(s, key=det), key=det):
        if k!=i:
            return i
        i += 1
    return i

Extensions

a(7)-a(41) from Hiroaki Yamanouchi, Oct 17 2015