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

1,2

Links

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

Example

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

Prog

(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

Crossrefs

Sequence in context: A067680 A115052 A025203 * A238702 A162539 A259474

Adjacent sequences: A262716 A262717 A262718 * A262720 A262721 A262722

Keyword

nonn

Author

Christian Perfect, Sep 28 2015

Extensions

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

Status

approved