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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
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 08:31 EST 2020. Contains 331293 sequences. (Running on oeis4.)