|
%I #16 Oct 18 2015 12:23:07
%S 1,6,21,55,110,203,357,544,808,1177,1670,2215,2865,3599,4558,5621,
%T 6637,8041,9769,11413,13394,15593,17683,20317,23249,26063,29506,33287,
%U 37461,41692,46306,50707,55667,61723,67547,73939,80767,87941,94913,101613,111422
%N 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.
%H Hiroaki Yamanouchi, <a href="/A262719/b262719.txt">Table of n, a(n) for n = 1..50</a>
%e For n=1, the only matrix is the matrix of all 1s, which has determinant 0. Hence, a(1)=1.
%o (Python)
%o from itertools import product,groupby,count
%o .
%o def det(m):
%o ...a,b,c,d,e,f,g,h,i = m
%o ...return abs(a*(e*i-f*h)-b*(d*i-f*g)+c*(d*h-e*g))
%o .
%o def a262719(n):
%o ...s = list(product(range(1,n+1),repeat=9))
%o ...i = 0
%o ...for k,ms in groupby(sorted(s,key=det),key=det):
%o ......if k!=i:
%o .........return i
%o ......i += 1
%o ...return i
%K nonn
%O 1,2
%A _Christian Perfect_, Sep 28 2015
%E a(7)-a(41) from _Hiroaki Yamanouchi_, Oct 17 2015
|
