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A279063 Number of 2 X 2 matrices having entries in {0,1,...,n} and determinant in the closed interval [-n,n] with no entry repeated.

%I A279063 #16 Aug 24 2025 11:20:53
%S A279063 0,0,0,16,56,136,296,512,864,1280,1912,2616,3680,4760,6200,7848,9792,
%T A279063 11832,14632,17280,20784,24352,28480,32584,38200,43168,49160,55472,
%U A279063 62936,69784,79008,86944,96952,106816,117672,128592,142352,154088,167968
%N A279063 Number of 2 X 2 matrices having entries in {0,1,...,n} and determinant in the closed interval [-n,n] with no entry repeated.
%C A279063 a(n) mod 8 = 0.
%H A279063 Indranil Ghosh, <a href="/A279063/b279063.txt">Table of n, a(n) for n = 0..150</a>
%p A279063 f:= proc(n) local C;
%p A279063      C:= combinat:-choose([$0..n],4);
%p A279063      C:= map(t -> (t[1]*t[2]-t[3]*t[4],t[1]*t[3]-t[2]*t[4],t[1]*t[4]-t[2]*t[3]), C);
%p A279063      8*nops(select(t -> abs(t)<=n, C))
%p A279063 end proc:
%p A279063 map(f, [$0..40]); # _Robert Israel_, Dec 05 2016
%o A279063 (Python)
%o A279063 def a(n):
%o A279063     s=0
%o A279063     for a in range(0,n+1):
%o A279063         for b in range(0,n+1):
%o A279063             for c in range(0,n+1):
%o A279063                 for d in range(0,n+1):
%o A279063                    if (a!=b  and a!=d and b!=d and c!=a and c!=b and c!=d):
%o A279063                         if (a*d-b*c) in range(-n,n+1):
%o A279063                             s+=1
%o A279063     return s
%o A279063 print([a(n) for n in range(39)])
%Y A279063 Cf. A211031 (where in the entries can be repeated).
%K A279063 nonn,changed
%O A279063 0,4
%A A279063 _Indranil Ghosh_, Dec 05 2016