cp's OEIS Frontend

A279273 Number of 2 X 2 matrices having entries in {0,1,...,n} and determinant in the open interval (-n,n) with no entry repeated.

%I A279273 #12 May 27 2025 18:46:32
%S A279273 0,0,0,8,40,104,216,440,720,1160,1656,2432,3216,4472,5680,7280,9128,
%T A279273 11328,13504,16632,19424,23216,27088,31600,35832,41912,47192,53544,
%U A279273 60152,68192,75168
%N A279273 Number of 2 X 2 matrices having entries in {0,1,...,n} and determinant in the open interval (-n,n) with no entry repeated.
%C A279273 a(n) mod 8 = 0.
%H A279273 Indranil Ghosh, <a href="/A279273/b279273.txt">Table of n, a(n) for n = 0..121</a>
%o A279273 (Python)
%o A279273 def t(n):
%o A279273     s=0
%o A279273     for a in range(0,n+1):
%o A279273         for b in range(0,n+1):
%o A279273             for c in range(0,n+1):
%o A279273                 for d in range(0,n+1):
%o A279273                    if (a!=b  and a!=d and b!=d and c!=a and c!=b and c!=d):
%o A279273                         if (a*d-b*c) in range(-n+1,n):
%o A279273                             s+=1
%o A279273     return s
%o A279273 for i in range(0,122):
%o A279273     print(f"{i} {t(i)}")
%Y A279273 Cf. A211032 (where the entries can be repeated).
%K A279273 nonn
%O A279273 0,4
%A A279273 _Indranil Ghosh_, Dec 09 2016