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A278377 Number of 2 X 2 matrices with all elements in {0,1,...,n} and determinant n with no elements repeated.

%I A278377 #42 Jun 11 2024 23:46:20
%S A278377 0,0,0,4,8,16,40,36,72,60,128,92,232,144,260,284,332,252,564,324,680,
%T A278377 568,696,492,1184,628,984,964,1392,796,1920,924,1820,1512,1752,1568,
%U A278377 2820,1380,2244,2104,3340,1660,3864,1900,3544,3388,3300,2264,5652,2632,4616
%N A278377 Number of 2 X 2 matrices with all elements in {0,1,...,n} and determinant n with no elements repeated.
%H A278377 Indranil Ghosh and Chai Wah Wu, <a href="/A278377/b278377.txt">Table of n, a(n) for n = 0..3000</a> (terms for n = 0..100 from Indranil Ghosh)
%o A278377 (Python)
%o A278377 def a(n):
%o A278377     s=0
%o A278377     for a in range(0, n+1):
%o A278377         for b in range(0, n+1):
%o A278377             for c in range(0, n+1):
%o A278377                 for d in range(0, n+1):
%o A278377                     if (a!=b  and a!=d and b!=d and c!=a and c!=b and c!=d):
%o A278377                         if a*d-b*c==n:
%o A278377                             s+=1
%o A278377     return s
%o A278377 print([a(n) for n in range(0, 52)]) # _Indranil Ghosh_, Nov 20 2016
%Y A278377 Cf. A210282 (where the matrix elements can be repeated).
%K A278377 nonn
%O A278377 0,4
%A A278377 _Indranil Ghosh_, Nov 20 2016