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A278902 Number of 2 X 2 matrices with entries in {0,1,...,n} with determinant = trace and no entry repeated.

%I A278902 #19 Jun 08 2020 07:20:49
%S A278902 0,0,0,0,0,8,12,24,28,40,48,68,72,100,120,132,144,188,208,252,280,304,
%T A278902 336,396,416,464,512,556,592,668,704,776,844,900,960,1020,1056,1148,
%U A278902 1240,1308,1348,1456,1524,1628,1728,1792,1872,2004,2080,2188,2292
%N A278902 Number of 2 X 2 matrices with entries in {0,1,...,n} with determinant = trace and no entry repeated.
%C A278902 a(n) mod 4=0.
%H A278902 Indranil Ghosh and Chai Wah Wu, <a href="/A278902/b278902.txt">Table of n, a(n) for n = 0..10000</a> (terms for n = 0..240 from Indranil Ghosh)
%o A278902 (Python)
%o A278902 def t(n):
%o A278902     s=0
%o A278902     for a in range(n+1):
%o A278902         for b in range(n+1):
%o A278902             for c in range(n+1):
%o A278902                 for d in range(n+1):
%o A278902                     if (a!=b and a!=d and b!=d and c!=a and c!=b and c!=d):
%o A278902                         if (a*d-b*c)==a+d:
%o A278902                             s+=1
%o A278902     return s
%o A278902 for i in range(241):
%o A278902     print(str(i)+" "+str(t(i)))
%Y A278902 Cf. A210286 (wherein the entries can be repeated).
%K A278902 nonn
%O A278902 0,6
%A A278902 _Indranil Ghosh_, Nov 30 2016