A278902 - OEIS

%I #19 Jun 08 2020 07:20:49

%S 0,0,0,0,0,8,12,24,28,40,48,68,72,100,120,132,144,188,208,252,280,304,

%T 336,396,416,464,512,556,592,668,704,776,844,900,960,1020,1056,1148,

%U 1240,1308,1348,1456,1524,1628,1728,1792,1872,2004,2080,2188,2292

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

%C a(n) mod 4=0.

%H 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 (Python)

%o def t(n):

%o     s=0

%o     for a in range(n+1):

%o         for b in range(n+1):

%o             for c in range(n+1):

%o                 for d in range(n+1):

%o                     if (a!=b and a!=d and b!=d and c!=a and c!=b and c!=d):

%o                         if (a*d-b*c)==a+d:

%o                             s+=1

%o     return s

%o for i in range(241):

%o     print(str(i)+" "+str(t(i)))

%Y Cf. A210286 (wherein the entries can be repeated).

%K nonn

%O 0,6

%A _Indranil Ghosh_, Nov 30 2016