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A276113 Number of 2 X 2 matrices with entries in {0,1,...,n} and permanent = (trace)^2 with no entry repeated.

%I A276113 #19 Jun 06 2020 13:00:37
%S A276113 0,0,0,0,4,4,4,8,12,24,24,24,32,52,56,56,76,76,88,120,124,152,152,152,
%T A276113 160,192,212,236,288,288,288,352,372,372,372,376,420,496,528,600,604,
%U A276113 604,632,724,728,740,740,740,788,932,964
%N A276113 Number of 2 X 2 matrices with entries in {0,1,...,n} and permanent = (trace)^2 with no entry repeated.
%C A276113 All terms are multiples of 4 since the diagonals can be permuted. - _Charles R Greathouse IV_, Dec 12 2016
%H A276113 Indranil Ghosh and Charles R Greathouse IV, <a href="/A276113/b276113.txt">Table of n, a(n) for n = 0..5000</a> (terms up to 200 from Indranil Ghosh)
%o A276113 (Python)
%o A276113 def t(n):
%o A276113     s=0
%o A276113     for a in range(n+1):
%o A276113         for b in range(n+1):
%o A276113             for c in range(n+1):
%o A276113                 for d in range(n+1):
%o A276113                    if (a!=b  and a!=d and b!=d and c!=a and c!=b and c!=d):
%o A276113                         if a*d+b*c==(a+d)**2:
%o A276113                             s+=1
%o A276113     return s
%o A276113 for i in range(201):
%o A276113     print(str(i)+" "+str(t(i)))
%o A276113 (PARI) a(n)=my(n2=n^2); 4*sum(a=0,n, sum(d=a+1,n, my(t=(a+d)^2-a*d,c); if(t>0 && t<n2, sumdiv(t, b, b^2<t && a!=b && b!=d && (c=t/b)<=n && a!=c && c!=d), 0))) \\ _Charles R Greathouse IV_, Dec 12 2016
%Y A276113 Cf. A210289.
%K A276113 nonn
%O A276113 0,5
%A A276113 _Indranil Ghosh_, Dec 11 2016