A276113 - OEIS

%I #19 Jun 06 2020 13:00:37

%S 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 160,192,212,236,288,288,288,352,372,372,372,376,420,496,528,600,604,

%U 604,632,724,728,740,740,740,788,932,964

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

%C All terms are multiples of 4 since the diagonals can be permuted. - _Charles R Greathouse IV_, Dec 12 2016

%H 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 (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)**2:

%o                             s+=1

%o     return s

%o for i in range(201):

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

%o (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 Cf. A210289.

%K nonn

%O 0,5

%A _Indranil Ghosh_, Dec 11 2016