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

0, 0, 0, 0, 4, 4, 4, 8, 12, 24, 24, 24, 32, 52, 56, 56, 76, 76, 88, 120, 124, 152, 152, 152, 160, 192, 212, 236, 288, 288, 288, 352, 372, 372, 372, 376, 420, 496, 528, 600, 604, 604, 632, 724, 728, 740, 740, 740, 788, 932, 964

Offset: 0

Author

Indranil Ghosh, Dec 11 2016

Keywords

• nonn

Comments

All terms are multiples of 4 since the diagonals can be permuted. - Charles R Greathouse IV, Dec 12 2016

Links

• Indranil Ghosh and Charles R Greathouse IV, Table of n, a(n) for n = 0..5000 (terms up to 200 from Indranil Ghosh)

Crossrefs

Cf. A210289.

Programs

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 && tCharles R Greathouse IV, Dec 12 2016

Python

def t(n):
    s=0
    for a in range(n+1):
        for b in range(n+1):
            for c in range(n+1):
                for d in range(n+1):
                   if (a!=b  and a!=d and b!=d and c!=a and c!=b and c!=d):
                        if a*d+b*c==(a+d)**2:
                            s+=1
    return s
for i in range(201):
    print(str(i)+" "+str(t(i)))