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

0,5

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)

Prog

(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)))
(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

Crossrefs

Cf. A210289.

Sequence in context: A110757 A377468 A167184 * A232406 A322040 A085071

Adjacent sequences: A276110 A276111 A276112 * A276114 A276115 A276116

Keyword

nonn

Author

Indranil Ghosh, Dec 11 2016

Status

approved