A279018 Number of 2 X 2 matrices having entries in {-n,...,0,..,n} and permanent=trace with no entry repeated.

0, 0, 8, 24, 56, 100, 156, 236, 320, 408, 540, 692, 844, 1044, 1228, 1368, 1592, 1884, 2180, 2500, 2764, 2996, 3356, 3756, 4080, 4456, 4884, 5276, 5740, 6252, 6740, 7316, 7868, 8340, 8860, 9352, 9896, 10628, 11324

Offset: 0

Author

Indranil Ghosh, Dec 03 2016

Keywords

• nonn

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..150

Crossrefs

Cf. A211145 (wherein the entries can be repeated).

Programs

Mathematica

f[n_] := f[n] = Block[{a, b, c, d, s = 0}, a = -n; While[a < n +1, b = -n; While[b < n +1, c = -n; While[c < n +1, d = -n; While[d < n +1, If[ a != b && a != c && a != d && b != c && b != d && c != d && a*d + b*c == a + d, s++]; d++]; c++]; b++]; a++]; s]; Array[f, 40, 0] (* Robert G. Wilson v, Dec 03 2016 *)

Python

def t(n):
    s=0
    for a in range(-n,n+1):
        for b in range(-n,n+1):
            for c in range(-n,n+1):
                for d in range(-n,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:
                            s+=1
    return s
for i in range(0,151):
    print(i, t(i))