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

0,3

Links

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

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 *)

Prog

(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 str(i)+" "+str(t(i))

Crossrefs

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

Sequence in context: A212972 A316541 A152134 * A011925 A256052 A159741

Adjacent sequences: A279015 A279016 A279017 * A279019 A279020 A279021

Keyword

nonn

Author

Indranil Ghosh, Dec 03 2016

Status

approved