A279063 Number of 2 X 2 matrices having entries in {0,1,...,n} and determinant in the closed interval [-n,n] with no entry repeated.

0, 0, 0, 16, 56, 136, 296, 512, 864, 1280, 1912, 2616, 3680, 4760, 6200, 7848, 9792, 11832, 14632, 17280, 20784, 24352, 28480, 32584, 38200, 43168, 49160, 55472, 62936, 69784, 79008, 86944, 96952, 106816, 117672, 128592, 142352, 154088, 167968

Offset: 0

Author

Indranil Ghosh, Dec 05 2016

Keywords

• nonn
• changed

Comments

a(n) mod 8 = 0.

Links

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

Crossrefs

Cf. A211031 (where in the entries can be repeated).

Programs

Maple

f:= proc(n) local C;
     C:= combinat:-choose([$0..n],4);
     C:= map(t -> (t[1]*t[2]-t[3]*t[4],t[1]*t[3]-t[2]*t[4],t[1]*t[4]-t[2]*t[3]), C);
     8*nops(select(t -> abs(t)<=n, C))
end proc:
map(f, [$0..40]); # Robert Israel, Dec 05 2016

Python

def a(n):
    s=0
    for a in range(0,n+1):
        for b in range(0,n+1):
            for c in range(0,n+1):
                for d in range(0,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) in range(-n,n+1):
                            s+=1
    return s
print([a(n) for n in range(39)])