A279273 Number of 2 X 2 matrices having entries in {0,1,...,n} and determinant in the open interval (-n,n) with no entry repeated.

0, 0, 0, 8, 40, 104, 216, 440, 720, 1160, 1656, 2432, 3216, 4472, 5680, 7280, 9128, 11328, 13504, 16632, 19424, 23216, 27088, 31600, 35832, 41912, 47192, 53544, 60152, 68192, 75168

Offset: 0

Author

Indranil Ghosh, Dec 09 2016

Keywords

• nonn

Comments

a(n) mod 8 = 0.

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..121

Crossrefs

Cf. A211032 (where the entries can be repeated).

Programs

Python

def t(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+1,n):
                            s+=1
    return s
for i in range(0,122):
    print(f"{i} {t(i)}")