A278377 Number of 2 X 2 matrices with all elements in {0,1,...,n} and determinant n with no elements repeated.

0, 0, 0, 4, 8, 16, 40, 36, 72, 60, 128, 92, 232, 144, 260, 284, 332, 252, 564, 324, 680, 568, 696, 492, 1184, 628, 984, 964, 1392, 796, 1920, 924, 1820, 1512, 1752, 1568, 2820, 1380, 2244, 2104, 3340, 1660, 3864, 1900, 3544, 3388, 3300, 2264, 5652, 2632, 4616

Offset: 0

Author

Indranil Ghosh, Nov 20 2016

Keywords

• nonn

Links

• Indranil Ghosh and Chai Wah Wu, Table of n, a(n) for n = 0..3000 (terms for n = 0..100 from Indranil Ghosh)

Crossrefs

Cf. A210282 (where the matrix elements can be repeated).

Programs

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==n:
                            s+=1
    return s
print([a(n) for n in range(0, 52)]) # Indranil Ghosh, Nov 20 2016