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

0,4

Links

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

Prog

(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

Crossrefs

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

Sequence in context: A141069 A306621 A144687 * A065605 A065978 A077447

Adjacent sequences: A278374 A278375 A278376 * A278378 A278379 A278380

Keyword

nonn

Author

Indranil Ghosh, Nov 20 2016

Status

approved