A278902 Number of 2 X 2 matrices with entries in {0,1,...,n} with determinant = trace and no entry repeated.

0, 0, 0, 0, 0, 8, 12, 24, 28, 40, 48, 68, 72, 100, 120, 132, 144, 188, 208, 252, 280, 304, 336, 396, 416, 464, 512, 556, 592, 668, 704, 776, 844, 900, 960, 1020, 1056, 1148, 1240, 1308, 1348, 1456, 1524, 1628, 1728, 1792, 1872, 2004, 2080, 2188, 2292

Offset: 0

Author

Indranil Ghosh, Nov 30 2016

Keywords

• nonn

Comments

a(n) mod 4=0.

Links

• Indranil Ghosh and Chai Wah Wu, Table of n, a(n) for n = 0..10000 (terms for n = 0..240 from Indranil Ghosh)

Crossrefs

Cf. A210286 (wherein the entries can be repeated).

Programs

Python

def t(n):
    s=0
    for a in range(n+1):
        for b in range(n+1):
            for c in range(n+1):
                for d in range(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(241):
    print(str(i)+" "+str(t(i)))