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

0,4

Comments

a(n) mod 8 = 0.

Links

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

Prog

(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 str(i)+" "+str(t(i))

Crossrefs

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

Sequence in context: A069083 A014642 A211631 * A143943 A135796 A105374

Adjacent sequences: A279270 A279271 A279272 * A279274 A279275 A279276

Keyword

nonn

Author

Indranil Ghosh, Dec 09 2016

Status

approved