A278846 Number of unimodular 2 X 2 matrices having entries in {0,1,...,n} with no entry repeated.

0, 0, 0, 0, 0, 8, 8, 40, 48, 80, 88, 152, 160, 232, 264, 304, 344, 448, 480, 608, 648, 720, 784, 944, 968, 1104, 1176, 1304, 1376, 1576, 1616, 1840, 1944, 2080, 2184, 2352, 2424, 2688, 2816, 2984, 3072, 3368, 3440, 3760, 3896, 4064, 4224, 4576, 4664, 4984, 5120

Offset: 0

Author

Indranil Ghosh, Nov 29 2016

Keywords

• nonn

Comments

a(n) mod 8 = 0.

Links

• Robert Israel, Table of n, a(n) for n = 0..1000 (terms 0..241 from Indranil Ghosh)

Crossrefs

Cf. A210000 (where the matrix entries can be repeated).

Programs

Maple

df:= proc(n) local count, c,d,q,av,bc,a,b;
  count:= 0:
  for d from 1 to n-1 do
      av:= {$1..n-1} minus {d};
      for q in [-1,1] do
        bc:= n*d+q;
        for b in numtheory:-divisors(bc) intersect av do
          c:= bc/b;
          if c < b and member(c,av) then count:=count+8 fi;
  od od od;
  count
end proc:
ListTools:-PartialSums(map(df, [$0..100])); # Robert Israel, Nov 29 2016

Mathematica

df[n_] := Module[{count = 0, c, d, q, av, bc, a, b}, Do[av = Range[n - 1]  ~Complement~ {d}; Do[bc = n d + q; Do[c = bc/b; If[c < b && MemberQ[av, c], count += 8], {b, Divisors[bc] ~Intersection~ av}], {q, {-1 , 1}}], {d, 1, n - 1}]; count];
df /@ Range[0, 100] // Accumulate (* Jean-François Alcover, Jul 29 2020, after Robert Israel *)

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 abs(a*d-b*c)==1:
                            s+=1
    return s
print([a(n) for n in range(0, 52)]) # Indranil Ghosh, Nov 29 2016