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

0,6

Comments

a(n) mod 8 = 0.

Links

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

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 *)

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

Crossrefs

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

Sequence in context: A341247 A188275 A319019 * A339323 A240037 A241867

Adjacent sequences: A278843 A278844 A278845 * A278847 A278848 A278849

Keyword

nonn

Author

Indranil Ghosh, Nov 29 2016

Status

approved