A227433 Number of pairs of 2 X 2 matrices over Z/nZ that do not commute.

0, 168, 5616, 59136, 372000, 1596456, 5630688, 16343040, 42305328, 98361000, 212427600, 423933696, 810534816, 1463987112, 2545290000, 4266393600, 6950204928, 10954717992, 16934047920, 25480800000, 37696122576, 54705920808, 78156525216, 109665017856, 152287500000

Offset

1,2

Links

Table of n, a(n) for n=1..25.

Formula

a(n) = n^8 - A227479(n).

Conjecturally, a(p) = p^3(p^3-1)(p^2-1), for p prime. - Giovanni Resta, Jul 13 2013

Mathematica

lon[n_]:=Length@matrices[n]; matrices[n_] := Flatten[Table[{{a, b}, {c, d}}, {a, n}, {b, n}, {c, n}, {d, n}], 3]; nocom[n_] := Sum[If[Mod[matrices[n][[i]].matrices[n][[j]] - matrices[n][[j]].matrices[n][[i]], n] == {{0, 0}, {0, 0}}, 0, 1], {i, lon[n]}, {j, i, lon[n]}]; Table[2*nocom[i], {i, 5}]

Crossrefs

Cf. A227479.

Sequence in context: A282614 A003807 A011785 * A003800 A373501 A278010

Adjacent sequences: A227430 A227431 A227432 * A227434 A227435 A227436

Keyword

nonn

Author

José María Grau Ribas, Jul 11 2013

Extensions

a(7)-a(25) from Giovanni Resta, Jul 13 2013

Status

approved