A227479 Number of pairs of 2 X 2 matrices over Z/nZ that commute.

1, 88, 945, 6400, 18625, 83160, 134113, 434176, 741393, 1639000, 1931281, 6048000, 5195905, 11801944, 17600625, 28573696, 25552513, 65242584, 49515121, 119200000, 126736785, 169952728, 154460065, 410296320, 300390625

Offset

1,2

Links

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

Formula

a(n) = n^8 - A227433(n).

Mathematica

lon[n_] := Length@matrices[n]; matrices[n_] := Flatten[Table[{{a, b}, {c, d}}, {a, n}, {b, n}, {c, n}, {d, n}], 3]; com[n_] := Sum[If[Mod[matrices[n][[i]].matrices[n][[j]] - matrices[n][[j]].matrices[n][[i]], n] == {{0, 0}, {0, 0}}, 1, 0], {i, lon[n]}, {j, i, lon[n]}]; Table[2*com[i] - i^4, {i, 4}]

Crossrefs

Cf. A227433.

Sequence in context: A137049 A157730 A055749 * A321061 A295591 A182676

Adjacent sequences: A227476 A227477 A227478 * A227480 A227481 A227482

Keyword

nonn,mult

Author

José María Grau Ribas, Jul 13 2013

Status

approved