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A227433 Number of pairs of 2 X 2 matrices over Z/nZ that do not commute. 2
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 (list; graph; refs; listen; history; text; internal format)
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 A278010 A006363

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

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Last modified August 19 06:22 EDT 2022. Contains 356216 sequences. (Running on oeis4.)