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%I #24 Jan 12 2017 01:27:59
%S 0,168,5616,59136,372000,1596456,5630688,16343040,42305328,98361000,
%T 212427600,423933696,810534816,1463987112,2545290000,4266393600,
%U 6950204928,10954717992,16934047920,25480800000,37696122576,54705920808,78156525216,109665017856,152287500000
%N Number of pairs of 2 X 2 matrices over Z/nZ that do not commute.
%F a(n) = n^8 - A227479(n).
%F Conjecturally, a(p) = p^3(p^3-1)(p^2-1), for p prime. - _Giovanni Resta_, Jul 13 2013
%t 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}]
%Y Cf. A227479.
%K nonn
%O 1,2
%A _José María Grau Ribas_, Jul 11 2013
%E a(7)-a(25) from _Giovanni Resta_, Jul 13 2013
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