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A121670 a(n) = n^3 - 3*n.

%I A121670 #28 Nov 30 2021 12:17:14
%S A121670 0,-2,2,18,52,110,198,322,488,702,970,1298,1692,2158,2702,3330,4048,
%T A121670 4862,5778,6802,7940,9198,10582,12098,13752,15550,17498,19602,21868,
%U A121670 24302,26910,29698,32672,35838,39202,42770,46548,50542,54758,59202,63880,68798,73962
%N A121670 a(n) = n^3 - 3*n.
%C A121670 Previous name was: Real part of (n + i)^3, companion to A080663.
%C A121670 Reversing the order of terms in (n + i)^3 to (1 + ni)^3 generates the terms of A080663. E.g, A080663(4) = 47 since (1 + 4i)^3 = (-47 - 52i). Or, (n + i)^3 = (a(n) + A080663(a)i) and (1 + ni)^3 = (-A080663(n) - a(n)i).
%C A121670 Also, numbers n such that the polynomial x^6 - n*x^3 + 1 is reducible. - _Ralf Stephan_, Oct 24 2013
%H A121670 Vincenzo Librandi, <a href="/A121670/b121670.txt">Table of n, a(n) for n = 0..1000</a>
%H A121670 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A121670 a(n) = Re( (n + i)^3 ).
%F A121670 a(n) = n^3-3*n. a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). G.f.: -2*x*(x^2-5*x+1) / (x-1)^4. - _Colin Barker_, Oct 16 2013
%F A121670 a(n)^2 = A028872(n)^3 + 3*A028872(n)^2 for n>1. - _Bruno Berselli_, May 03 2018
%F A121670 a(n) = A058794(n-2) for n>1. - _Altug Alkan_, May 03 2018
%e A121670 a(4) = 52 since (4 + i)^3 = (52 + 47i); where 47 = A080663(4).
%t A121670 CoefficientList[Series[-2 x (x^2 - 5 x + 1)/(x - 1)^4, {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 11 2014 *)
%t A121670 Table[n^3-3n,{n,0,60}] (* or *) LinearRecurrence[{4,-6,4,-1},{0,-2,2,18},60] (* _Harvey P. Dale_, Nov 30 2021 *)
%o A121670 (PARI) Vec(-2*x*(x^2-5*x+1)/(x-1)^4 + O(x^100)); \\ _Colin Barker_, Oct 16 2013
%Y A121670 Cf. A058794, A080663.
%K A121670 sign,easy
%O A121670 0,2
%A A121670 _Gary W. Adamson_, Aug 14 2006
%E A121670 Terms corrected, new name, and more terms from _Colin Barker_, Oct 16 2013