cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A132998 a(n) = n^4 - n^3 - n^2.

This page as a plain text file.
%I A132998 #25 Sep 08 2022 08:45:31
%S A132998 0,-1,4,45,176,475,1044,2009,3520,5751,8900,13189,18864,26195,35476,
%T A132998 47025,61184,78319,98820,123101,151600,184779,223124,267145,317376,
%U A132998 374375,438724,511029,591920,682051,782100,892769
%N A132998 a(n) = n^4 - n^3 - n^2.
%H A132998 Vincenzo Librandi, <a href="/A132998/b132998.txt">Table of n, a(n) for n = 0..1000</a>
%H A132998 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A132998 a(n) = n^4 - n^3 - n^2.
%F A132998 G.f.: x*(-1+9*x+15*x^2+x^3)/(1-x)^5. - _R. J. Mathar_, Nov 14 2007
%e A132998 a(7)=2009 because 7^4=2401, 7^3=343, 7^2=49 and we can write 2401-343-49=2009.
%p A132998 A132998:=n->n^4-n^3-n^2; seq(A132998(n), n=0..50); # _Wesley Ivan Hurt_, May 21 2014
%t A132998 f[n_]:=n^4-n^3-n^2; Table[f[n],{n,5!}] (* _Vladimir Joseph Stephan Orlovsky_, Dec 04 2009 *)
%t A132998 CoefficientList[Series[- x (-1 + 9 x + 15 x^2 + x^3)/(-1 + x)^5, {x, 0, 50}], x] (* _Vincenzo Librandi_, May 21 2014 *)
%t A132998 LinearRecurrence[{5,-10,10,-5,1}, {0, -1, 4, 45, 176}, 50] (* _G. C. Greubel_, Sep 28 2017 *)
%o A132998 (Magma)[n^4-n^3-n^2: n in [0..50]]; // _Vincenzo Librandi_, Dec 15 2010
%o A132998 (PARI) x='x+O('x^50); Vec(x*(-1+9*x+15*x^2+x^3)/(1-x)^5) \\ _G. C. Greubel_, Sep 28 2017
%Y A132998 Cf. A000290, A000578, A000583, A011379, A045991.
%K A132998 sign,easy
%O A132998 0,3
%A A132998 _Omar E. Pol_, Nov 01 2007