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.

A152016 a(n) = n^4 - n^3 - n^2 - n.

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%I A152016 #36 Apr 13 2024 01:51:16
%S A152016 0,-2,2,42,172,470,1038,2002,3512,5742,8890,13178,18852,26182,35462,
%T A152016 47010,61168,78302,98802,123082,151580,184758,223102,267122,317352,
%U A152016 374350,438698,511002,591892,682022,782070,892738,1014752,1148862
%N A152016 a(n) = n^4 - n^3 - n^2 - n.
%H A152016 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A152016 a(n) = n*(n*(n*(n - 1) - 1) - 1). - _Peter M. Chema_, Jan 19 2017
%F A152016 From _Chai Wah Wu_, Mar 16 2017: (Start)
%F A152016 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 4.
%F A152016 G.f.: 2*x*(-x^3 - 6*x^2 - 6*x + 1)/(x - 1)^5. (End)
%p A152016 A152016:=n->n^4-n^3-n^2-n: seq(A152016(n), n=0..50); # _Wesley Ivan Hurt_, Jan 28 2017
%t A152016 lst={};Do[AppendTo[lst,n^4-n^3-n^2-n],{n,0,5!}];lst
%t A152016 (* Second program: *)
%t A152016 Table[Total@ MapIndexed[(2 Boole[First@ #2 == 1] - 1) n^#1 &, Reverse@ Range@ 4], {n, 0, 33}] (* _Michael De Vlieger_, Jan 21 2017 *)
%o A152016 (Python)
%o A152016 def A152016(n): return n*(n*(n*(n-1)-1)-1) # _Chai Wah Wu_, Apr 13 2024
%K A152016 sign,easy
%O A152016 0,2
%A A152016 _Vladimir Joseph Stephan Orlovsky_, Nov 20 2008
%E A152016 Offset changed by _Bruno Berselli_, Jul 27 2012