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.

A158127 a(n) = 100*n^2 + 2*n.

This page as a plain text file.
%I A158127 #27 Sep 08 2022 08:45:42
%S A158127 102,404,906,1608,2510,3612,4914,6416,8118,10020,12122,14424,16926,
%T A158127 19628,22530,25632,28934,32436,36138,40040,44142,48444,52946,57648,
%U A158127 62550,67652,72954,78456,84158,90060,96162,102464,108966,115668,122570
%N A158127 a(n) = 100*n^2 + 2*n.
%C A158127 The identity (100*n + 1)^2 - (100*n^2 + 2*n)*10^2 = 1 can be written as A158128(n)^2 - a(n)*10^2 = 1. - _Vincenzo Librandi_, Feb 11 2012
%H A158127 Vincenzo Librandi, <a href="/A158127/b158127.txt">Table of n, a(n) for n = 1..10000</a>
%H A158127 E. J. Barbeau, <a href="http://www.math.toronto.edu/barbeau/home.html">Polynomial Excursions</a>, Chapter 10: <a href="http://www.math.toronto.edu/barbeau/hxpol10.pdf">Diophantine equations</a> (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(10^2*t+2)).
%H A158127 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A158127 G.f.: x*(102 + 98*x)/(1-x)^3. - _Vincenzo Librandi_, Feb 11 2012
%F A158127 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Feb 11 2012
%t A158127 Table[100n^2 +2n,{n,45}]  (* _Harvey P. Dale_, Mar 15 2011 *)
%t A158127 LinearRecurrence[{3, -3, 1}, {102, 404, 906}, 50] (* _Vincenzo Librandi_, Feb 11 2012 *)
%o A158127 (Magma) I:=[102, 404, 906]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Feb 11 2012
%o A158127 (PARI) for(n=1, 50, print1(100*n^2 + 2*n", ")); \\ _Vincenzo Librandi_, Feb 11 2012
%Y A158127 Cf. A158128.
%K A158127 nonn,easy
%O A158127 1,1
%A A158127 _Vincenzo Librandi_, Mar 13 2009