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.

A167682 Expansion of (1 - 2*x + 5*x^2) / (1 - 3*x)^2.

This page as a plain text file.
%I A167682 #20 Jan 21 2017 16:40:57
%S A167682 1,4,20,84,324,1188,4212,14580,49572,166212,551124,1810836,5904900,
%T A167682 19131876,61647156,197696052,631351908,2008846980,6370914708,
%U A167682 20145865428,63536960196,199908972324,627621192180,1966546402164,6150687683364,19205208480708
%N A167682 Expansion of (1 - 2*x + 5*x^2) / (1 - 3*x)^2.
%H A167682 Harvey P. Dale, <a href="/A167682/b167682.txt">Table of n, a(n) for n = 0..1000</a>
%H A167682 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9).
%F A167682 a(0)=1, a(1)=4, a(2)=20, a(n) = 6*a(n-1) - 9*a(n-2) for n>2.
%F A167682 a(n) = 4*A081038(n-1) for n>0.
%F A167682 a(n) = Sum_{k=0..n} A167666(n,k)*3^k.
%F A167682 a(n) = 3^(n - 2)*(8*n + 4) for n>0. - _Colin Barker_, Jan 21 2017
%t A167682 CoefficientList[Series[(1-2x+5*x^2)/(1-3x)^2,{x,0,40}],x] (* or *) Join[{1},LinearRecurrence[{6,-9},{4,20},40]] (* _Harvey P. Dale_, Oct 20 2011 *)
%o A167682 (PARI) Vec((1-2*x+5*x^2) / (1-3*x)^2 + O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%K A167682 nonn,easy
%O A167682 0,2
%A A167682 _Philippe Deléham_, Nov 09 2009
%E A167682 Corrected and extended by _Harvey P. Dale_, Oct 20 2011
%E A167682 PARI code corrected by _Colin Barker_, Jan 21 2017