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.

A099271 Unsigned member r=-13 of the family of Chebyshev sequences S_r(n) defined in A092184.

This page as a plain text file.
%I A099271 #14 Jul 31 2015 13:23:13
%S A099271 0,1,13,196,2925,43681,652288,9740641,145457325,2172119236,
%T A099271 32436331213,484372848961,7233156403200,108012973199041,
%U A099271 1612961441582413,24086408650537156,359683168316474925,5371161116096586721
%N A099271 Unsigned member r=-13 of the family of Chebyshev sequences S_r(n) defined in A092184.
%C A099271 ((-1)^(n+1))*a(n) = S_{-13}(n), n>=0, defined in A092184.
%H A099271 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A099271 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (14, 14, -1).
%F A099271 a(n)= 2*(T(n, 15/2)-(-1)^n)/17, with twice Chebyshev's polynomials of the first kind evaluated at x=15/2: 2*T(n, 15/2)=A078365(n)=((15+sqrt(221))^n + (15-sqrt(221))^n)/2^n.
%F A099271 a(n)= 15*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.
%F A099271 a(n)= 14*a(n-1) + 14*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=13.
%F A099271 G.f.: x*(1-x)/((1+x)*(1-15*x+x^2)) = x*(1-x)/(1-14*x-14*x^2+x^3) (from the Stephan link, see A092184).
%t A099271 LinearRecurrence[{14,14,-1},{0,1,13},41] (* or *) CoefficientList[Series[ (x-x^2)/(1-14 x-14 x^2+x^3),{x,0,40}],x] (* _Harvey P. Dale_, Jun 18 2011 *)
%K A099271 nonn,easy
%O A099271 0,3
%A A099271 _Wolfdieter Lang_, Oct 18 2004