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.

A099273 Unsigned member r=-15 of the family of Chebyshev sequences S_r(n) defined in A092184.

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%I A099273 #11 Jul 31 2015 13:23:35
%S A099273 0,1,15,256,4335,73441,1244160,21077281,357069615,6049106176,
%T A099273 102477735375,1736072395201,29410752983040,498246728316481,
%U A099273 8440783628397135,142995074954434816,2422475490596994735
%N A099273 Unsigned member r=-15 of the family of Chebyshev sequences S_r(n) defined in A092184.
%C A099273 ((-1)^(n+1))*a(n) = S_{-15}(n), n>=0, defined in A092184.
%H A099273 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A099273 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (16, 16, -1).
%F A099273 a(n)= 2*(T(n, 17/2)-(-1)^n)/19, with twice Chebyshev's polynomials of the first kind evaluated at x=17/2: 2*T(n, 17/2)=A078367(n)= ((17+sqrt(285))^n +(17-sqrt(285))^n)/2^n.
%F A099273 a(n)= 17*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.
%F A099273 a(n)= 16*a(n-1) + 16*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=15.
%F A099273 G.f.: x*(1-x)/((1+x)*(1-17*x+x^2)) = x*(1-x)/(1-16*x-16*x^2+x^3) (from the Stephan link, see A092184).
%t A099273 LinearRecurrence[{16,16,-1},{0,1,15},30] (* _Harvey P. Dale_, Oct 09 2011 *)
%K A099273 nonn,easy
%O A099273 0,3
%A A099273 _Wolfdieter Lang_, Oct 18 2004