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.

A098310 Unsigned member r=-11 of the family of Chebyshev sequences S_r(n) defined in A092184.

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%I A098310 #8 Mar 20 2023 11:19:29
%S A098310 0,1,11,144,1859,24025,310464,4012009,51845651,669981456,8657913275,
%T A098310 111882891121,1445819671296,18683772835729,241443227193179,
%U A098310 3120078180675600,40319573121589619,521034372399989449
%N A098310 Unsigned member r=-11 of the family of Chebyshev sequences S_r(n) defined in A092184.
%C A098310 ((-1)^(n+1))*a(n) = S_{-11}(n), n>=0, defined in A092184.
%H A098310 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A098310 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,12,-1).
%F A098310 a(n)= 2*(T(n, 13/2)-(-1)^n)/15, with twice Chebyshev's polynomials of the first kind evaluated at x=13/2: 2*T(n, 13/2)=A078363(n)=((13+sqrt(165))^n + (13-sqrt(165))^n)/2^n.
%F A098310 a(n)= 13*a(n-1)-a(n-2)+2*(-1)^(n+1), n>=2, a(0)=0, a(1)=1.
%F A098310 a(n)= 12*a(n-1) + 12*a(n-2) - a(n-3), n>=3, a(0)=0, a(1)=1, a(2)=11.
%F A098310 G.f.: x*(1-x)/((1+x)*(1-13*x+x^2)) = x*(1-x)/(1-12*x-12*x^2+x^3) (from the Stephan link, see A092184).
%t A098310 LinearRecurrence[{12,12,-1},{0,1,11},30] (* _Harvey P. Dale_, Mar 20 2023 *)
%K A098310 nonn,easy
%O A098310 0,3
%A A098310 _Wolfdieter Lang_, Oct 18 2004