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.
%I A097827 #13 Jul 02 2023 18:48:22 %S A097827 1,13,156,1860,22165,264121,3147288,37503336,446892745,5325209605, %T A097827 63455622516,756142260588,9010251504541,107366875793905, %U A097827 1279392258022320,15245340220473936,181664690387664913 %N A097827 Partial sums of Chebyshev sequence S(n,12)= U(n,6)=A004191(n). %H A097827 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a> %H A097827 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (13, -13, 1). %F A097827 a(n) = sum(S(k, 12), k=0..n) with S(k, 12) = U(k, 6) = A004191(k) Chebyshev's polynomials of the second kind. %F A097827 G.f.: 1/((1-x)*(1-12*x+x^2)) = 1/(1-13*x+13*x^2-x^3). %F A097827 a(n) = 13*a(n-1)-13*a(n-2)+a(n-3) with n>=2, a(-1)=0, a(0)=1, a(1)=13. %F A097827 a(n) = 12*a(n-1)-a(n-2)+1 with n>=1, a(-1)=0, a(0)=1. %F A097827 a(n) = (S(n+1, 12) - S(n, 12) -1)/10. %Y A097827 Cf. A212336 for more sequences with g.f. of the type 1/(1-k*x+k*x^2-x^3). %K A097827 nonn,easy %O A097827 0,2 %A A097827 _Wolfdieter Lang_, Aug 31 2004