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 A097829 #15 Jul 02 2023 18:50:10 %S A097829 1,16,240,3585,53536,799456,11938305,178275120,2662188496,39754552321, %T A097829 593656096320,8865086892480,132382647290881,1976874622470736, %U A097829 29520736689770160,440834175724081665,6582991899171454816 %N A097829 Partial sums of Chebyshev sequence S(n,15)= U(n,15/2)=A078364(n). %H A097829 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a> %H A097829 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (16, -16, 1). %F A097829 a(n) = sum(S(k, 15), k=0..n) with S(k, 15) = U(k, 15/2) = A078364(k) Chebyshev's polynomials of the second kind. %F A097829 G.f.: 1/((1-x)*(1-15*x+x^2)) = 1/(1-16*x+16*x^2-x^3). %F A097829 a(n) = 16*a(n-1)-16*a(n-2)+a(n-3) with n>=2, a(-1)=0, a(0)=1, a(1)=16. %F A097829 a(n) = 15*a(n-1)-a(n-2)+1 with n>=1, a(-1)=0, a(0)=1. %F A097829 a(n) = (S(n+1, 15) - S(n, 15) -1)/13. %Y A097829 Cf. A212336 for more sequences with g.f. of the type 1/(1-k*x+k*x^2-x^3). %K A097829 nonn,easy %O A097829 0,2 %A A097829 _Wolfdieter Lang_, Aug 31 2004