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 A097831 #14 Nov 20 2022 14:43:23
%S A097831 1,18,306,5185,87840,1488096,25209793,427078386,7235122770,
%T A097831 122570008705,2076455025216,35177165419968,595935357114241,
%U A097831 10095723905522130,171031371036761970,2897437583719431361,49085407552193571168
%N A097831 Partial sums of Chebyshev sequence S(n,17)= U(n,17/2)=A078366(n).
%H A097831 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A097831 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (18,-18,1).
%F A097831 a(n) = sum(S(k, 17), k=0..n) with S(k, 17) = U(k, 17/2) = A078366(k) Chebyshev's polynomials of the second kind.
%F A097831 G.f.: 1/((1-x)*(1-17*x+x^2)) = 1/(1-18*x+18*x^2-x^3).
%F A097831 a(n) = 18*a(n-1)-18*a(n-2)+a(n-3), n>=2, a(-1)=0, a(0)=1, a(1)=18.
%F A097831 a(n) = 17*a(n-1)-a(n-2)+1, n>=1, a(-1)=0, a(0)=1.
%F A097831 a(n) = (S(n+1, 17) - S(n, 17) -1)/15.
%t A097831 LinearRecurrence[{18,-18,1},{1,18,306},20] (* _Harvey P. Dale_, Nov 20 2022 *)
%Y A097831 Cf. A212336 for more sequences with g.f. of the type 1/(1-k*x+k*x^2-x^3).
%K A097831 nonn,easy
%O A097831 0,2
%A A097831 _Wolfdieter Lang_, Aug 31 2004