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 A097316 #28 Sep 08 2022 08:45:14
%S A097316 1,66,4355,287364,18961669,1251182790,82559102471,5447649580296,
%T A097316 359462313197065,23719065021425994,1565098829100918539,
%U A097316 103272803655639197580,6814439942443086121741,449649763397588044837326
%N A097316 Chebyshev U(n,x) polynomial evaluated at x=33.
%C A097316 Used to form integer solutions of Pell equation a^2 - 17*b^2 =-1. See A078989 with A078988.
%H A097316 Indranil Ghosh, <a href="/A097316/b097316.txt">Table of n, a(n) for n = 0..548</a>
%H A097316 Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Nemeth/nemeth7.html">Ellipse Chains and Associated Sequences</a>, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
%H A097316 R. Flórez, R. A. Higuita, and A. Mukherjee, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Mukherjee/mukh2.html">Alternating Sums in the Hosoya Polynomial Triangle</a>, Article 14.9.5 Journal of Integer Sequences, Vol. 17 (2014).
%H A097316 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A097316 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (66,-1).
%F A097316 a(n) = 66*a(n-1) - a(n-2), n>=1, a(0)=1, a(-1):=0.
%F A097316 a(n) = S(n, 66) with S(n, x) := U(n, x/2), Chebyshev's polynomials of the second kind. See A049310.
%F A097316 G.f.: 1/(1-66*x+x^2).
%F A097316 a(n) = Sum_{k=0..floor(n/2)} (-1)^k*binomial(n-k, k)*66^(n-2*k).
%F A097316 a(n) = ((33+8*sqrt(17))^(n+1) - (33-8*sqrt(17))^(n+1))/(16*sqrt(17)).
%p A097316 seq( simplify(ChebyshevU(n, 33)), n=0..20); # _G. C. Greubel_, Dec 22 2019
%t A097316 LinearRecurrence[{66, -1},{1, 66},14] (* _Ray Chandler_, Aug 11 2015 *)
%t A097316 ChebyshevU[Range[21] -1, 33] (* _G. C. Greubel_, Dec 22 2019 *)
%o A097316 (PARI) vector( 21, n, polchebyshev(n-1, 2, 33) ) \\ _G. C. Greubel_, Dec 22 2019
%o A097316 (Magma) m:=33; I:=[1, 2*m]; [n le 2 select I[n] else 2*m*Self(n-1) -Self(n-2): n in [1..20]]; // _G. C. Greubel_, Dec 22 2019
%o A097316 (Sage) [chebyshev_U(n,33) for n in (0..20)] # _G. C. Greubel_, Dec 22 2019
%o A097316 (GAP) m:=33;; a:=[1,2*m];; for n in [3..20] do a[n]:=2*m*a[n-1]-a[n-2]; od; a; # _G. C. Greubel_, Dec 22 2019
%Y A097316 Chebyshev sequence U(n, m): A000027 (m=1), A001353 (m=2), A001109 (m=3), A001090 (m=4), A004189 (m=5), A004191 (m=6), A007655 (m=7), A077412 (m=8), A049660 (m=9), A075843 (m=10), A077421 (m=11), A077423 (m=12), A097309 (m=13), A097311 (m=14), A097313 (m=15), A029548 (m=16), A029547 (m=17), A144128 (m=18), A078987 (m=19), this sequence (m=33).
%K A097316 nonn,easy
%O A097316 0,2
%A A097316 _Wolfdieter Lang_, Aug 31 2004