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 A099397 #30 Sep 08 2022 08:45:15
%S A099397 1,51,5201,530451,54100801,5517751251,562756526801,57395647982451,
%T A099397 5853793337683201,597029524795704051,60891157735824130001,
%U A099397 6210301059529265556051,633389816914249262587201
%N A099397 Chebyshev polynomial of the first kind, T(n,x), evaluated at x=51.
%C A099397 Used in A099374.
%C A099397 Numbers n such that 26*(n^2-1) is square. - _Vincenzo Librandi_, Nov 17 2010
%H A099397 Indranil Ghosh, <a href="/A099397/b099397.txt">Table of n, a(n) for n = 0..497</a>
%H A099397 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A099397 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A099397 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (102, -1).
%F A099397 a(n) = 102*a(n-1) - a(n-2), n>=1; a(-1):= 51, a(0)=1.
%F A099397 a(n) = T(n, 51) = (S(n, 102)-S(n-2, 102))/2 = S(n, 102)-51*S(n-1, 102) with T(n, x), resp. S(n, x), Chebyshev polynomials of the first, resp. second, kind. See A053120 and A049310. S(n, 102)=(n).
%F A099397 a(n) = (ap^n + am^n)/2 with ap := 51+10*sqrt(26) and am := 51-10*sqrt(26).
%F A099397 a(n) = Sum_{k=0..floor(n/2)} (((-1)^k)*(n/(2*(n-k)))*binomial(n-k, k)*(2*51)^(n-2*k)), n >= 1. a(0):=1.
%F A099397 G.f.: (1 - 51*x)/(1 - 102*x + x^2).
%t A099397 LinearRecurrence[{102, -1},{1, 51},13] (* _Ray Chandler_, Aug 11 2015 *)
%o A099397 (Magma) [n: n in [1..1000] |IsSquare(26*(n^2-1))] // _Vincenzo Librandi_, Nov 17 2010
%o A099397 (PARI) a(n) = polchebyshev(n, 1, 51); \\ _Michel Marcus_, Jan 20 2018
%Y A099397 Row 5 of array A188645.
%K A099397 nonn,easy
%O A099397 0,2
%A A099397 _Wolfdieter Lang_, Oct 18 2004