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 A275794 #21 May 30 2018 12:38:22
%S A275794 2,15,88,513,2990,17427,101572,592005,3450458,20110743,117214000,
%T A275794 683173257,3981825542,23207779995,135264854428,788381346573,
%U A275794 4595023225010,26781758003487,156095524795912,909791390771985,5302652819835998,30906125528244003
%N A275794 One half of the y members of the positive proper solutions (x = x1(n), y = y1(n)) of the first class for the Pell equation x^2 - 2*y^2 = +7^2.
%C A275794 See A275793(n) for the x1(n) members and details as well as a reference.
%H A275794 Colin Barker, <a href="/A275794/b275794.txt">Table of n, a(n) for n = 0..1000</a>
%H A275794 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A275794 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-1).
%F A275794 a(n) = 15*S(n-1,6) - 2*S(n-2,6), with the Chebyshev polynomials S(n, 6) = A001109(n+1) for n >= -1, with S(-2, 6) = -1.
%F A275794 O.g.f: (2 + 3*x)/(1 - 6*x + x^2).
%F A275794 a(n) = 6*a(n-1) - a(n-2) for n >= 1, with a(-1) = -3 and a(0) = 2.
%F A275794 a(n) = (((3-2*sqrt(2))^n*(-9+4*sqrt(2))+(3+2*sqrt(2))^n*(9+4*sqrt(2)))) / (4*sqrt(2)). - _Colin Barker_, Sep 28 2016
%e A275794 See A275793.
%t A275794 CoefficientList[Series[(2 + 3*x)/(1 - 6*x + x^2), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Jan 29 2017 *)
%t A275794 LinearRecurrence[{6,-1},{2,15},30] (* _Harvey P. Dale_, May 30 2018 *)
%o A275794 (PARI) a(n) = round((((3-2*sqrt(2))^n*(-9+4*sqrt(2))+(3+2*sqrt(2))^n*(9+4*sqrt(2))))/(4*sqrt(2))) \\ _Colin Barker_, Sep 28 2016
%o A275794 (PARI) Vec((2+3*x)/(1-6*x+x^2) + O(x^30)) \\ _Colin Barker_, Oct 02 2016
%Y A275794 Cf. A001109, A275793.
%K A275794 nonn,easy
%O A275794 0,1
%A A275794 _Wolfdieter Lang_, Sep 27 2016