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 A295337 #9 Nov 29 2017 04:06:54
%S A295337 1,1,7,8,23,31,209,240,689,929,6263,7192,20647,27839,187681,215520,
%T A295337 618721,834241,5624167,6458408,18540983,24999391,168537329,193536720,
%U A295337 555610769,749147489,5050495703,5799643192,16649782087
%N A295337 Denominators of the convergents to sqrt(14)/2 = A294969.
%C A295337 The corresponding numerators are given in A295336.
%C A295337 The recurrence is a(n) = b(n)*a(n-1) + a(n-2), n >= 0, with a(0) = 1, a(-1) = 0, (a(-2) = 1) with b(n) from the continued fraction b = {1,repeat(1, 6, 1, 2)}.
%C A295337 The g.f.s G_j(x) = Sum_{n>=0} a(4*n+j)*x^k, for j=1..4 satisfy (arguments are omitted): G_0 = 2*x*G_3 + 1 + x*G_2, G_1= G_0 + x*G_3, G_2 = 6*G_1 + G_0, G_3 = G_2 + G_1. After solving for the G_j(x), one finds for G(x) = Sum_{n>=0} a(n)*x^n = Sum_{j=1..4} x^j*G_j(x^4) the o.g.f. given in the formula section.
%H A295337 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,30,0,0,0,-1).
%F A295337 G.f.: (1 + x - x^2)*(1 + 8*x^2 + x^4)/(1- 30*x^4 + x^8).
%F A295337 a(n) = 30*a(n-4) - a(n-8), n >= 8, with inputs a(0)..a(7).
%t A295337 Denominator[Convergents[Sqrt[14]/2, 50]] (* _Vaclav Kotesovec_, Nov 29 2017 *)
%Y A295337 Cf. A294969, A295336.
%K A295337 nonn,frac,cofr,easy
%O A295337 0,3
%A A295337 _Wolfdieter Lang_, Nov 27 2017