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 A041029 #27 Jul 09 2025 00:10:39
%S A041029 1,2,3,11,14,39,326,691,1017,3742,4759,13260,110839,234938,345777,
%T A041029 1272269,1618046,4508361,37684934,79878229,117563163,432567718,
%U A041029 550130881,1532829480,12812766721,27158362922
%N A041029 Denominators of continued fraction convergents to sqrt(19).
%H A041029 Vincenzo Librandi, <a href="/A041029/b041029.txt">Table of n, a(n) for n = 0..1000</a>
%H A041029 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,340,0,0,0,0,0,-1).
%F A041029 a(n) = 340*a(n-6)-a(n-12). G.f.: -(x^10- 2*x^9+ 3*x^8 -11*x^7 +14*x^6 -39*x^5 -14*x^4 -11*x^3 -3*x^2 -2*x -1)/(x^12-340*x^6+1). [_Colin Barker_, Jul 16 2012]
%t A041029 Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[19],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 17 2011 *)
%t A041029 CoefficientList[Series[- (x^10 - 2 x^9 + 3 x^8 - 11 x^7 + 14 x^6 - 39 x^5 - 14 x^4 - 11 x^3 - 3 x^2 - 2 x - 1)/(x^12 - 340 x^6 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 22 2013 *)
%Y A041029 Cf. A010124, A010475, A041028.
%K A041029 nonn,cofr,frac,easy
%O A041029 0,2
%A A041029 _N. J. A. Sloane_