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 A041031 #41 Aug 11 2024 05:00:26
%S A041031 1,2,17,36,305,646,5473,11592,98209,208010,1762289,3732588,31622993,
%T A041031 66978574,567451585,1201881744,10182505537,21566892818,182717648081,
%U A041031 387002188980,3278735159921,6944472508822
%N A041031 Denominators of continued fraction convergents to sqrt(20).
%H A041031 Vincenzo Librandi, <a href="/A041031/b041031.txt">Table of n, a(n) for n = 0..200</a>
%H A041031 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,18,0,-1).
%F A041031 G.f.: (1+2*x-x^2)/(1-18*x^2+x^4). - _Colin Barker_, Jan 01 2012
%F A041031 From _Gerry Martens_, Jul 11 2015: (Start)
%F A041031 Interspersion of 2 sequences [a0(n),a1(n)] for n>0:
%F A041031 a0(n) = ((5+2*sqrt(5))/(9+4*sqrt(5))^n+(5-2*sqrt(5))*(9+4*sqrt(5))^n)/10.
%F A041031 a1(n) = (-1/(9+4*sqrt(5))^n+(9+4*sqrt(5))^n)/(4*sqrt(5)). (End)
%t A041031 Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[20],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 17 2011 *)
%t A041031 a0[n_] := ((5+2*Sqrt[5])/(9+4*Sqrt[5])^n+(5-2*Sqrt[5])*(9+4*Sqrt[5])^n)/10 //Simplify
%t A041031 a1[n_] := (-1/(9+4*Sqrt[5])^n+(9+4*Sqrt[5])^n)/(4*Sqrt[5]) //Simplify
%t A041031 Flatten[MapIndexed[{a0[#], a1[#]} &,Range[20]]] (* _Gerry Martens_, Jul 11 2015 *)
%Y A041031 Cf. A010476, A040015, A041030 (numerators).
%K A041031 nonn,cofr,frac,easy
%O A041031 0,2
%A A041031 _N. J. A. Sloane_