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 A041062 #29 Aug 14 2025 06:05:41
%S A041062 6,37,450,2737,33294,202501,2463306,14982337,182251350,1108490437,
%T A041062 13484136594,82013310001,997643856606,6067876449637,73812161252250,
%U A041062 448940843963137,5461102288809894,33215554576822501
%N A041062 Numerators of continued fraction convergents to sqrt(38).
%H A041062 Vincenzo Librandi, <a href="/A041062/b041062.txt">Table of n, a(n) for n = 0..100</a>
%H A041062 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,74,0,-1).
%F A041062 G.f.: -(x^3-6*x^2-37*x-6) / (x^4-74*x^2+1). - _Colin Barker_, Nov 04 2013
%F A041062 From _Gerry Martens_, Jul 11 2015: (Start)
%F A041062 Interspersion of 2 sequences [a0(n),a1(n)] for n>0:
%F A041062 a0(n) = (-3+sqrt(19/2))*(37+6*sqrt(38))^n-(6+sqrt(38))/(2*(37+6*sqrt(38))^n).
%F A041062 a1(n) = (1/(37+6*sqrt(38))^n+(37+6*sqrt(38))^n)/2. (End)
%t A041062 Numerator[Convergents[Sqrt[38], 30]] (* _Vincenzo Librandi_, Oct 29 2013 *)
%t A041062 a0[n_] := (-3+Sqrt[19/2])*(37+6*Sqrt[38])^n-(6+Sqrt[38])/(2*(37+6*Sqrt[38])^n) // Simplify
%t A041062 a1[n_] := (1/(37+6*Sqrt[38])^n+(37+6*Sqrt[38])^n)/2 // FullSimplify
%t A041062 Flatten[MapIndexed[{a0[#], a1[#]}&, Range[20]]] (* _Gerry Martens_, Jul 11 2015 *)
%t A041062 LinearRecurrence[{0,74,0,-1},{6,37,450,2737},20] (* _Harvey P. Dale_, Oct 17 2020 *)
%Y A041062 Cf. A041063, A010492.
%K A041062 nonn,cofr,frac,easy
%O A041062 0,1
%A A041062 _N. J. A. Sloane_