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 A041034 #24 Jul 09 2025 00:10:57
%S A041034 4,5,14,61,136,197,1712,1909,5530,24029,53588,77617,674524,752141,
%T A041034 2178806,9467365,21113536,30580901,265760744,296341645,858444034,
%U A041034 3730117781,8318679596,12048797377,104709058612
%N A041034 Numerators of continued fraction convergents to sqrt(22).
%H A041034 Vincenzo Librandi, <a href="/A041034/b041034.txt">Table of n, a(n) for n = 0..1000</a>
%H A041034 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,394,0,0,0,0,0,-1).
%F A041034 a(n) = 394*a(n-6)-a(n-12). G.f.: -(x^11 -4*x^10 +5*x^9 -14*x^8 +61*x^7 -136*x^6 -197*x^5 -136*x^4 -61*x^3 -14*x^2 -5*x -4)/(x^12-394*x^6+1). [_Colin Barker_, Jul 16 2012]
%t A041034 Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[22],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 17 2011 *)
%t A041034 CoefficientList[Series[- (x^11 - 4 x^10 + 5 x^9 - 14 x^8 + 61 x^7 - 136 x^6 - 197 x^5 - 136 x^4 - 61 x^3 - 14 x^2 - 5 x - 4)/(x^12 - 394 x^6 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 22 2013 *)
%t A041034 LinearRecurrence[{0,0,0,0,0,394,0,0,0,0,0,-1},{4,5,14,61,136,197,1712,1909,5530,24029,53588,77617},30] (* _Harvey P. Dale_, Mar 14 2017 *)
%Y A041034 Cf. A010478, A041035.
%K A041034 nonn,cofr,frac,easy
%O A041034 0,1
%A A041034 _N. J. A. Sloane_