cp's OEIS Frontend

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.

A041020 Numerators of continued fraction convergents to sqrt(14).

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%I A041020 #29 Aug 04 2025 15:16:43
%S A041020 3,4,11,15,101,116,333,449,3027,3476,9979,13455,90709,104164,299037,
%T A041020 403201,2718243,3121444,8961131,12082575,81456581,93539156,268534893,
%U A041020 362074049,2440979187,2803053236,8047085659
%N A041020 Numerators of continued fraction convergents to sqrt(14).
%H A041020 Vincenzo Librandi, <a href="/A041020/b041020.txt">Table of n, a(n) for n = 0..200</a>
%H A041020 <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 A041020 G.f.: (3+4*x+11*x^2+15*x^3+11*x^4-4*x^5+3*x^6-x^7)/(1-30*x^4+x^8). - _Colin Barker_, Jan 03 2012
%F A041020 a(n) = 30*a(n-4) - a(n-8). - _Wesley Ivan Hurt_, Aug 04 2025
%t A041020 Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[14],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 17 2011*)
%Y A041020 Cf. A010471, A041021.
%K A041020 nonn,cofr,frac,easy
%O A041020 0,1
%A A041020 _N. J. A. Sloane_