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.

A041040 Numerators of continued fraction convergents to sqrt(26).

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%I A041040 #34 Dec 26 2023 07:41:43
%S A041040 5,51,515,5201,52525,530451,5357035,54100801,546365045,5517751251,
%T A041040 55723877555,562756526801,5683289145565,57395647982451,
%U A041040 579639768970075,5853793337683201,59117573145802085,597029524795704051
%N A041040 Numerators of continued fraction convergents to sqrt(26).
%H A041040 Vincenzo Librandi, <a href="/A041040/b041040.txt">Table of n, a(n) for n = 0..200</a>
%H A041040 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A041040 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,1).
%F A041040 From _Philippe Deléham_, Nov 20 2008: (Start)
%F A041040 a(n) = 10*a(n-1) + a(n-2), a(0)=5, a(1)=51.
%F A041040 G.f.: (5+x)/(1-10*x-x^2). (End)
%t A041040 Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[26],n]]],{n,1,50}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 18 2011*)
%t A041040 CoefficientList[Series[(5 + x)/(1 - 10 x - x^2), {x, 0, 30}], x]  (* Vincenzo Librandi_, Oct 28 2013 *)
%Y A041040 Cf. A010481, A041041.
%K A041040 nonn,cofr,frac,easy
%O A041040 0,1
%A A041040 _N. J. A. Sloane_