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

5, 51, 515, 5201, 52525, 530451, 5357035, 54100801, 546365045, 5517751251, 55723877555, 562756526801, 5683289145565, 57395647982451, 579639768970075, 5853793337683201, 59117573145802085, 597029524795704051

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (10,1).

Crossrefs

Cf. A010481, A041041.

Programs

Mathematica

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[26],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011*)
CoefficientList[Series[(5 + x)/(1 - 10 x - x^2), {x, 0, 30}], x]  (* Vincenzo Librandi_, Oct 28 2013 *)

Formula

From Philippe Deléham, Nov 20 2008: (Start)

a(n) = 10*a(n-1) + a(n-2), a(0)=5, a(1)=51.

G.f.: (5+x)/(1-10*x-x^2). (End)