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

0,1

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).

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)

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 *)

Crossrefs

Cf. A010481, A041041.

Sequence in context: A195211 A106415 A212819 * A088320 A223002 A370172

Adjacent sequences: A041037 A041038 A041039 * A041041 A041042 A041043

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved