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A041040 Numerators of continued fraction convergents to sqrt(26). 3
5, 51, 515, 5201, 52525, 530451, 5357035, 54100801, 546365045, 5517751251, 55723877555, 562756526801, 5683289145565, 57395647982451, 579639768970075, 5853793337683201, 59117573145802085, 597029524795704051 (list; graph; refs; listen; history; text; internal format)
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

a(n)=10*a(n-1)+a(n-2), a(0)=5, a(1)=51. G.f.: (5+x)/(1-10*x-x^2). [From Philippe Deléham, Nov 20 2008]

a(n)=(5/2)*{[5+sqrt(26)]^n+[5-sqrt(26)]^n}+(1/2)*sqrt(26)*{[5+sqrt(26)]^n-[5-sqrt(26)]^n}, with n>=0 [From Paolo P. Lava, Nov 28 2008]

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: A106415 A212819 A088320 * A223002 A180511 A245926

Adjacent sequences:  A041037 A041038 A041039 * A041041 A041042 A041043

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 26 18:46 EDT 2017. Contains 284137 sequences.