A042200 Numerators of continued fraction convergents to sqrt(626).

25, 1251, 62575, 3130001, 156562625, 7831261251, 391719625175, 19593812520001, 980082345625225, 49023711093781251, 2452165637034687775, 122657305562828170001, 6135317443778443187825, 306888529494484987561251

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 (50, 1).

Formula

a(n) = 50*a(n-1)+a(n-2) for n>1; a(0)=25, a(1)=1251. G.f.: (25+x)/(1-50*x-x^2). [Philippe Deléham, Nov 23 2008]

Mathematica

Numerator[Convergents[Sqrt[626], 30]] (* Harvey P. Dale, Jul 15 2012 *)
CoefficientList[Series[(25 + x)/(1 - 50 x - x^2), {x, 0, 20}], x] (* Vincenzo Librandi, Nov 19 2013 *)

Prog

(Magma) I:=[25, 1251]; [n le 2 select I[n] else 50*Self(n-1)+Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 19 2013

Crossrefs

Cf. A042201.

Sequence in context: A096330 A174751 A042203 * A104593 A046910 A278851

Adjacent sequences: A042197 A042198 A042199 * A042201 A042202 A042203

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved