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A042200 Numerators of continued fraction convergents to sqrt(626). 2
25, 1251, 62575, 3130001, 156562625, 7831261251, 391719625175, 19593812520001, 980082345625225, 49023711093781251, 2452165637034687775, 122657305562828170001, 6135317443778443187825, 306888529494484987561251 (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 (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]

a(n) = (1/2)*sqrt(626)*((25+sqrt(626))^n-(25-sqrt(626))^n)+(25/2)*((25+sqrt(626))^n+(25-sqrt(626))^n). [Paolo P. Lava, Nov 28 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

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Last modified August 21 23:43 EDT 2017. Contains 290940 sequences.