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A041084 Numerators of continued fraction convergents to sqrt(50). 2
7, 99, 1393, 19601, 275807, 3880899, 54608393, 768398401, 10812186007, 152139002499, 2140758220993, 30122754096401, 423859315570607, 5964153172084899, 83922003724759193, 1180872205318713601, 16616132878186749607, 233806732499933208099, 3289910387877251662993 (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 (14,1).

FORMULA

a(n) = 14*a(n-1)+a(n-2), n>1 ; a(0)=7, a(1)=99 . G.f.: (7+x)/(1-14*x-x^2). - Philippe Deléham, Nov 21 2008

a(n) = (5/2)*sqrt(2)*{[7+5*sqrt(2)]^n-[7-5*sqrt(2)]^n}+(7/2)*{[7+5*sqrt(2)]^n +[7-5*sqrt(2)]^n}, with n>=0. - Paolo P. Lava, Nov 28 2008

MATHEMATICA

Numerator[Convergents[Sqrt[50], 30]] (* or *) LinearRecurrence[{14, 1}, {7, 99}, 30] (* Harvey P. Dale, Aug 18 2013 *)

CoefficientList[Series[(7 + x)/(1 - 14 x - x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 29 2013 *)

CROSSREFS

Cf. A010503, A041085.

Sequence in context: A092818 A238472 A041087 * A115066 A272957 A123616

Adjacent sequences:  A041081 A041082 A041083 * A041085 A041086 A041087

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 04 2013

STATUS

approved

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Last modified April 27 00:46 EDT 2017. Contains 285506 sequences.