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A042404 Numerators of continued fraction convergents to sqrt(730). 2
27, 1459, 78813, 4257361, 229976307, 12422977939, 671070785013, 36250245368641, 1958184320691627, 105778203562716499, 5713981176707382573, 308660761745761375441, 16673395115447821656387, 900671996995928130820339, 48652961232895566885954693 (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 (54, 1).

FORMULA

a(n)=54*a(n-1)+a(n-2), n>1; a(0)=27, a(1)=1459. G.f.: (27+x)/(1-54*x-x^2). - Philippe Deléham, Nov 23 2008

a(n)=(27/2)*{[27+sqrt(730)]^n+[27-sqrt(730)]^n}+(1/2)*sqrt(730)*{[27+sqrt(730)]^n-[27 -sqrt(730)]^n}, with n>=0. - Paolo P. Lava, Nov 28 2008

MATHEMATICA

Numerator[Convergents[Sqrt[730], 30]] (* Vincenzo Librandi, Nov 23 2013 *)

CROSSREFS

Cf. A042405, A040702.

Sequence in context: A167732 A017103 A042407 * A073224 A184689 A059118

Adjacent sequences:  A042401 A042402 A042403 * A042405 A042406 A042407

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

a(14) from Colin Barker, Dec 11 2013

STATUS

approved

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Last modified June 24 05:50 EDT 2017. Contains 288697 sequences.