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A041684 Numerators of continued fraction convergents to sqrt(362). 2
19, 723, 27493, 1045457, 39754859, 1511730099, 57485498621, 2185960677697, 83123991251107, 3160897628219763, 120197233863602101, 4570655784445099601, 173805117042777386939, 6609165103409985803283, 251322079046622237911693, 9556848168875055026447617 (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 (38,1).

FORMULA

From Philippe Deléham, Nov 23 2008: (Start)

a(n) = 38*a(n-1) + a(n-2), n > 1; a(0)=19, a(1)=723.

G.f.: (19+x)/(1-38*x-x^2). (End)

a(n) = (1/2)*sqrt(362)*((19+sqrt(362))^n - (19-sqrt(362))^n) + (19/2)*((19-sqrt(362))^n + (19+sqrt(362))^n), with n >= 0. - Paolo P. Lava, Nov 28 2008

MATHEMATICA

Numerator[Convergents[Sqrt[362], 30]] (* Vincenzo Librandi, Nov 06 2013 *)

LinearRecurrence[{38, 1}, {19, 723}, 20] (* Harvey P. Dale, Feb 10 2019 *)

CROSSREFS

Cf. A041685.

Sequence in context: A078986 A180990 A041687 * A157165 A201708 A280625

Adjacent sequences:  A041681 A041682 A041683 * A041685 A041686 A041687

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

Additional term from Colin Barker, Nov 09 2013

STATUS

approved

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Last modified January 16 21:00 EST 2021. Contains 340213 sequences. (Running on oeis4.)