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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

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). [From Philippe Deléham, Nov 23 2008]

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 [From Paolo P. Lava, Nov 28 2008]

MATHEMATICA

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

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 June 26 02:24 EDT 2017. Contains 288749 sequences.