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A041312 Numerators of continued fraction convergents to sqrt(170). 2
13, 339, 8827, 229841, 5984693, 155831859, 4057613027, 105653770561, 2751055647613, 71633100608499, 1865211671468587, 48567136558791761, 1264610762200054373, 32928446953760205459, 857404231559965396307, 22325438467512860509441, 581318804386894338641773 (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 (26,1).

FORMULA

a(n) = 26*a(n-1)+a(n-2) for n>1, a(0)=13, a(1)=339. G.f.: (13+x)/(1-26*x-x^2). [Philippe Deléham, Nov 21 2008]

a(n) = (1/2)*sqrt(170)*((13+sqrt(170))^n-(13-sqrt(170)]^n)+13/2*((13 +sqrt(170))^n+(13-sqrt(170))^n). [Paolo P. Lava, Nov 28 2008]

MATHEMATICA

Numerator[Convergents[Sqrt[170], 30]] (* Vincenzo Librandi, Nov 01 2013 *)

CROSSREFS

Cf. A041313.

Sequence in context: A204195 A238652 A041315 * A096717 A125119 A160396

Adjacent sequences:  A041309 A041310 A041311 * A041313 A041314 A041315

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Corrected second formula from Paolo P. Lava, Dec 01 2008

More terms from Colin Barker, Nov 06 2013

STATUS

approved

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Last modified March 23 20:15 EDT 2017. Contains 283957 sequences.