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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 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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