A041312 Numerators of continued fraction convergents to sqrt(170).

13, 339, 8827, 229841, 5984693, 155831859, 4057613027, 105653770561, 2751055647613, 71633100608499, 1865211671468587, 48567136558791761, 1264610762200054373, 32928446953760205459, 857404231559965396307, 22325438467512860509441, 581318804386894338641773

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

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).

Crossrefs

Cf. A041313.

Programs

Mathematica

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

Formula

From Philippe Deléham, Nov 21 2008: (Start)

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). (End)

Extensions

More terms from Colin Barker, Nov 06 2013