A041144 Numerators of continued fraction convergents to sqrt(82).

9, 163, 2943, 53137, 959409, 17322499, 312764391, 5647081537, 101960232057, 1840931258563, 33238722886191, 600137943210001, 10835721700666209, 195643128555201763, 3532412035694297943, 63779059771052564737, 1151555487914640463209, 20791777842234580902499

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 (18,1).

Crossrefs

Cf. A010533, A041145.

Programs

Mathematica

CoefficientList[Series[(9 + x)/(1 - 18 x - x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 29 2013 *)

Formula

From Philippe Deléham, Nov 21 2008: (Start)

a(n) = 18*a(n-1) + a(n-2), n > 1; a(0)=9, a(1)=163.

G.f.: (9+x)/(1-18*x-x^2). (End)

Extensions

More terms from Colin Barker, Nov 05 2013