A041220 Numerators of continued fraction convergents to sqrt(122).

11, 243, 5357, 118097, 2603491, 57394899, 1265291269, 27893802817, 614928953243, 13556330774163, 298854205984829, 6588348862440401, 145242529179673651, 3201923990815260723, 70587570327115409557, 1556128471187354270977, 34305413936448909371051

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 (22,1).

Crossrefs

Cf. A041221.

Programs

Mathematica

Numerator/@Convergents[Sqrt[122],20] (* Harvey P. Dale, Jun 04 2011 *)
CoefficientList[Series[(11 + x)/(1 - 22 x - x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 31 2013 *)

Formula

From Philippe Deléham, Nov 21 2008: (Start)

a(n) = 22*a(n-1) + a(n-2) for n > 1, a(0)=11, a(1)=243.

G.f.: (11+x) / (1-22*x-x^2). (End)

Extensions

More terms from Colin Barker, Nov 05 2013