A041364 Numerators of continued fraction convergents to sqrt(197).

14, 393, 11018, 308897, 8660134, 242792649, 6806854306, 190834713217, 5350178824382, 149995841795913, 4205233749109946, 117896540816874401, 3305308376621593174, 92666531086221483273, 2597968178790823124818, 72835775537229268978177, 2041999683221210354513774

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 (28,1).

Crossrefs

Cf. A041365.

Programs

Mathematica

Numerator[Convergents[Sqrt[197], 30]] (* Vincenzo Librandi, Nov 01 2013 *)

Formula

From Philippe Deléham, Nov 21 2008: (Start)

a(n) = 28*a(n-1) + a(n-2), n > 1; a(0)=14, a(1)=393.

G.f.: (14+x)/(1-28*x-x^2). (End)

Extensions

More terms from Colin Barker, Nov 07 2013