A041084 Numerators of continued fraction convergents to sqrt(50).

7, 99, 1393, 19601, 275807, 3880899, 54608393, 768398401, 10812186007, 152139002499, 2140758220993, 30122754096401, 423859315570607, 5964153172084899, 83922003724759193, 1180872205318713601, 16616132878186749607, 233806732499933208099, 3289910387877251662993

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 (14,1).

Crossrefs

Cf. A010503, A041085.

Programs

Mathematica

Numerator[Convergents[Sqrt[50],30]] (* or *) LinearRecurrence[{14,1},{7,99},30] (* Harvey P. Dale, Aug 18 2013 *)
CoefficientList[Series[(7 + x)/(1 - 14 x - x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 29 2013 *)

Formula

a(n) = 14*a(n-1)+a(n-2), n>1 ; a(0)=7, a(1)=99 . G.f.: (7+x)/(1-14*x-x^2). - Philippe Deléham, Nov 21 2008

Extensions

More terms from Colin Barker, Nov 04 2013