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

0,1

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).

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

a(n) = (5/2)*sqrt(2)*{[7+5*sqrt(2)]^n-[7-5*sqrt(2)]^n}+(7/2)*{[7+5*sqrt(2)]^n +[7-5*sqrt(2)]^n}, with n>=0. - Paolo P. Lava, Nov 28 2008

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 *)

Crossrefs

Cf. A010503, A041085.

Sequence in context: A092818 A238472 A041087 * A115066 A340887 A272957

Adjacent sequences: A041081 A041082 A041083 * A041085 A041086 A041087

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 04 2013

Status

approved