A042012 Numerators of continued fraction convergents to sqrt(530).

23, 1059, 48737, 2242961, 103224943, 4750590339, 218630380537, 10061748095041, 463059042752423, 21310777714706499, 980758833919251377, 45136217138000269841, 2077246747181931664063, 95598486587506856816739, 4399607629772497345234057

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy
• less

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 (46,1).

Crossrefs

Cf. A042013, A040506.

Programs

Mathematica

Numerator[Convergents[Sqrt[530], 30]] (* Vincenzo Librandi, Nov 13 2013 *)
LinearRecurrence[{46,1},{23,1059},30] (* Harvey P. Dale, May 05 2016 *)

Formula

From Philippe Deléham, Nov 23 2008: (Start)

a(n) = 46*a(n-1) + a(n-2), n > 1; a(0)=23, a(1)=1059.

G.f.: (23+x)/(1-46*x-x^2). (End)

Extensions

Additional term from Colin Barker, Nov 29 2013