A153318 Numerators of continued fraction convergents to sqrt(6/5).

1, 11, 23, 241, 505, 5291, 11087, 116161, 243409, 2550251, 5343911, 55989361, 117322633, 1229215691, 2575754015, 26986755841, 56549265697, 592479412811, 1241508091319, 13007560326001, 27256628743321, 285573847759211, 598404324261743, 6269617090376641, 13137638505015025

Offset

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,22,0,-1).

Formula

For n>0, a(2*n) = 2*a(2*n-1) + a(2*n-2) and a(2*n+1) = 10*a(2*n) + a(2*n-1).

G.f.: (1+11*x+x^2-x^3)/(1-22*x^2+x^4). - Colin Barker, Jan 01 2012

Example

The initial convergents are 1, 11/10, 23/21, 241/220, 505/461, 5291/4830, 11087/10121, 116161/106040, 243409/222201, 2550251/2328050, 55989361/4878301, ...

Mathematica

Numerator[Convergents[Sqrt[6/5], 20]] (* Harvey P. Dale, Jul 30 2018 *)
(* Alternative: *)
LinearRecurrence[{0, 22, 0, -1}, {1, 11, 23, 241}, 20] (* Harvey P. Dale, Jul 30 2018 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -1, 0, 22, 0]^n*[1; 11; 23; 241])[1, 1] \\ Charles R Greathouse IV, May 13 2026

Crossrefs

Cf. A000129, A001333, A142238, A142239, A153315, A153316, A153317.

Sequence in context: A181147 A059327 A042005 * A005485 A041240 A193855

Adjacent sequences: A153315 A153316 A153317 * A153319 A153320 A153321

Keyword

nonn,easy,changed

Author

Charlie Marion, Jan 07 2009

Status

approved