A153317 Denominators of continued fraction convergents to sqrt(6/5).

1, 10, 21, 220, 461, 4830, 10121, 106040, 222201, 2328050, 4878301, 51111060, 107100421, 1122115270, 2351330961, 24635424880, 51622180721, 540857232090, 1133336644901, 11874223681100, 24881784007101, 260692063752110, 546265911511321, 5723351178865320, 11992968269241961

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+10*x-x^2)/(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

Denominator[Convergents[Sqrt[6/5], 25]] (* Paolo Xausa, Jan 16 2025 *)

Prog

(PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; -1, 0, 22, 0]^n*[1; 10; 21; 220])[1, 1] \\ Charles R Greathouse IV, May 16 2026

Crossrefs

Cf. A000129, A001333, A142238, A142239, A153315, A153316, A153318.

Sequence in context: A177180 A275248 A041833 * A110418 A336759 A368635

Adjacent sequences: A153314 A153315 A153316 * A153318 A153319 A153320

Keyword

nonn,easy

Author

Charlie Marion, Jan 07 2009

Status

approved