A041221 Denominators of continued fraction convergents to sqrt(122).

1, 22, 485, 10692, 235709, 5196290, 114554089, 2525386248, 55673051545, 1227332520238, 27056988496781, 596481079449420, 13149640736384021, 289888577279897882, 6390698340894137425, 140885252076950921232, 3105866244033814404529, 68469942620820867820870

Offset

0,2

Comments

From Michael A. Allen, May 04 2023: (Start)

Also called the 22-metallonacci sequence; the g.f. 1/(1-k*x-x^2) gives the k-metallonacci sequence.

a(n) is the number of tilings of an n-board (a board with dimensions n X 1) using unit squares and dominoes (with dimensions 2 X 1) if there are 22 kinds of squares available. (End)

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Michael A. Allen and Kenneth Edwards, Fence tiling derived identities involving the metallonacci numbers squared or cubed, Fib. Q. 60:5 (2022) 5-17.

Tanya Khovanova, Recursive Sequences

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

Formula

a(n) = F(n, 22), the n-th Fibonacci polynomial evaluated at x=22. - T. D. Noe, Jan 19 2006

From Philippe Deléham, Nov 21 2008: (Start)

a(n) = 22*a(n-1) + a(n-2) for n > 1; a(0)=1, a(1)=22.

G.f.: 1/(1 - 22*x - x^2). (End)

Mathematica

Denominator[Convergents[Sqrt[122], 30]]  (* Vincenzo Librandi, Dec 13 2013 *)

Crossrefs

Cf. A041220, A040110.

Row n=22 of A073133, A172236 and A352361 and column k=22 of A157103.

Sequence in context: A171296 A009966 A285876 * A041926 A230350 A180780

Adjacent sequences: A041218 A041219 A041220 * A041222 A041223 A041224

Keyword

nonn,frac,easy,less

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved