A041421 Denominators of continued fraction convergents to sqrt(226).

1, 30, 901, 27060, 812701, 24408090, 733055401, 22016070120, 661215159001, 19858470840150, 596415340363501, 17912318681745180, 537965975792718901, 16156891592463312210, 485244713749692085201, 14573498304083225868240

Offset

0,2

Comments

From Michael A. Allen, May 16 2023: (Start)

Also called the 30-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 30 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 (30,1).

Formula

a(n) = F(n, 30), the n-th Fibonacci polynomial evaluated at x=30. - T. D. Noe, Jan 19 2006

From Philippe Deléham, Nov 22 2008: (Start)

a(n) = 30*a(n-1) + a(n-2) for n > 1; a(0)=1, a(1)=30.

G.f.: 1/(1-30*x-x^2). (End)

Mathematica

Denominator[Convergents[Sqrt[226], 30]] (* Vincenzo Librandi, Dec 17 2013 *)
LinearRecurrence[{30, 1}, {1, 30}, 20] (* Harvey P. Dale, Jun 30 2022 *)

Crossrefs

Cf. A041420, A040210.

Row n=30 of A073133, A172236 and A352361 and column k=30 of A157103.

Sequence in context: A320670 A171304 A009974 * A042742 A144350 A111216

Adjacent sequences: A041418 A041419 A041420 * A041422 A041423 A041424

Keyword

nonn,frac,easy,changed

Author

N. J. A. Sloane

Extensions

Additional term from Colin Barker, Nov 17 2013

Status

approved