login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A041421 Denominators of continued fraction convergents to sqrt(226). 3
1, 30, 901, 27060, 812701, 24408090, 733055401, 22016070120, 661215159001, 19858470840150, 596415340363501, 17912318681745180, 537965975792718901, 16156891592463312210, 485244713749692085201, 14573498304083225868240 (list; graph; refs; listen; history; text; internal format)
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
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
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
Row n=30 of A073133, A172236 and A352361 and column k=30 of A157103.
Sequence in context: A320670 A171304 A009974 * A042742 A144350 A111216
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
Additional term from Colin Barker, Nov 17 2013
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)