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A042405 Denominators of continued fraction convergents to sqrt(730). 3
1, 54, 2917, 157572, 8511805, 459795042, 24837444073, 1341681774984, 72475653293209, 3915026959608270, 211483931472139789, 11424047326455156876, 617110039560050611093, 33335366183569188155898, 1800726883952296211029585, 97272587099607564583753488 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
From Michael A. Allen, Dec 17 2023: (Start)
Also called the 54-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 54 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, 54), the n-th Fibonacci polynomial evaluated at x=54. - T. D. Noe, Jan 19 2006
From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 54*a(n-1) + a(n-2) for n > 1; a(0)=1, a(1)=54.
G.f.: 1/(1 - 54*x - x^2). (End)
MATHEMATICA
Denominator[Convergents[Sqrt[730], 30]] (* Vincenzo Librandi, Jan 21 2014 *)
CROSSREFS
Cf. A042404.
Row n=54 of A073133, A172236 and A352361 and column k=54 of A157103.
Sequence in context: A207093 A188990 A189200 * A187304 A309422 A212705
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
a(15) from Colin Barker, Dec 11 2013
STATUS
approved

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Last modified March 28 21:57 EDT 2024. Contains 371254 sequences. (Running on oeis4.)