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A041545 Denominators of continued fraction convergents to sqrt(290). 3
1, 34, 1157, 39372, 1339805, 45592742, 1551493033, 52796355864, 1796627592409, 61138134497770, 2080493200516589, 70797906952061796, 2409209329570617653, 81983915112353061998, 2789862323149574725585, 94937302902197893731888 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
From Michael A. Allen, Jul 13 2023: (Start)
Also called the 34-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 34 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, 34), the n-th Fibonacci polynomial evaluated at x=34. - T. D. Noe, Jan 19 2006
From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 34*a(n-1) + a(n-2) for n > 1; a(0)=1, a(1)=34.
G.f.: 1/(1-34*x-x^2). (End)
MATHEMATICA
a=0; lst={}; s=0; Do[a=s-(a-1); AppendTo[lst, a]; s+=a*34, {n, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 27 2009 *)
Denominator[Convergents[Sqrt[290], 30]] (* Vincenzo Librandi, Dec 20 2013 *)
LinearRecurrence[{34, 1}, {1, 34}, 20] (* Harvey P. Dale, Oct 08 2021 *)
CROSSREFS
Row n=34 of A073133, A172236 and A352361 and column k=34 of A157103.
Sequence in context: A264134 A264019 A009978 * A189434 A167258 A251924
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 18 2013
STATUS
approved

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Last modified May 19 14:45 EDT 2024. Contains 372698 sequences. (Running on oeis4.)