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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 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 (34,1). 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 Cf. A041544, A040272. Row n=34 of A073133, A172236 and A352361 and column k=34 of A157103. Sequence in context: A264134 A264019 A009978 * A189434 A167258 A251924 Adjacent sequences: A041542 A041543 A041544 * A041546 A041547 A041548 KEYWORD nonn,frac,easy AUTHOR N. J. A. Sloane 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.)