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 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 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 AUTHOR N. J. A. Sloane EXTENSIONS Additional term from Colin Barker, Nov 17 2013 STATUS approved

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Last modified September 15 16:35 EDT 2024. Contains 375938 sequences. (Running on oeis4.)