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 A042201 Denominators of continued fraction convergents to sqrt(626). 3
 1, 50, 2501, 125100, 6257501, 313000150, 15656265001, 783126250200, 39171968775001, 1959381565000250, 98008250218787501, 4902371892504375300, 245216602875437552501, 12265732515664382000350, 613531842386094537570001, 30688857851820391260500400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS From Michael A. Allen, Dec 02 2023: (Start) Also called the 50-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 50 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 (50,1). FORMULA a(n) = F(n, 50), the n-th Fibonacci polynomial evaluated at x=50. - T. D. Noe, Jan 19 2006 From Philippe Deléham, Nov 23 2008: (Start) a(n) = 50*a(n-1) + a(n-2) for n > 1, a(0)=1, a(1)=50. G.f.: 1/(1 - 50*x - x^2). (End) MATHEMATICA Denominator[Convergents[Sqrt[626], 30]] (* Vincenzo Librandi, Jan 16 2014 *) CROSSREFS Cf. A042200, A040600. Row n=50 of A073133, A172236 and A352361 and column k=50 of A157103. Sequence in context: A223871 A223796 A165800 * A097838 A203842 A251058 Adjacent sequences: A042198 A042199 A042200 * A042202 A042203 A042204 KEYWORD nonn,frac,easy AUTHOR N. J. A. Sloane EXTENSIONS Additional term from Colin Barker, Dec 04 2013 STATUS approved

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Last modified September 10 21:37 EDT 2024. Contains 375795 sequences. (Running on oeis4.)