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 A041841 Denominators of continued fraction convergents to sqrt(442). 3
 1, 42, 1765, 74172, 3116989, 130987710, 5504600809, 231324221688, 9721121911705, 408518444513298, 17167495791470221, 721443341686262580, 30317787846614498581, 1274068532899495202982, 53541196169625413023825, 2250004307657166842203632 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS From Michael A. Allen, Aug 08 2023: (Start) Also called the 42-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 42 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 (42,1). FORMULA a(n) = F(n, 42), the n-th Fibonacci polynomial evaluated at x=42. - T. D. Noe, Jan 19 2006 From Philippe Deléham, Nov 23 2008: (Start) a(n) = 42*a(n-1) + a(n-2) for n > 1; a(0)=1, a(1)=42. G.f.: 1/(1 - 42*x - x^2). (End) MATHEMATICA a=0; lst={}; s=0; Do[a=s-(a-1); AppendTo[lst, a]; s+=a*42, {n, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *) Denominator[Convergents[Sqrt[442], 30]] (* Vincenzo Librandi, Dec 25 2013 *) CROSSREFS Cf. A041840, A040420. Row n=42 of A073133, A172236 and A352361 and column k=42 of A157103. Sequence in context: A207716 A208077 A009986 * A236270 A216703 A258393 Adjacent sequences: A041838 A041839 A041840 * A041842 A041843 A041844 KEYWORD nonn,frac,easy AUTHOR N. J. A. Sloane EXTENSIONS Additional term from Colin Barker, Nov 25 2013 STATUS approved

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