%I #48 Jan 05 2025 19:51:35
%S 1,54,2917,157572,8511805,459795042,24837444073,1341681774984,
%T 72475653293209,3915026959608270,211483931472139789,
%U 11424047326455156876,617110039560050611093,33335366183569188155898,1800726883952296211029585,97272587099607564583753488
%N Denominators of continued fraction convergents to sqrt(730).
%C From _Michael A. Allen_, Dec 17 2023: (Start)
%C Also called the 54-metallonacci sequence; the g.f. 1/(1-k*x-x^2) gives the k-metallonacci sequence.
%C 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 54 kinds of squares available. (End)
%H Vincenzo Librandi, <a href="/A042405/b042405.txt">Table of n, a(n) for n = 0..200</a>
%H Michael A. Allen and Kenneth Edwards, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/60-5/allen.pdf">Fence tiling derived identities involving the metallonacci numbers squared or cubed</a>, Fib. Q. 60:5 (2022) 5-17.
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (54,1).
%F a(n) = F(n, 54), the n-th Fibonacci polynomial evaluated at x=54. - _T. D. Noe_, Jan 19 2006
%F From _Philippe Deléham_, Nov 23 2008: (Start)
%F a(n) = 54*a(n-1) + a(n-2) for n > 1; a(0)=1, a(1)=54.
%F G.f.: 1/(1 - 54*x - x^2). (End)
%t Denominator[Convergents[Sqrt[730], 30]] (* _Vincenzo Librandi_, Jan 21 2014 *)
%Y Cf. A042404.
%Y Row n=54 of A073133, A172236 and A352361 and column k=54 of A157103.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_
%E a(15) from _Colin Barker_, Dec 11 2013