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%I #41 Jun 28 2023 22:14:25
%S 1,26,677,17628,459005,11951758,311204713,8103274296,210996336409,
%T 5494008020930,143055204880589,3724929334916244,96991217912702933,
%U 2525496595065192502,65759902689607707985,1712282966524865600112,44585117032336113310897
%N Denominators of continued fraction convergents to sqrt(170).
%C From _Michael A. Allen_, May 04 2023: (Start)
%C Also called the 26-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 26 kinds of squares available. (End)
%H Vincenzo Librandi, <a href="/A041313/b041313.txt">Table of n, a(n) for n = 0..200</a>
%H Michael A. Allen and Kenneth Edwards, <a href="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 (26,1).
%F a(n) = F(n, 26), the n-th Fibonacci polynomial evaluated at x=26. - _T. D. Noe_, Jan 19 2006
%F From _Philippe Deléham_, Nov 21 2008: (Start)
%F a(n) = 26*a(n-1) + a(n-2) for n > 1, a(0)=1, a(1)=26.
%F G.f.: 1/(1-26*x-x^2). (End)
%t Denominator[Convergents[Sqrt[170], 30]] (* _Vincenzo Librandi_, Dec 15 2013 *)
%t LinearRecurrence[{26,1},{1,26},20] (* _Harvey P. Dale_, Jul 26 2017 *)
%Y Cf. A041312, A040156.
%Y Row n=26 of A073133, A172236 and A352361 and column k=26 of A157103.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_
%E An additional term from _Colin Barker_, Nov 15 2013
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