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%I #37 Dec 17 2023 10:26:13
%S 1,50,2501,125100,6257501,313000150,15656265001,783126250200,
%T 39171968775001,1959381565000250,98008250218787501,
%U 4902371892504375300,245216602875437552501,12265732515664382000350,613531842386094537570001,30688857851820391260500400
%N Denominators of continued fraction convergents to sqrt(626).
%C From _Michael A. Allen_, Dec 02 2023: (Start)
%C Also called the 50-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 50 kinds of squares available. (End)
%H Vincenzo Librandi, <a href="/A042201/b042201.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 (50,1).
%F a(n) = F(n, 50), the n-th Fibonacci polynomial evaluated at x=50. - _T. D. Noe_, Jan 19 2006
%F From _Philippe Deléham_, Nov 23 2008: (Start)
%F a(n) = 50*a(n-1) + a(n-2) for n > 1, a(0)=1, a(1)=50.
%F G.f.: 1/(1 - 50*x - x^2). (End)
%t Denominator[Convergents[Sqrt[626], 30]] (* _Vincenzo Librandi_, Jan 16 2014 *)
%Y Cf. A042200, A040600.
%Y Row n=50 of A073133, A172236 and A352361 and column k=50 of A157103.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_
%E Additional term from _Colin Barker_, Dec 04 2013
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