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%I #48 Feb 13 2024 23:05:20
%S 1,60,3601,216120,12970801,778464180,46720821601,2804027760240,
%T 168288386436001,10100107213920300,606174721221654001,
%U 36380583380513160360,2183441177552011275601,131042851236501189696420,7864754515367623393060801,472016313773293904773344480
%N Denominators of continued fraction convergents to sqrt(901).
%C From _Michael A. Allen_, Jan 22 2024: (Start)
%C Also called the 60-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 60 kinds of squares available. (End)
%H Vincenzo Librandi, <a href="/A042741/b042741.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 (60,1).
%F a(n) = F(n, 60), the n-th Fibonacci polynomial evaluated at x=60. - _T. D. Noe_, Jan 19 2006
%F From _Philippe Deléham_, Nov 23 2008: (Start)
%F a(n) = 60*a(n-1) + a(n-2) for n>1; a(0)=1, a(1)=60.
%F G.f.: 1/(1 - 60*x - x^2). (End)
%F E.g.f.: exp(30*x)*cosh(sqrt(901)*x) + 30*exp(30*x)*sinh(sqrt(901)*x)/sqrt(901). - _Stefano Spezia_, May 14 2023
%t Denominator[Convergents[Sqrt[901],30]] (* or *) LinearRecurrence[{60,1},{1,60},30] (* _Harvey P. Dale_, Sep 09 2012 *)
%o (Magma) I:=[1,60]; [n le 2 select I[n] else 60*Self(n-1)+Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Jan 28 2014
%Y Cf. A042740, A040870.
%Y Row n=60 of A073133, A172236 and A352361 and column k=60 of A157103.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_
%E Additional term from _Colin Barker_, Dec 22 2013
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