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A041265 Denominators of continued fraction convergents to sqrt(145).

%I A041265 #41 Jan 05 2025 19:51:35
%S A041265 1,24,577,13872,333505,8017992,192765313,4634385504,111418017409,
%T A041265 2678666803320,64399421297089,1548264777933456,37222754091700033,
%U A041265 894894362978734248,21514687465581321985,517247393536930461888,12435452132351912407297
%N A041265 Denominators of continued fraction convergents to sqrt(145).
%C A041265 From _Michael A. Allen_, May 04 2023: (Start)
%C A041265 Also called the 24-metallonacci sequence; the g.f. 1/(1-k*x-x^2) gives the k-metallonacci sequence.
%C A041265 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 24 kinds of squares available. (End)
%H A041265 Vincenzo Librandi, <a href="/A041265/b041265.txt">Table of n, a(n) for n = 0..200</a>
%H A041265 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 A041265 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A041265 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (24,1).
%F A041265 a(n) = F(n, 24), the n-th Fibonacci polynomial evaluated at x=24. - _T. D. Noe_, Jan 19 2006
%F A041265 From _Philippe Deléham_, Nov 21 2008: (Start)
%F A041265 a(n) = 24*a(n-1) + a(n-2) for n > 1, a(0)=1, a(1)=24.
%F A041265 G.f.: 1/(1-24*x-x^2). (End)
%t A041265 Denominator[Convergents[Sqrt[145], 30]] (* _Vincenzo Librandi_, Dec 14 2013 *)
%Y A041265 Cf. A041264, A176910, A040132.
%Y A041265 Row n=24 of A073133, A172236 and A352361 and column k=24 of A157103.
%K A041265 nonn,frac,easy,less
%O A041265 0,2
%A A041265 _N. J. A. Sloane_
%E A041265 More terms from _Colin Barker_, Nov 14 2013