This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A041925 #42 Jan 05 2025 19:51:35
%S A041925 1,44,1937,85272,3753905,165257092,7275065953,320268159024,
%T A041925 14099074063009,620679526931420,27323998259045489,1202876602924932936,
%U A041925 52953894526956094673,2331174235788993098548,102624620269242652430785,4517814466082465700053088
%N A041925 Denominators of continued fraction convergents to sqrt(485).
%C A041925 From _Michael A. Allen_, Aug 08 2023: (Start)
%C A041925 Also called the 44-metallonacci sequence; the g.f. 1/(1-k*x-x^2) gives the k-metallonacci sequence.
%C A041925 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 44 kinds of squares available. (End)
%H A041925 Vincenzo Librandi, <a href="/A041925/b041925.txt">Table of n, a(n) for n = 0..200</a>
%H A041925 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 A041925 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A041925 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (44,1).
%F A041925 a(n) = F(n, 44), the n-th Fibonacci polynomial evaluated at x=44. - _T. D. Noe_, Jan 19 2006
%F A041925 From _Philippe Deléham_, Nov 23 2008: (Start)
%F A041925 a(n) = 44*a(n-1) + a(n-2) for n>1; a(0)=1, a(1)=44.
%F A041925 G.f.: 1/(1-44*x-x^2). (End)
%t A041925 a=0;lst={};s=0;Do[a=s-(a-1);AppendTo[lst,a];s+=a*44,{n,3*4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 03 2009 *)
%t A041925 Denominator[Convergents[Sqrt[485],20]] (* _Harvey P. Dale_, Oct 20 2011 *)
%t A041925 CoefficientList[Series[1/(1 - 44 x - x^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 27 2013 *)
%Y A041925 Cf. A041924, A040462.
%Y A041925 Row n=44 of A073133, A172236 and A352361 and column k=44 of A157103.
%K A041925 nonn,frac,easy
%O A041925 0,2
%A A041925 _N. J. A. Sloane_
%E A041925 Additional term from _Colin Barker_, Nov 27 2013