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 A041365 #38 Jan 05 2025 19:51:35
%S A041365 1,28,785,22008,617009,17298260,484968289,13596410352,381184458145,
%T A041365 10686761238412,299610499133681,8399780736981480,235493471134615121,
%U A041365 6602216972506204868,185097568701308351425,5189334140609140044768
%N A041365 Denominators of continued fraction convergents to sqrt(197).
%C A041365 From _Michael A. Allen_, May 16 2023: (Start)
%C A041365 Also called the 28-metallonacci sequence; the g.f. 1/(1-k*x-x^2) gives the k-metallonacci sequence.
%C A041365 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 28 kinds of squares available. (End)
%H A041365 Vincenzo Librandi, <a href="/A041365/b041365.txt">Table of n, a(n) for n = 0..200</a>
%H A041365 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 A041365 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A041365 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (28,1).
%F A041365 a(n) = F(n, 28), the n-th Fibonacci polynomial evaluated at x=28. - _T. D. Noe_, Jan 19 2006
%F A041365 From _Philippe Deléham_, Nov 21 2008: (Start)
%F A041365 a(n) = 28*a(n-1) + a(n-2), n > 1; a(0)= 1, a(1)=28.
%F A041365 G.f.: 1/(1-28*x-x^2). (End)
%t A041365 a=0;lst={};s=0;Do[a=s-(a-1);AppendTo[lst,a];s+=a*28,{n,3*4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 27 2009 *)
%t A041365 Denominator[Convergents[Sqrt[197], 30]] (* _Vincenzo Librandi_, Dec 16 2013 *)
%t A041365 LinearRecurrence[{28,1},{1,28},20] (* _Harvey P. Dale_, Mar 07 2021 *)
%Y A041365 Cf. A041364, A040182.
%Y A041365 Row n=28 of A073133, A172236 and A352361 and column k=28 of A157103.
%K A041365 nonn,frac,easy
%O A041365 0,2
%A A041365 _N. J. A. Sloane_
%E A041365 Additional term from _Colin Barker_, Nov 16 2013