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 A041545 #42 Jan 05 2025 19:51:35
%S A041545 1,34,1157,39372,1339805,45592742,1551493033,52796355864,
%T A041545 1796627592409,61138134497770,2080493200516589,70797906952061796,
%U A041545 2409209329570617653,81983915112353061998,2789862323149574725585,94937302902197893731888
%N A041545 Denominators of continued fraction convergents to sqrt(290).
%C A041545 From _Michael A. Allen_, Jul 13 2023: (Start)
%C A041545 Also called the 34-metallonacci sequence; the g.f. 1/(1-k*x-x^2) gives the k-metallonacci sequence.
%C A041545 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 34 kinds of squares available. (End)
%H A041545 Vincenzo Librandi, <a href="/A041545/b041545.txt">Table of n, a(n) for n = 0..200</a>
%H A041545 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 A041545 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A041545 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (34,1).
%F A041545 a(n) = F(n, 34), the n-th Fibonacci polynomial evaluated at x=34. - _T. D. Noe_, Jan 19 2006
%F A041545 From _Philippe Deléham_, Nov 23 2008: (Start)
%F A041545 a(n) = 34*a(n-1) + a(n-2) for n > 1; a(0)=1, a(1)=34.
%F A041545 G.f.: 1/(1-34*x-x^2). (End)
%t A041545 a=0;lst={};s=0;Do[a=s-(a-1);AppendTo[lst,a];s+=a*34,{n,3*4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 27 2009 *)
%t A041545 Denominator[Convergents[Sqrt[290], 30]] (* _Vincenzo Librandi_, Dec 20 2013 *)
%t A041545 LinearRecurrence[{34,1},{1,34},20] (* _Harvey P. Dale_, Oct 08 2021 *)
%Y A041545 Cf. A041544, A040272.
%Y A041545 Row n=34 of A073133, A172236 and A352361 and column k=34 of A157103.
%K A041545 nonn,frac,easy
%O A041545 0,2
%A A041545 _N. J. A. Sloane_
%E A041545 More terms from _Colin Barker_, Nov 18 2013