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 A041841 #31 Jan 05 2025 19:51:35
%S A041841 1,42,1765,74172,3116989,130987710,5504600809,231324221688,
%T A041841 9721121911705,408518444513298,17167495791470221,721443341686262580,
%U A041841 30317787846614498581,1274068532899495202982,53541196169625413023825,2250004307657166842203632
%N A041841 Denominators of continued fraction convergents to sqrt(442).
%C A041841 From _Michael A. Allen_, Aug 08 2023: (Start)
%C A041841 Also called the 42-metallonacci sequence; the g.f. 1/(1-k*x-x^2) gives the k-metallonacci sequence.
%C A041841 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 42 kinds of squares available. (End)
%H A041841 Vincenzo Librandi, <a href="/A041841/b041841.txt">Table of n, a(n) for n = 0..200</a>
%H A041841 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 A041841 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A041841 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (42,1).
%F A041841 a(n) = F(n, 42), the n-th Fibonacci polynomial evaluated at x=42. - _T. D. Noe_, Jan 19 2006
%F A041841 From _Philippe Deléham_, Nov 23 2008: (Start)
%F A041841 a(n) = 42*a(n-1) + a(n-2) for n > 1; a(0)=1, a(1)=42.
%F A041841 G.f.: 1/(1 - 42*x - x^2).
%F A041841 (End)
%t A041841 a=0;lst={};s=0;Do[a=s-(a-1);AppendTo[lst,a];s+=a*42,{n,3*4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 03 2009 *)
%t A041841 Denominator[Convergents[Sqrt[442], 30]] (* _Vincenzo Librandi_, Dec 25 2013 *)
%Y A041841 Cf. A041840, A040420.
%Y A041841 Row n=42 of A073133, A172236 and A352361 and column k=42 of A157103.
%K A041841 nonn,frac,easy
%O A041841 0,2
%A A041841 _N. J. A. Sloane_
%E A041841 Additional term from _Colin Barker_, Nov 25 2013