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 A041685 #38 Jan 05 2025 19:51:35
%S A041685 1,38,1445,54948,2089469,79454770,3021370729,114891542472,
%T A041685 4368899984665,166133090959742,6317426356454861,240228334636244460,
%U A041685 9134994142533744341,347370005750918529418,13209195212677437862225,502296788087493557293968
%N A041685 Denominators of continued fraction convergents to sqrt(362).
%C A041685 From _Michael A. Allen_, Jul 13 2023: (Start)
%C A041685 Also called the 38-metallonacci sequence; the g.f. 1/(1-k*x-x^2) gives the k-metallonacci sequence.
%C A041685 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 38 kinds of squares available. (End)
%H A041685 Vincenzo Librandi, <a href="/A041685/b041685.txt">Table of n, a(n) for n = 0..200</a>
%H A041685 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 A041685 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A041685 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (38,1).
%F A041685 a(n) = F(n, 38), the n-th Fibonacci polynomial evaluated at x=38. - _T. D. Noe_, Jan 19 2006
%F A041685 From _Philippe Deléham_, Nov 23 2008: (Start)
%F A041685 a(n) = 38*a(n-1) + a(n-2), n > 1; a(0)=1, a(1)=38.
%F A041685 G.f.: 1/(1-38*x-x^2). (End)
%t A041685 Denominator[Convergents[Sqrt[362], 30]] (* _Vincenzo Librandi_, Dec 22 2013 *)
%t A041685 LinearRecurrence[{38,1},{1,38},30] (* _Harvey P. Dale_, May 23 2017 *)
%Y A041685 Cf. A041684, A040342.
%Y A041685 Row n=38 of A073133, A172236 and A352361 and column k=38 of A157103.
%K A041685 nonn,frac,easy
%O A041685 0,2
%A A041685 _N. J. A. Sloane_
%E A041685 More terms from _Colin Barker_, Nov 21 2013