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 A041481 #35 Jul 09 2025 00:54:02
%S A041481 1,32,1025,32832,1051649,33685600,1078990849,34561392768,
%T A041481 1107043559425,35459955294368,1135825612979201,36381879570628800,
%U A041481 1165355971873100801,37327772979509854432,1195654091316188442625,38298258695097540018432,1226739932334437469032449
%N A041481 Denominators of continued fraction convergents to sqrt(257).
%C A041481 From _Michael A. Allen_, May 16 2023: (Start)
%C A041481 Also called the 32-metallonacci sequence; the g.f. 1/(1-k*x-x^2) gives the k-metallonacci sequence.
%C A041481 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 32 kinds of squares available. (End)
%H A041481 Vincenzo Librandi, <a href="/A041481/b041481.txt">Table of n, a(n) for n = 0..200</a>
%H A041481 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 A041481 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A041481 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (32,1).
%F A041481 a(n) = F(n, 32), the n-th Fibonacci polynomial evaluated at x=32. - _T. D. Noe_, Jan 19 2006
%F A041481 a(n) = 32*a(n-1)+a(n-2) for n>1; a(0)=1, a(1)=32. G.f.: 1/(1-32*x-x^2). [_Philippe Deléham_, Nov 23 2008]
%t A041481 a=0; lst={}; s=0; Do[a=s-(a-1); AppendTo[lst,a]; s+=a*32,{n,3*4!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 27 2009 *)
%t A041481 Denominator[Convergents[Sqrt[257], 30]] (* _Vincenzo Librandi_, Dec 18 2013 *)
%t A041481 LinearRecurrence[{32,1},{1,32},30] (* _Harvey P. Dale_, Nov 03 2015 *)
%Y A041481 Cf. A041480, A040240.
%Y A041481 Row n=32 of A073133, A172236 and A352361 and column k=32 of A157103.
%K A041481 nonn,frac,easy
%O A041481 0,2
%A A041481 _N. J. A. Sloane_
%E A041481 More terms from _Colin Barker_, Nov 18 2013