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 A041181 #57 Jan 05 2025 19:51:35
%S A041181 1,20,401,8040,161201,3232060,64802401,1299280080,26050404001,
%T A041181 522307360100,10472197606001,209966259480120,4209797387208401,
%U A041181 84405914003648140,1692328077460171201,33930967463207072160,680311677341601614401
%N A041181 Denominators of continued fraction convergents to sqrt(101).
%C A041181 Generalized Pell numbers (A000129). Antidiagonals of A038207. - _Mark Dols_, Aug 31 2009
%C A041181 a(n) equals the number of words of length n on alphabet {0,1,...,20} avoiding runs of zeros of odd lengths. - _Milan Janjic_, Jan 28 2015
%C A041181 From _Michael A. Allen_, May 03 2023: (Start)
%C A041181 Also called the 20-metallonacci sequence; the g.f. 1/(1-k*x-x^2) gives the k-metallonacci sequence.
%C A041181 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 20 kinds of squares available. (End)
%H A041181 Vincenzo Librandi, <a href="/A041181/b041181.txt">Table of n, a(n) for n = 0..200</a>
%H A041181 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 A041181 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A041181 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,1).
%F A041181 a(n) = Fibonacci(n+1, 20), the n-th Fibonacci polynomial evaluated at x=20. - _T. D. Noe_, Jan 19 2006
%F A041181 From _Philippe Deléham_, Nov 21 2008: (Start)
%F A041181 a(n) = 20*a(n-1) + a(n-2) for n>1, a(0)=1, a(1)=20.
%F A041181 G.f.: 1/(1-20*x-x^2). (End)
%t A041181 Denominator[Convergents[Sqrt[101], 30]] (* _Vincenzo Librandi_, Dec 12 2013 *)
%t A041181 LinearRecurrence[{20,1},{1,20},20] (* _Harvey P. Dale_, Mar 17 2020 *)
%o A041181 (Magma) [n le 2 select (20)^(n-1) else 20*Self(n-1)+Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Dec 12 2013
%o A041181 (SageMath)
%o A041181 A041181=BinaryRecurrenceSequence(20,1,1,20)
%o A041181 [A041181(n) for n in range(31)] # _G. C. Greubel_, Sep 29 2024
%Y A041181 Cf. A000129, A038207, A040090, A041180.
%Y A041181 Cf. similar sequences listed in A243399.
%Y A041181 Row n=20 of A073133, A172236 and A352361 and column k=20 of A157103.
%K A041181 nonn,frac,easy,less
%O A041181 0,2
%A A041181 _N. J. A. Sloane_