cp's OEIS Frontend

A042861 Denominators of continued fraction convergents to sqrt(962).

%I A042861 #37 Jan 05 2025 19:51:35
%S A042861 1,62,3845,238452,14787869,917086330,56874140329,3527113786728,
%T A042861 218737928917465,13565278706669558,841266017742430061,
%U A042861 52172058378737333340,3235508885499457097141,200653722959345077356082,12443766332364894253174225,771714166329582788774158032
%N A042861 Denominators of continued fraction convergents to sqrt(962).
%C A042861 From _Michael A. Allen_, Jan 22 2024: (Start)
%C A042861 Also called the 62-metallonacci sequence; the g.f. 1/(1-k*x-x^2) gives the k-metallonacci sequence.
%C A042861 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 62 kinds of squares available. (End)
%H A042861 Vincenzo Librandi, <a href="/A042861/b042861.txt">Table of n, a(n) for n = 0..200</a>
%H A042861 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 A042861 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A042861 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (62,1).
%F A042861 a(n) = F(n, 62), the n-th Fibonacci polynomial evaluated at x=62. - _T. D. Noe_, Jan 19 2006
%F A042861 From _Philippe Deléham_, Nov 23 2008: (Start)
%F A042861 a(n) = 62*a(n-1) + a(n-2), n>1; a(0)=1, a(1)=62.
%F A042861 G.f.: 1/(1 - 62*x - x^2). (End)
%t A042861 Denominator[Convergents[Sqrt[962],20]] (* _Harvey P. Dale_, Jun 15 2013 *)
%Y A042861 Cf. A042860, A040930.
%Y A042861 Row n=62 of A073133, A172236 and A352361 and column k=62 of A157103.
%K A042861 nonn,frac,easy
%O A042861 0,2
%A A042861 _N. J. A. Sloane_
%E A042861 Additional term from _Colin Barker_, Dec 25 2013