|
%I #38 May 16 2023 07:04:08
%S 1,22,485,10692,235709,5196290,114554089,2525386248,55673051545,
%T 1227332520238,27056988496781,596481079449420,13149640736384021,
%U 289888577279897882,6390698340894137425,140885252076950921232,3105866244033814404529,68469942620820867820870
%N Denominators of continued fraction convergents to sqrt(122).
%C From _Michael A. Allen_, May 04 2023: (Start)
%C Also called the 22-metallonacci sequence; the g.f. 1/(1-k*x-x^2) gives the k-metallonacci sequence.
%C 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 22 kinds of squares available. (End)
%H Vincenzo Librandi, <a href="/A041221/b041221.txt">Table of n, a(n) for n = 0..200</a>
%H Michael A. Allen and Kenneth Edwards, <a href="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 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (22,1).
%F a(n) = F(n, 22), the n-th Fibonacci polynomial evaluated at x=22. - _T. D. Noe_, Jan 19 2006
%F From _Philippe Deléham_, Nov 21 2008: (Start)
%F a(n) = 22*a(n-1) + a(n-2) for n > 1; a(0)=1, a(1)=22.
%F G.f.: 1/(1 - 22*x - x^2). (End)
%t Denominator[Convergents[Sqrt[122], 30]] (* _Vincenzo Librandi_, Dec 13 2013 *)
%Y Cf. A041220, A040110.
%Y Row n=22 of A073133, A172236 and A352361 and column k=22 of A157103.
%K nonn,frac,easy,less
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Colin Barker_, Nov 14 2013
| 