cp's OEIS Frontend

A042625 Denominators of continued fraction convergents to sqrt(842).

%I A042625 #40 Jan 05 2025 19:51:35
%S A042625 1,58,3365,195228,11326589,657137390,38125295209,2211924259512,
%T A042625 128329732346905,7445336400380002,431957840954387021,
%U A042625 25061000111754827220,1453969964322734365781,84355318930830348042518,4894062467952482920831825,283939978460174839756288368
%N A042625 Denominators of continued fraction convergents to sqrt(842).
%C A042625 From _Michael A. Allen_, Jan 22 2024: (Start)
%C A042625 Also called the 58-metallonacci sequence; the g.f. 1/(1-k*x-x^2) gives the k-metallonacci sequence.
%C A042625 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 58 kinds of squares available. (End)
%H A042625 Vincenzo Librandi, <a href="/A042625/b042625.txt">Table of n, a(n) for n = 0..200</a>
%H A042625 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 A042625 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A042625 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (58,1).
%F A042625 a(n) = F(n, 58), the n-th Fibonacci polynomial evaluated at x=58. - _T. D. Noe_, Jan 19 2006
%F A042625 From _Philippe Deléham_, Nov 23 2008: (Start)
%F A042625 a(n) = 58*a(n-1) + a(n-2) for n>1; a(0)=1, a(1)=58.
%F A042625 G.f.: 1/(1 - 58*x - x^2). (End)
%t A042625 Denominator[Convergents[Sqrt[842], 30]] (* _Vincenzo Librandi_, Jan 26 2014 *)
%Y A042625 Cf. A042624, A040812.
%Y A042625 Row n=58 of A073133, A172236 and A352361 and column k=58 of A157103.
%K A042625 nonn,frac,easy
%O A042625 0,2
%A A042625 _N. J. A. Sloane_
%E A042625 Additional term from _Colin Barker_, Dec 20 2013