A042013 Denominators of continued fraction convergents to sqrt(530).

1, 46, 2117, 97428, 4483805, 206352458, 9496696873, 437054408616, 20113999493209, 925681031096230, 42601441429919789, 1960591986807406524, 90229832834570619893, 4152532902377055921602, 191106743342179143013585, 8795062726642617634546512

Offset

0,2

Comments

From Michael A. Allen, Dec 02 2023: (Start)

Also called the 46-metallonacci sequence; the g.f. 1/(1-k*x-x^2) gives the k-metallonacci sequence.

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 46 kinds of squares available. (End)

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Michael A. Allen and Kenneth Edwards, Fence tiling derived identities involving the metallonacci numbers squared or cubed, Fib. Q. 60:5 (2022) 5-17.

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (46,1).

Formula

a(n) = F(n, 46), the n-th Fibonacci polynomial evaluated at x=46. - T. D. Noe, Jan 19 2006

From Philippe Deléham, Nov 23 2008: (Start)

a(n) = 46*a(n-1) + a(n-2) for n > 1; a(0)=1, a(1)=46.

G.f.: 1/(1-46*x-x^2). (End)

Mathematica

Denominator[Convergents[Sqrt[530], 40]] (* Vincenzo Librandi, Jan 12 2014 *)

Crossrefs

Cf. A042012, A040506.

Row n=46 of A073133, A172236 and A352361 and column k=46 of A157103.

Sequence in context: A264525 A223971 A009990 * A333718 A234153 A123830

Adjacent sequences: A042010 A042011 A042012 * A042014 A042015 A042016

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

Additional term from Colin Barker, Nov 29 2013

Status

approved