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

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

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).

Crossrefs

Cf. A042012, A040506.

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

Programs

Mathematica

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

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)

Extensions

Additional term from Colin Barker, Nov 29 2013