A041265 Denominators of continued fraction convergents to sqrt(145).

1, 24, 577, 13872, 333505, 8017992, 192765313, 4634385504, 111418017409, 2678666803320, 64399421297089, 1548264777933456, 37222754091700033, 894894362978734248, 21514687465581321985, 517247393536930461888, 12435452132351912407297

Offset

0,2

Comments

From Michael A. Allen, May 04 2023: (Start)

Also called the 24-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 24 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 (24,1).

Formula

a(n) = F(n, 24), the n-th Fibonacci polynomial evaluated at x=24. - T. D. Noe, Jan 19 2006

From Philippe Deléham, Nov 21 2008: (Start)

a(n) = 24*a(n-1) + a(n-2) for n > 1, a(0)=1, a(1)=24.

G.f.: 1/(1-24*x-x^2). (End)

Mathematica

Denominator[Convergents[Sqrt[145], 30]] (* Vincenzo Librandi, Dec 14 2013 *)

Crossrefs

Cf. A041264, A176910, A040132.

Row n=24 of A073133, A172236 and A352361 and column k=24 of A157103.

Sequence in context: A171298 A268027 A009968 * A042106 A158637 A179059

Adjacent sequences: A041262 A041263 A041264 * A041266 A041267 A041268

Keyword

nonn,frac,easy,less

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved