A042861 Denominators of continued fraction convergents to sqrt(962).

1, 62, 3845, 238452, 14787869, 917086330, 56874140329, 3527113786728, 218737928917465, 13565278706669558, 841266017742430061, 52172058378737333340, 3235508885499457097141, 200653722959345077356082, 12443766332364894253174225, 771714166329582788774158032

Offset

0,2

Comments

From Michael A. Allen, Jan 22 2024: (Start)

Also called the 62-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 62 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 (62,1).

Formula

a(n) = F(n, 62), the n-th Fibonacci polynomial evaluated at x=62. - T. D. Noe, Jan 19 2006

From Philippe Deléham, Nov 23 2008: (Start)

a(n) = 62*a(n-1) + a(n-2), n>1; a(0)=1, a(1)=62.

G.f.: 1/(1 - 62*x - x^2). (End)

Mathematica

Denominator[Convergents[Sqrt[962], 20]] (* Harvey P. Dale, Jun 15 2013 *)

Crossrefs

Cf. A042860, A040930.

Row n=62 of A073133, A172236 and A352361 and column k=62 of A157103.

Sequence in context: A206841 A206895 A207285 * A056639 A289297 A123806

Adjacent sequences: A042858 A042859 A042860 * A042862 A042863 A042864

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

Additional term from Colin Barker, Dec 25 2013

Status

approved