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

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

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).

Crossrefs

Cf. A042860, A040930.

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

Programs

Mathematica

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

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)

Extensions

Additional term from Colin Barker, Dec 25 2013