A042625 Denominators of continued fraction convergents to sqrt(842).

1, 58, 3365, 195228, 11326589, 657137390, 38125295209, 2211924259512, 128329732346905, 7445336400380002, 431957840954387021, 25061000111754827220, 1453969964322734365781, 84355318930830348042518, 4894062467952482920831825, 283939978460174839756288368

Offset

0,2

Comments

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

Also called the 58-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 58 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 (58,1).

Formula

a(n) = F(n, 58), the n-th Fibonacci polynomial evaluated at x=58. - T. D. Noe, Jan 19 2006

From Philippe Deléham, Nov 23 2008: (Start)

a(n) = 58*a(n-1) + a(n-2) for n>1; a(0)=1, a(1)=58.

G.f.: 1/(1 - 58*x - x^2). (End)

Mathematica

Denominator[Convergents[Sqrt[842], 30]] (* Vincenzo Librandi, Jan 26 2014 *)

Crossrefs

Cf. A042624, A040812.

Row n=58 of A073133, A172236 and A352361 and column k=58 of A157103.

Sequence in context: A207278 A207474 A207530 * A250919 A282438 A308391

Adjacent sequences: A042622 A042623 A042624 * A042626 A042627 A042628

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

Additional term from Colin Barker, Dec 20 2013

Status

approved