A042201 Denominators of continued fraction convergents to sqrt(626).

1, 50, 2501, 125100, 6257501, 313000150, 15656265001, 783126250200, 39171968775001, 1959381565000250, 98008250218787501, 4902371892504375300, 245216602875437552501, 12265732515664382000350, 613531842386094537570001, 30688857851820391260500400

Offset

0,2

Comments

From Michael A. Allen, Dec 02 2023: (Start)

Also called the 50-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 50 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 (50,1).

Formula

a(n) = F(n, 50), the n-th Fibonacci polynomial evaluated at x=50. - T. D. Noe, Jan 19 2006

From Philippe Deléham, Nov 23 2008: (Start)

a(n) = 50*a(n-1) + a(n-2) for n > 1, a(0)=1, a(1)=50.

G.f.: 1/(1 - 50*x - x^2). (End)

Mathematica

Denominator[Convergents[Sqrt[626], 30]] (* Vincenzo Librandi, Jan 16 2014 *)

Crossrefs

Cf. A042200, A040600.

Row n=50 of A073133, A172236 and A352361 and column k=50 of A157103.

Sequence in context: A223871 A223796 A165800 * A097838 A203842 A251058

Adjacent sequences: A042198 A042199 A042200 * A042202 A042203 A042204

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

Additional term from Colin Barker, Dec 04 2013

Status

approved