A041925 Denominators of continued fraction convergents to sqrt(485).

1, 44, 1937, 85272, 3753905, 165257092, 7275065953, 320268159024, 14099074063009, 620679526931420, 27323998259045489, 1202876602924932936, 52953894526956094673, 2331174235788993098548, 102624620269242652430785, 4517814466082465700053088

Offset

0,2

Comments

From Michael A. Allen, Aug 08 2023: (Start)

Also called the 44-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 44 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 (44,1).

Formula

a(n) = F(n, 44), the n-th Fibonacci polynomial evaluated at x=44. - T. D. Noe, Jan 19 2006

From Philippe Deléham, Nov 23 2008: (Start)

a(n) = 44*a(n-1) + a(n-2) for n>1; a(0)=1, a(1)=44.

G.f.: 1/(1-44*x-x^2). (End)

Mathematica

a=0; lst={}; s=0; Do[a=s-(a-1); AppendTo[lst, a]; s+=a*44, {n, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *)
Denominator[Convergents[Sqrt[485], 20]] (* Harvey P. Dale, Oct 20 2011 *)
CoefficientList[Series[1/(1 - 44 x - x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 27 2013 *)

Crossrefs

Cf. A041924, A040462.

Row n=44 of A073133, A172236 and A352361 and column k=44 of A157103.

Sequence in context: A188751 A188871 A009988 * A094506 A121008 A250446

Adjacent sequences: A041922 A041923 A041924 * A041926 A041927 A041928

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

Additional term from Colin Barker, Nov 27 2013

Status

approved