OFFSET
0,2
COMMENTS
From Michael A. Allen, Dec 17 2023: (Start)
Also called the 52-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 52 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 (52,1).
FORMULA
a(n) = F(n, 52), the n-th Fibonacci polynomial evaluated at x=52. - T. D. Noe, Jan 19 2006
From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 52*a(n-1) + a(n-2) for n > 1, a(0)=1, a(1)=52.
G.f.: 1/(1 - 52*x - x^2). (End)
MATHEMATICA
a = 0; lst = {}; s = 0; Do[a = s - (a - 1); AppendTo[lst, a]; s += a*52, {n, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *)
Denominator[Convergents[Sqrt[677], 30]] (* Vincenzo Librandi, Jan 19 2014 *)
LinearRecurrence[{52, 1}, {1, 52}, 20] (* Harvey P. Dale, Mar 24 2023 *)
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
Additional term from Colin Barker, Dec 07 2013
STATUS
approved