OFFSET
0,2
COMMENTS
From Michael A. Allen, Dec 02 2023: (Start)
Also called the 48-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 48 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 (48,1).
FORMULA
a(n) = F(n, 48), the n-th Fibonacci polynomial evaluated at x=48. - T. D. Noe, Jan 19 2006
From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 48*a(n-1) + a(n-2), n>1; a(0)=1, a(1)=48.
G.f.: 1/(1 - 48*x - x^2). (End)
MATHEMATICA
a=0; lst={}; s=0; Do[a=s-(a-1); AppendTo[lst, a]; s+=a*48, {n, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *)
Denominator[Convergents[Sqrt[577], 30]] (* Vincenzo Librandi, Jan 14 2014 *)
LinearRecurrence[{48, 1}, {1, 48}, 20] (* Harvey P. Dale, Aug 21 2019 *)
CROSSREFS
KEYWORD
nonn,frac,easy,changed
AUTHOR
EXTENSIONS
Additional term from Colin Barker, Dec 01 2013
STATUS
approved