OFFSET
0,2
COMMENTS
From Michael A. Allen, Dec 17 2023: (Start)
Also called the 56-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 56 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 (56,1).
FORMULA
a(n) = F(n, 56), the n-th Fibonacci polynomial evaluated at x=56. - T. D. Noe, Jan 19 2006
From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 56*a(n-1) + a(n-2) for n > 1, a(0)=1, a(1)=56.
G.f.: 1/(1 - 56*x - x^2). (End)
MATHEMATICA
a=0; lst={}; s=0; Do[a = s-(a-1); AppendTo[lst, a]; s+=a*56, {n, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 03 2009 *)
Denominator[Convergents[Sqrt[785], 30]] (* Harvey P. Dale, Jun 26 2012 *)
CoefficientList[Series[1/(1 - 56 x - x^2), {x, 0, 25}], x] (* Vincenzo Librandi, Jan 23 2014 *)
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
Additional term from Colin Barker, Dec 17 2013
STATUS
approved