OFFSET
0,2
COMMENTS
From Michael A. Allen, May 16 2023: (Start)
Also called the 30-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 30 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 (30,1).
FORMULA
a(n) = F(n, 30), the n-th Fibonacci polynomial evaluated at x=30. - T. D. Noe, Jan 19 2006
From Philippe Deléham, Nov 22 2008: (Start)
a(n) = 30*a(n-1) + a(n-2) for n > 1; a(0)=1, a(1)=30.
G.f.: 1/(1-30*x-x^2). (End)
MATHEMATICA
Denominator[Convergents[Sqrt[226], 30]] (* Vincenzo Librandi, Dec 17 2013 *)
LinearRecurrence[{30, 1}, {1, 30}, 20] (* Harvey P. Dale, Jun 30 2022 *)
CROSSREFS
KEYWORD
nonn,frac,easy,changed
AUTHOR
EXTENSIONS
Additional term from Colin Barker, Nov 17 2013
STATUS
approved