OFFSET
0,2
COMMENTS
From Michael A. Allen, May 04 2023: (Start)
Also called the 22-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 22 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 (22,1).
FORMULA
a(n) = F(n, 22), the n-th Fibonacci polynomial evaluated at x=22. - T. D. Noe, Jan 19 2006
From Philippe Deléham, Nov 21 2008: (Start)
a(n) = 22*a(n-1) + a(n-2) for n > 1; a(0)=1, a(1)=22.
G.f.: 1/(1 - 22*x - x^2). (End)
MATHEMATICA
Denominator[Convergents[Sqrt[122], 30]] (* Vincenzo Librandi, Dec 13 2013 *)
Fibonacci[1+Range[0, 30], 22] (* G. C. Greubel, Oct 25 2024 *)
PROG
(Magma)
[n le 2 select (22)^(n-1) else 22*Self(n-1)+Self(n-2): n in [1..31]]; // G. C. Greubel, Oct 25 2024
(SageMath)
A041221=BinaryRecurrenceSequence(22, 1, 1, 22)
[A041221(n) for n in range(31)] # G. C. Greubel, Oct 25 2024
CROSSREFS
KEYWORD
nonn,frac,easy,less
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 14 2013
STATUS
approved