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A022089 Fibonacci sequence beginning 0, 6. 5
0, 6, 6, 12, 18, 30, 48, 78, 126, 204, 330, 534, 864, 1398, 2262, 3660, 5922, 9582, 15504, 25086, 40590, 65676, 106266, 171942, 278208, 450150, 728358, 1178508, 1906866, 3085374, 4992240, 8077614, 13069854, 21147468, 34217322, 55364790, 89582112, 144946902 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Starting with a(0)=1, a(1)=3, a(n) = the number of ternary length-2 squarefree words of length n.
REFERENCES
A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, p. 15.
LINKS
C. Dalfó, M. A. Fiol, A Note on the Order of Iterated Line Digraphs, Journal of Graph Theory, Volume 85, Issue 2, June 2017, Pages 395-39, 2016; DOI: 10.1002/jgt.22068; arXiv:1607.08832 [math.CO], 2016.
Tanya Khovanova, Recursive Sequences
C. Richard and U. Grimm, On the entropy and letter frequencies of ternary squarefree words, arXiv:math/0302302 [math.CO], 2003.
FORMULA
a(n) = round( (12*phi-6)/5 * phi^n) for n>3. - Thomas Baruchel, Sep 08 2004
a(n) = 6F(n) = F(n+3) + F(n+1) + F(n-4), n>3.
a(n) = A119457(n+4,n-1) for n>1. - Reinhard Zumkeller, May 20 2006
G.f.: 6*x/(1-x-x^2). - Philippe Deléham, Nov 20 2008
a(n) = 6 * A000045(n). - Alois P. Heinz, Jan 18 2019
MAPLE
a:= n-> 6*(<<0|1>, <1|1>>^n)[1, 2]:
seq(a(n), n=0..40); # Alois P. Heinz, Jan 18 2019
MATHEMATICA
a={}; b=0; c=6; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 12, 1}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *)
LinearRecurrence[{1, 1}, {0, 6}, 50] (* Harvey P. Dale, Dec 05 2015 *)
CROSSREFS
Sequence in context: A315795 A315796 A242951 * A275288 A110357 A091827
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified June 13 09:43 EDT 2024. Contains 373383 sequences. (Running on oeis4.)