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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

Table of n, a(n) for n=0..37.

Tanya Khovanova, Recursive Sequences

C. Richard and U. Grimm, On the entropy and letter frequencies of ternary squarefree words

Index entries for linear recurrences with constant coefficients, signature (1, 1).

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

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

Cf. A000032.

Sequence in context: A029682 A014201 A242951 * A275288 A110357 A091827

Adjacent sequences:  A022086 A022087 A022088 * A022090 A022091 A022092

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 23 07:01 EDT 2017. Contains 286909 sequences.