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A254990
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4-bonacci word. Fixed point of morphism 0->01, 1->02, 2->03, 3->0.
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6
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0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 3
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OFFSET
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0,4
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COMMENTS
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Special case of k-bonacci word for k = 4 (see crossrefs).
The lengths of iterations S(i) are Tetranacci numbers (A000078).
Set S(0) = 0; S(1) = 0,1; S(2) = 0,1,0,2; S(3) = 0,1,0,2,0,1,0,3; for n >= 4: S(n) = S(n-1) S(n-2) S(n-3) S(n-4). The sequence is the limit S(infinity).
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LINKS
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Elena Barcucci, Luc Belanger and Srecko Brlek, On tribonacci sequences, Fib. Q., 42 (2004), 314-320. See Section 4.
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EXAMPLE
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The iterates are:
0
01
0102
01020103
010201030102010
01020103010201001020103010201
01020103010201001020103010201010201030102010010201030102
...
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MATHEMATICA
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Nest[Flatten[#/.{0->{0, 1}, 1->{0, 2}, 2->{0, 3}, 3->0}]&, 0, 7] (* Harvey P. Dale, Mar 26 2015 *)
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CROSSREFS
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Cf. A000078 (lengths of iterations).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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