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4, 17, 28, 41, 48, 61, 72, 85, 98, 109, 122, 129, 142, 153, 166, 177, 190, 197, 210, 221, 234, 247, 258, 271, 278, 291, 302, 315, 322, 335, 346, 359, 372, 383, 396, 403, 416, 427, 440, 451, 464, 471, 484, 495, 508, 521, 532, 545, 552, 565, 576, 589, 602, 613
(list;
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OFFSET
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1,1
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COMMENTS
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This sequence gives the positions of the word cabaa in the tribonacci word t = abacabaa..., fixed point of the morphism a->ab, b->ac, c->a. This follows from the fact that the word baa is always preceded in t by the word ca, and the formula CA = BB-2, where A := A003144, B := A003145, C := A003146. See A319968 for BB. - Michel Dekking, Apr 09 2019
The fact that this sequence is the positional sequence of cabaa in the tribonacci word permits to apply Theorem 5.1. in the paper by Huang and Wen. This gives that the sequence (a(n+1)-a(n)) equals the tribonacci word on the alphabet {a(2)-a(1), a(3)-a(2), a(5)-a(4)} = {13, 11, 7}. - Michel Dekking, Oct 04 2019
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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. Compare page 318.
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FORMULA
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a(1) = 4, a(n+1)= 4 + Sum_{k=1..n} d(k), where d is the tribonacci sequence on the alphabet (13,11,7}. - Michel Dekking, Oct 04 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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