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24, 68, 105, 149, 173, 217, 254, 298, 342, 379, 423, 447, 491, 528, 572, 609, 653, 677, 721, 758, 802, 846, 883, 927, 951, 995, 1032, 1076, 1100, 1144, 1181, 1225, 1269, 1306, 1350, 1374, 1418, 1455, 1499, 1536, 1580, 1604, 1648, 1685, 1729, 1773, 1810, 1854
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OFFSET
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1,1
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COMMENTS
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By analogy with the Wythoff compound sequences A003622 etc., the nine compounds of A003144, A003145, A003146 might be called the tribonacci compound sequences. They are A278040, A278041, and A319966-A319972.
This sequence gives the positions of the word cabac in the tribonacci word t = abacabaa..., fixed point of the morphism a->ab, b->ac, c->a. This follows from the fact that the positional sequences of cabaa, cabab and cabac give a splitting of the positional sequence of the word caba (the unique word in t with prefix the letter c), and that the three sets CA(N), CB(N) and CC(N), give a splitting of the set C(N), where A := A003144, B := A003145, C := A003146. Here N is the set of positive integers. - Michel Dekking, Apr 09 2019
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LINKS
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Rémy Sigrist, Table of n, a(n) for n = 1..10000
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(n) = A003146(A003146(n)).
a(n) = 6*A003144(n) + 7*A003145(n) + 4*n = 7*A278040(n-1) + 6*A278039(n-1) + 4*n + 13, n >= 1. For a proof see the W. Lang link in A278040, Proposition 9, eq. (56). - Wolfdieter Lang, Apr 11 2019
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CROSSREFS
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Cf. A003144, A003145, A003146, A003622, A278039, A278040, A278041, and A319966-A319972.
Sequence in context: A039331 A043934 A087406 * A304157 A051876 A069174
Adjacent sequences: A319969 A319970 A319971 * A319973 A319974 A319975
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Oct 05 2018
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EXTENSIONS
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More terms from Rémy Sigrist, Oct 16 2018
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STATUS
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approved
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