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A319972 a(n) = A003146(A003146(n)). 16
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
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
LINKS
Elena Barcucci, Luc Belanger and Srecko Brlek, On tribonacci sequences, Fib. Q., 42 (2004), 314-320. Compare page 318.
FORMULA
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
CROSSREFS
Sequence in context: A039331 A043934 A087406 * A304157 A051876 A069174
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 05 2018
EXTENSIONS
More terms from Rémy Sigrist, Oct 16 2018
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)