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%I #19 Apr 11 2019 10:09:19
%S 24,68,105,149,173,217,254,298,342,379,423,447,491,528,572,609,653,
%T 677,721,758,802,846,883,927,951,995,1032,1076,1100,1144,1181,1225,
%U 1269,1306,1350,1374,1418,1455,1499,1536,1580,1604,1648,1685,1729,1773,1810,1854
%N a(n) = A003146(A003146(n)).
%C 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.
%C 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
%H Rémy Sigrist, <a href="/A319972/b319972.txt">Table of n, a(n) for n = 1..10000</a>
%H Elena Barcucci, Luc Belanger and Srecko Brlek, <a href="http://www.fq.math.ca/Papers1/42-4/quartbarcucci04_2004.pdf">On tribonacci sequences</a>, Fib. Q., 42 (2004), 314-320. Compare page 318.
%F a(n) = A003146(A003146(n)).
%F 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
%Y Cf. A003144, A003145, A003146, A003622, A278039, A278040, A278041, and A319966-A319972.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, Oct 05 2018
%E More terms from _Rémy Sigrist_, Oct 16 2018
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