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%I #29 Apr 09 2019 03:28:50
%S 2,9,15,22,26,33,39,46,53,59,66,70,77,83,90,96,103,107,114,120,127,
%T 134,140,147,151,158,164,171,175,182,188,195,202,208,215,219,226,232,
%U 239,245,252,256,263,269,276,283,289,296,300,307,313,320,327,333,340,344
%N a(n) = A003145(A003144(n)) where A003144 and A003145 are positions of '1' and '2' in the tribonacci word A092782.
%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 bac 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 ac is always preceded in t by the letter b, and the formula BA = C-2, where A := A003144, B := A003145, C := A003146. - _Michel Dekking_, Apr 09 2019
%H Rémy Sigrist, <a href="/A319967/b319967.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.
%H L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., <a href="http://www.fq.math.ca/Scanned/10-1/carlitz3-a.pdf">Fibonacci representations of higher order</a>, Fib. Quart., 10 (1972), 43-69, Theorem 13.
%F a(n+1) = B(A(n)) = B(A(n) + 1) - 2 = A(n) + B(n) + n + 1, for n >= 0, where B = A278039 and A = A278040. For a proof see the W. Lang link in A278040, Proposition 9, eq. (51). - _Wolfdieter Lang_, Dec 13 2018
%Y Cf. A003144, A003145, A003146, A003622, A278039, A278040, A278041, and A319966-A319972.
%Y Cf. A092782 (ternary tribonacci word).
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_, Oct 05 2018
%E More terms from _Rémy Sigrist_, Oct 16 2018
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