



2, 9, 15, 22, 26, 33, 39, 46, 53, 59, 66, 70, 77, 83, 90, 96, 103, 107, 114, 120, 127, 134, 140, 147, 151, 158, 164, 171, 175, 182, 188, 195, 202, 208, 215, 219, 226, 232, 239, 245, 252, 256, 263, 269, 276, 283, 289, 296, 300, 307, 313, 320, 327, 333, 340, 344
(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 A319966A319972.
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 = C2, where A := A003144, B := A003145, C := A003146.  Michel Dekking, Apr 09 2019


LINKS

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), 314320. Compare page 318.
L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Fibonacci representations of higher order, Fib. Quart., 10 (1972), 4369, Theorem 13.


FORMULA

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


CROSSREFS

Cf. A003144, A003145, A003146, A003622, A278039, A278040, A278041, and A319966A319972.
Cf. A092782 (ternary tribonacci word).
Sequence in context: A063105 A215035 A324522 * A063094 A108463 A056724
Adjacent sequences: A319964 A319965 A319966 * A319968 A319969 A319970


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Oct 05 2018


EXTENSIONS

More terms from Rémy Sigrist, Oct 16 2018


STATUS

approved



