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A278039 The tribonacci representation of a(n) is obtained by appending a 0 to the tribonacci representation of n (cf. A278038).

%I A278039 #35 Apr 04 2019 23:04:08
%S A278039 0,2,4,6,7,9,11,13,15,17,19,20,22,24,26,28,30,31,33,35,37,39,41,43,44,
%T A278039 46,48,50,51,53,55,57,59,61,63,64,66,68,70,72,74,75,77,79,81,83,85,87,
%U A278039 88,90,92,94,96,98,100,101,103,105,107,109,111,112,114,116,118,120,122,124,125,127,129,131,132,134,136
%N A278039 The tribonacci representation of a(n) is obtained by appending a 0 to the tribonacci representation of n (cf. A278038).
%C A278039 This sequence records the indices for the 0 values of A080843, ordered increasingly. In the W. Lang link a(n) = B(n). - _Wolfdieter Lang_, Dec 06 2018
%C A278039 Sequence gives the positions of letter a in the tribonacci word generated by a->ab, b->ac, c->a, when given offset 0. - _Michel Dekking_, Apr 03 2019
%H A278039 N. J. A. Sloane, <a href="/A278039/b278039.txt">Table of n, a(n) for n = 0..20000</a>
%H A278039 Wolfdieter Lang, <a href="https://arxiv.org/abs/1810.09787">The Tribonacci and ABC Representations of Numbers are Equivalent</a>, arXiv:1810.09787v1 [math.NT], 2018.
%H A278039 Bo Tan and Zhi-Ying Wen, <a href="http://dx.doi.org/10.1016/j.ejc.2006.07.007">Some properties of the Tribonacci sequence</a>, European Journal of Combinatorics, 28 (2007) 1703-1719. See the sequence O_1(n).
%F A278039 a(n) = A003144(n+1) - 1 = Sum_{k=1..n} A276788(k), n >= 0 (an empty sum is 0).
%F A278039 a(n) = 2*n - (A276798(n) - 1), n >= 0. For a proof see the link, Proposition 6 B). - _Wolfdieter Lang_, Dec 04 2018
%e A278039 The tribonacci representation of 7 is 1000 (see A278038), so a(7) has tribonacci representation 10000, which is 13, so a(7) = 13.
%Y A278039 Cf. A003144, A276798, A278038, A278040, A278041.
%Y A278039 Partial sums of A276788.
%K A278039 nonn,base
%O A278039 0,2
%A A278039 _N. J. A. Sloane_, Nov 18 2016