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%I #40 Oct 17 2022 01:45:47
%S 1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,
%T 0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,
%U 1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0
%N Indicator function for A003144.
%C a(n) = 1 iff n is a term of A003144.
%C The binary complement of (a(n)) is called the "binary Tribonacci word" in Mousavi and Shallit (see Theorem 23). It is defined to be the change of alphabet {0,1,2} -> {0,1,1} of the tribonacci word 0102010010... - _Michel Dekking_, Oct 12 2019
%H Michel Dekking, <a href="/A276793/b276793.txt">Table of n, a(n) for n = 1..10000</a>
%H Wolfdieter Lang, <a href="https://arxiv.org/abs/1810.09787">The Tribonacci and ABC Representations of Numbers are Equivalent</a>, arXiv preprint arXiv:1810.09787 [math.NT], 2018.
%H Hamoon Mousavi and Jeffrey Shallit, <a href="https://arxiv.org/abs/1407.5841">Mechanical Proofs of Properties of the Tribonacci Word</a>, arXiv:1407.5841 [cs.FL], 2014.
%H H. Mousavi and J. Shallit, <a href="https://doi.org/10.1007/978-3-319-23660-5_15">Mechanical Proofs of Properties of the Tribonacci Word</a>, In: Manea F., Nowotka D. (eds) Combinatorics on Words. WORDS 2015. Lecture Notes in Computer Science, vol 9304. Springer, 2015, pp. 170-190.
%F a(n) = (A080843(n-1)-1)*(A080843(n-1)-2)/2. - _Wolfdieter Lang_, Dec 06 2018
%Y Cf. A003144, A080843, A276796.
%Y A276793(n) + A276794(n) + A276791(n) = 1; A276796(n) + A276797(n) + A276798(n) = n+1.
%K nonn,easy
%O 1
%A _N. J. A. Sloane_, Oct 28 2016
%E Data and offset changed by _Michel Dekking_, Oct 12 2019
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