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%I #29 Oct 11 2022 14:18:37
%S 1,1,1,1,2,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,
%T 6,7,7,7,7,7,7,8,8,8,8,8,8,8,9,9,9,9,9,9,9,10,10,10,10,10,10,11,11,11,
%U 11,11,11,11,12,12,12,12,13,13,13,13,13,13,13,14,14,14,14,14,14,15,15,15,15,15
%N Partial sums of A276791.
%C a(n+1) - 1 = z_C(n), where z_C(n) is the number of C numbers A276798 not exceeding n, for n >= 0, and z_C(-1) = 0. - _Wolfdieter Lang_, Dec 05 2018
%C Conjecture: 3*n - A140101(n) = a(n-1). - _N. J. A. Sloane_, Oct 26 2016 (added Mar 21 2019). This is true - see the Dekking et al. paper. - _N. J. A. Sloane_, Jul 22 2019
%H N. J. A. Sloane, <a href="/A276798/b276798.txt">Table of n, a(n) for n = 0..10000</a>
%H F. Michel Dekking, Jeffrey Shallit, and N. J. A. Sloane, <a href="https://www.combinatorics.org/ojs/index.php/eljc/article/view/v27i1p52/8039">Queens in exile: non-attacking queens on infinite chess boards</a>, Electronic J. Combin., 27:1 (2020), #P1.52.
%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 Jeffrey Shallit, <a href="https://arxiv.org/abs/2210.03996">Some Tribonacci conjectures</a>, arXiv:2210.03996 [math.CO], 2022.
%F a(n) = Sum_{k=0..n} A276791(k), for n >= 0.
%F a(n) = n + 1 - (A276796(n) + A276797(n).
%F a(n) = 2*n + 1 - B(n), where B(n) = A278039(n), n >= 0. For a proof see the comment on z_C and Proposition 7, eq. 43, of the W. Lang link given in A080843. - _Wolfdieter Lang_, Dec 05 2018
%p M:=12;
%p S[1]:=`0`; S[2]:=`01`; S[3]:=`0102`;
%p for n from 4 to M do S[n]:=cat(S[n-1], S[n-2], S[n-3]); od:
%p t0:=S[M]: # has 927 terms of tribonacci ternary word A080843
%p # get numbers of 0's, 1's, 2's
%p N0:=[]: N1:=[]: N2:=[]: c0:=0: c1:=0: c2:=0:
%p L:=length(t0);
%p for i from 1 to L do
%p js := substring(t0, i..i);
%p j:=convert(js,decimal,10);
%p if j=0 then c0:=c0+1; elif j=1 then c1:=c1+1; else c2:=c2+1; fi;
%p N0:=[op(N0),c0]; N1:=[op(N1),c1]; N2:=[op(N2),c2];
%p od:
%p N0; N1; N2; # prints A276796, A276797, A276798 (except A276798 is off by 1 because it does not count the initial 0 in A003146). # _N. J. A. Sloane_, Jun 08 2018
%Y A276793(n) + A276794(n) + A276791(n) = 1;
%Y A276796(n) + A276797(n) + A276798(n) = n + 1.
%Y Cf. A276798, A278039.
%K nonn,easy
%O 0,5
%A _N. J. A. Sloane_, Oct 28 2016
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