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First differences of A140102.
9

%I #26 Mar 07 2020 13:50:20

%S 1,2,1,1,1,2,1,1,2,1,1,1,2,1,2,1,1,1,2,1,1,2,1,1,1,2,1,1,1,2,1,1,2,1,

%T 1,1,2,1,2,1,1,1,2,1,1,2,1,1,1,2,1,1,2,1,1,1,2,1,2,1,1,1,2,1,1,2,1,1,

%U 1,2,1,1,1,2,1,1,2,1,1,1,2,1,2,1,1,1,2,1,1,2,1,1,1,2,1,2,1,1

%N First differences of A140102.

%C Although initially this agrees with A293630, the sequences are distinct.

%C From _Michel Dekking_, Mar 18 2019: (Start)

%C Let x be the tribonacci word x = A092782 = 1,2,1,3,1,2,1,1,...

%C Consider the morphism delta:

%C 1 -> 1112,

%C 2 -> 112,

%C 3 -> 12.

%C Conjecture: (a(n)) = 12 delta(x).

%C (End)

%C Conjecture: This sequence (prefixed by 1 since A140102 should really begin with 0) is 1.TTW(1,2,1) where TTW is the ternary tribonacci word defined in A080843, or equally it is THETA(1,2,1), where THETA is defined in A275925. - _N. J. A. Sloane_, Mar 19 2019

%C All these conjectures are now theorems - see the Dekking et al. paper. - _N. J. A. Sloane_, Jul 22 2019

%H N. J. A. Sloane, <a href="/A305393/b305393.txt">Table of n, a(n) for n = 1..49999</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.

%F a(n) = A140102(n+1)-A140102(n), n >= 1.

%Y For first differences of A140100, A140101, A140102, A140103 see A305392, A305374, A305393, A305394.

%Y Cf. A293630.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jun 23 2018