A381101 - OEIS

%I #23 Feb 19 2025 11:47:41

%S 0,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0,0,1,1,0,0,0,0,1,0,1,1,1,0,0,0,0,1,

%T 0,1,1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,1,1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,

%U 1,0,1,1,1,0,1,1,1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0,1,1,0,1,1,1,0,1,1,1,1,0,0,1,1,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,0,1

%N Allouche-Johnson binary sequence based on the Narayana's cows sequence A000930.

%H J.-P. Allouche and T. Johnson, <a href="https://hal.science/hal-02986050v1">Narayana's cows and delayed morphisms</a>, in G. Assayag, M. Chemillier, and C. Eloy, Troisièmes Journées d'Informatique Musicale, JIM '96, Île de Tatihou, France, 1996, pp. 2-7. [The hal link does not always work. - _N. J. A. Sloane_, Feb 19 2025]

%H J.-P. Allouche and T. Johnson,  <a href="/A000930/a000930.pdf">Narayana's cows and delayed morphisms</a>, in G. Assayag, M. Chemillier, and C. Eloy, Troisièmes Journées d'Informatique Musicale, JIM '96, Île de Tatihou, France, 1996, pp. 2-7. [Local copy with annotations and a correction from _N. J. A. Sloane_, Feb 19 2025]

%F The sequence can be generated by iterating a morphism starting with a:  a->ab, b->c, c->d, d->de, e->f, f->a, and then replacing a,e,f with 0 and b,c,d with 1.

%F Alternatively it can be generated by setting X(0) = X(1) = X(2) = 0 and X(n) = X(n-1) X(n-3)', where ' means take the binary complement of each symbol.  We find X(3) = 01, X(4) = 011, X(5) = 0111, X(6) = 011110, X(7) = 011110100, ... and the limiting sequence is this one.

%F In both cases, the iterates are of length A000930(n).

%Y Cf. A000930.

%K nonn,new

%O 0

%A _Jeffrey Shallit_, Feb 16 2025