A381101 Allouche-Johnson binary sequence based on the Narayana's cows sequence A000930.

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, 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, 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

Offset

0

Links

Table of n, a(n) for n=0..129.

J.-P. Allouche and T. Johnson, Narayana's cows and delayed morphisms, 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]

J.-P. Allouche and T. Johnson, Narayana's cows and delayed morphisms, 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]

Formula

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.

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.

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

Crossrefs

Cf. A000930.

Sequence in context: A131720 A131719 A342460 * A100656 A285274 A189081

Adjacent sequences: A381097 A381098 A381100 * A381102 A381104 A381105

Keyword

nonn,new

Author

Jeffrey Shallit, Feb 16 2025

Status

approved