A189673 Fixed point of the morphism 0->010, 1->110.

0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1

Offset

1

Comments

Is this a shifted version of A137893? - R. J. Mathar, May 16 2011

A generalized choral sequence c(3n+r_0)=0, c(3n+r_1)=1, c(3n+r_c)=c(n), with r_0=2, r_1=1, r_c=0, and c(0)=0. - Joel Reyes Noche, Jun 14 2021

References

Joel Reyes Noche, Generalized Choral Sequences, Matimyas Matematika, 31(2008), 25-28.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Mazen Khodier, New Methods for Analyzing the Properties of Automatic Sequences, Master's Thesis, Univ. Waterloo (Canada 2026). See p. 27, Table 5.1.

Joel Reyes Noche, On generalized choral sequences, Gibon, IX(2011), 51-69.

Formula

a(3*k-2) = a(k), a(3*k - 1) = 1, a(3*k) = 0 for k >= 1, a(0) = 0.

G.f. satisfies g(x) = x^2/(1-x^3) + g(x^3)/x^2. - Robert Israel, Feb 15 2017

Example

0->010->010110010->

Maple

f:= proc(n) option remember;
  if n mod 3 = 1 then procname((n+2)/3) else -n mod 3 fi;
end proc:
f(1):= 0:
map(f, [$1..200]); # Robert Israel, Feb 15 2017

Mathematica

t = Nest[Flatten[# /. {0->{0, 1, 0}, 1->{1, 1, 0}}] &, {0}, 5] (*A189673*)
f[n_] := t[[n]]
Flatten[Position[t, 0]] (* A026227 conjectured *)
Flatten[Position[t, 1]] (* A026138 conjectured *)
s[n_] := Sum[f[i], {i, 1, n}]; s[0] = 0;
Table[s[n], {n, 1, 120}] (*A189674*)

Crossrefs

Cf. A189628, A026227, A026138, A189674.

Sequence in context: A118006 A372258 A285196 * A189014 A189017 A189132

Adjacent sequences: A189670 A189671 A189672 * A189674 A189675 A189676

Keyword

nonn

Author

Clark Kimberling, Apr 25 2011

Status

approved