A283318 Image of 0 under repeated applications of the morphism 0 -> 0,1,0,0, 1 -> 1,1,0,1.

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

Offset

1

References

Bernardino, André, Rui Pacheco, and Manuel Silva. "Coloring factors of substitutive infinite words." Discrete Mathematics 340.3 (2017): 443-451. See Example 3.

Links

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

A. Bernardino, M. Silva, R. Pacheco, Coloring factors of substitutive infinite words, arXiv:1605.09343 [math.CO], 2016. See Example 3.

Formula

From Robert Israel, Mar 15 2017: (Start)

a(n) = a(4n) = a(4n-3).

a(4n-1) = 0.

a(4n-2) = 1.

G.f. g(x) satisfies g(x) = (1+1/x^3) g(x^4) + x^2/(1-x^4). (End)

Maple

with(ListTools);
psi:=proc(S)
Flatten(subs( {0=[0, 1, 0, 0], 1=[1, 1, 0, 1]}, S));
end;
S:=[0];
for n from 1 to 6 do S:=psi(S): od:
S;

Mathematica

SubstitutionSystem[{0 -> {0, 1, 0, 0}, 1 -> {1, 1, 0, 1}}, {0}, 4] // Last (* Jean-François Alcover, Jan 21 2018 *)

Crossrefs

Cf. A283316, A283317.

Sequence in context: A157238 A337546 A059448 * A288633 A284775 A156259

Adjacent sequences: A283315 A283316 A283317 * A283319 A283320 A283321

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 09 2017

Status

approved