A283318 - OEIS

%I #18 Jan 21 2018 09:36:08

%S 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,

%T 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,

%U 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

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

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

%H Robert Israel, <a href="/A283318/b283318.txt">Table of n, a(n) for n = 1..10000</a>

%H A. Bernardino, M. Silva, R. Pacheco, <a href="https://arxiv.org/abs/1605.09343">Coloring factors of substitutive infinite words</a>, arXiv:1605.09343 [math.CO], 2016. See Example 3.

%F From _Robert Israel_, Mar 15 2017: (Start)

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

%F a(4n-1) = 0.

%F a(4n-2) = 1.

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

%p with(ListTools);

%p psi:=proc(S)

%p Flatten(subs( {0=[0,1,0,0], 1=[1,1,0,1]}, S));

%p end;

%p S:=[0];

%p for n from 1 to 6 do S:=psi(S): od:

%p S;

%t SubstitutionSystem[{0 -> {0, 1, 0, 0}, 1 -> {1, 1, 0, 1}}, {0}, 4] // Last (* _Jean-François Alcover_, Jan 21 2018 *)

%Y Cf. A283316, A283317.

%K nonn,easy

%O 1

%A _N. J. A. Sloane_, Mar 09 2017