A277731 Fixed point of the morphism 0 -> 01, 1 -> 012, 2 -> 0; starting with a(1) = 0.

0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 2

Offset: 1

Author

N. J. A. Sloane, Nov 07 2016

Keywords

• nonn

Comments

After k = 0,1,2,3,... applications of the morphism we have 0, 01, 01012, 01012010120, ... which have lengths 1, 2, 5, 11, 24, 53, 117, ..., satisfying b(n) = 2*b(n-1) + b(n-3) (cf. A052980).

Links

• N. J. A. Sloane, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A052980, A277732, A277733, A277734.

Programs

Maple

with(ListTools);
T:=proc(S) Flatten(subs( {0=[0,1], 1=[0,1,2], 2=[0]}, S)); end;
S:=[0];
for n from 1 to 10 do S:=T(S); od:
S;

Mathematica

m = 100; (* number of terms required *)
S[1] = {0};
S[n_] := S[n] = SubstitutionSystem[{0 -> {0, 1}, 1 -> {0, 1, 2}, 2 -> {0}}, S[n-1]];
For[n = 2, True, n++, If[PadRight[S[n], m] == PadRight[S[n-1], m], Print["n = ", n]; Break[]]];
Take[S[n], m] (* Jean-François Alcover, Mar 20 2023 *)