A221154 - OEIS

%I #15 Oct 02 2018 11:14:18

%S 1,131,1311,1311313,13113133133,131131331331311313,

%T 13113133133131131331331311311,

%U 13113133133131131331331311311313313113113133131,1311313313313113133133131131131331311311313313113113133133131131331331311311

%N The generalized Fibonacci words q_n^[3].

%H Lars Blomberg, <a href="/A221154/b221154.txt">Table of n, a(n) for n = 0..13</a>

%H José L. Ramírez, Gustavo N. Rubiano, and Rodrigo de Castro, <a href="http://arxiv.org/abs/1212.1368">A Generalization of the Fibonacci Word Fractal and the Fibonacci Snowflake</a>, arXiv preprint arXiv:1212.1368 [cs.DM], 2012.

%t bar[a_List] := a /. {1 -> 3, 3 -> 1};

%t q[0, _] = {}; q[1, _] = {1}; q[2, i_] := If[EvenQ[i], Table[{1, 3}, {i/2}], Append[Table[{1, 3}, {(i-1)/2}], 1]] // Flatten;

%t q[n_, i_] := q[n, i] = If[EvenQ[i], If[Mod[n, 3] == 1, Join[q[n-1, i], q[n-2, i]], Join[q[n-1, i], q[n-2, i] // bar]], If[Mod[n, 3] == 0, Join[q[n-1, i], q[n-2, i]], Join[q[n-1, i], q[n-2, i] // bar]]];

%t a[n_] := q[n+1, 3] // FromDigits;

%t Table[a[n], {n, 0, 8}] (* _Jean-François Alcover_, Oct 02 2018 *)

%Y Cf. A221153, A221154, A221155, A221156.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Jan 04 2013

%E a(6)-a(8) from _Lars Blomberg_, Sep 04 2017