A221153 The generalized Fibonacci words q_n^[2].

1, 13, 133, 13313, 13313311, 1331331131131, 133133113113113313311, 1331331131131133133113113113313313, 1331331131131133133113113113313313311311331331331131133, 13313311311311331331131131133133133113113313313311311331331331131131133133113113113313313

Offset

0,2

Links

Lars Blomberg, Table of n, a(n) for n = 0..14

José L. Ramírez, Gustavo N. Rubiano, and Rodrigo de Castro, A Generalization of the Fibonacci Word Fractal and the Fibonacci Snowflake, arXiv preprint arXiv:1212.1368 [cs.DM], 2012.

Mathematica

bar[a_List] := a /. {1 -> 3, 3 -> 1};
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;
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]]];
a[n_] := q[n+1, 2] // FromDigits;
Table[a[n], {n, 0, 9}] (* Jean-François Alcover, Oct 02 2018 *)

Crossrefs

Cf. A221153, A221154, A221155, A221156.

Sequence in context: A073556 A154999 A228277 * A297335 A262572 A132935

Adjacent sequences: A221150 A221151 A221152 * A221154 A221155 A221156

Keyword

nonn

Author

N. J. A. Sloane, Jan 04 2013

Extensions

a(6)-a(9) from Lars Blomberg, Sep 04 2017

Status

approved