|
%I #15 Oct 02 2018 11:14:06
%S 1,13131,131311,13131131313,13131131313313133,
%T 1313113131331313313131131313,
%U 131311313133131331313113131331313313131131311,1313113131331313313131131313313133131311313113131331313113131131313313131
%N The generalized Fibonacci words q_n^[5].
%H Lars Blomberg, <a href="/A221156/b221156.txt">Table of n, a(n) for n = 0..12</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, 5] // FromDigits;
%t Table[a[n], {n, 0, 7}] (* _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(5)-a(7) from _Lars Blomberg_, Sep 04 2017
|
