A221168 The infinite generalized Fibonacci word p^[4].

0, 1, 0, 1, 0, 3, 0, 3, 0, 3, 2, 3, 2, 3, 0, 3, 0, 3, 0, 1, 0, 1, 0, 1, 2, 1, 2, 1, 0, 1, 0, 1, 0, 3, 0, 3, 0, 1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1, 2, 1, 0, 1, 0, 1, 0, 3, 0, 3, 0, 1, 0, 1, 0, 1, 2, 1, 2, 1, 0, 1, 0, 1, 0, 3, 0, 3, 0, 3, 2, 3

Offset

0,6

Links

Table of n, a(n) for n=0..85.

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], 2012-2014.

Maple

# fmorph, sigma1f and sigma01f are defined in A221166.
A221168 := proc(n)
        sigma01f(n, 4) ;
end proc: # R. J. Mathar, Jul 09 2013

Mathematica

fibi[n_, i_] := fibi[n, i] = Which[n == 0, {0}, n == 1, Append[Table[0, {j, 1, i - 1}], 1], True, Join[fibi[n - 1, i], fibi[n - 2, i]]];
fibonni[n_, i_] := fibonni[n, i] = Module[{fn, Fn}, For[fn = 0, True, fn++, Fn = fibi[fn, i]; If[Length[Fn] >= n + 1 && Length[Fn] > i + 3, Return[Fn[[n + 1]]]]]];
fmorph[n_, i_] := If[fibonni[n, i] == 0, 2, 0];
sigma1f[n_, i_] := If[n == 0, 1, 1 + Mod[Sum[fmorph[j, i], {j, 0, n - 1}], 4]];
sigma01f[n_, i_] := If[n == 0, 0, Mod[Sum[sigma1f[j, i], {j, 0, n - 1}], 4]]; a[n_] := sigma01f[n, 4]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Nov 30 2017, after R. J. Mathar *)

Crossrefs

Cf. A221166, A221167, A221169, A221170, A221171.

Sequence in context: A221170 A307199 A141030 * A194084 A262281 A297871

Adjacent sequences: A221165 A221166 A221167 * A221169 A221170 A221171

Keyword

nonn

Author

N. J. A. Sloane, Jan 04 2013

Status

approved