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A221168 The infinite generalized Fibonacci word p^[4]. 5

%I #17 Nov 30 2017 04:06:05

%S 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,

%T 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,

%U 0,1,2,1,2,1,0,1,0,1,0,3,0,3,0,3,2,3

%N The infinite generalized Fibonacci word p^[4].

%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], 2012-2014.

%p # fmorph, sigma1f and sigma01f are defined in A221166.

%p A221168 := proc(n)

%p sigma01f(n,4) ;

%p end proc: # _R. J. Mathar_, Jul 09 2013

%t 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]]];

%t 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]]]]]];

%t fmorph[n_, i_] := If[fibonni[n, i] == 0, 2, 0];

%t sigma1f[n_, i_] := If[n == 0, 1, 1 + Mod[Sum[fmorph[j, i], {j, 0, n - 1}], 4]];

%t 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_ *)

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

%K nonn

%O 0,6

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

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