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a(n) = a(n - a(n-1)) + a(floor(2*n/3)).
2

%I #6 May 19 2020 12:58:49

%S 1,1,2,3,3,5,4,6,7,6,7,9,10,10,9,11,12,14,13,14,14,15,15,18,16,18,21,

%T 17,22,20,21,21,24,21,25,25,25,26,28,30,28,27,33,29,31,30,33,30,37,34,

%U 33,38,34,39,36,39,40,42,40,44,40,43,41,48,45,43,49,44,46,51,47,46,58,48

%N a(n) = a(n - a(n-1)) + a(floor(2*n/3)).

%t Clear[a, f, b, c, g] (*fractal noise chaotic sequence*) f[0] = 1; f[1] = 0; f[1] = 1; f[n_] := f[n] = f[n - f[n - 1]] + f[Floor[2*n/3]] (*Cantor like fractal stair step chaotic sequence*) g[0] = 1; g[1] = 0; g[1] = 1; g[n_] := g[n] = g[Floor[2*n/3]] + g[Floor[n/3]]; ListPlot[Table[{f[n], g[n]}, {n, 0, 200}], PlotJoined -> True]; Table[f[n], {n, 0, 200}]

%o (Python)

%o from sympy import cacheit

%o @cacheit

%o def A143089(n):

%o if n <= 1:

%o return 1

%o else:

%o return A143089(n-A143089(n-1))+A143089(2*n//3)

%o print([A143089(n) for n in range(40)]) # Oct 18 2009

%K nonn

%O 0,3

%A _Roger L. Bagula_, Oct 16 2008

%E Corrected offset, adopted OEIS standards of nomenclature - The Assoc. Editors of the OEIS, Oct 18 2009