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A143089 a(n) = a(n - a(n-1)) + a(floor(2*n/3)).

%I A143089 #6 May 19 2020 12:58:49
%S A143089 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 A143089 17,22,20,21,21,24,21,25,25,25,26,28,30,28,27,33,29,31,30,33,30,37,34,
%U A143089 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 A143089 a(n) = a(n - a(n-1)) + a(floor(2*n/3)).
%t A143089 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 A143089 (Python)
%o A143089 from sympy import cacheit
%o A143089 @cacheit
%o A143089 def A143089(n):
%o A143089     if n <= 1:
%o A143089         return 1
%o A143089     else:
%o A143089         return A143089(n-A143089(n-1))+A143089(2*n//3)
%o A143089 print([A143089(n) for n in range(40)]) # Oct 18 2009
%K A143089 nonn
%O A143089 0,3
%A A143089 _Roger L. Bagula_, Oct 16 2008
%E A143089 Corrected offset, adopted OEIS standards of nomenclature - The Assoc. Editors of the OEIS, Oct 18 2009