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

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, 17, 22, 20, 21, 21, 24, 21, 25, 25, 25, 26, 28, 30, 28, 27, 33, 29, 31, 30, 33, 30, 37, 34, 33, 38, 34, 39, 36, 39, 40, 42, 40, 44, 40, 43, 41, 48, 45, 43, 49, 44, 46, 51, 47, 46, 58, 48

Offset: 0

Author

Roger L. Bagula, Oct 16 2008

Keywords

• nonn

Programs

Mathematica

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}]

Python

from sympy import cacheit
@cacheit
def A143089(n):
    if n <= 1:
        return 1
    else:
        return A143089(n-A143089(n-1))+A143089(2*n//3)
print([A143089(n) for n in range(40)]) # Oct 18 2009

Extensions

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