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A140474
Fractional noise-like sequence: a(n)=a(n-a(n-1))+a(Floor[a0*n/b0]): a0<b0:a0=1;b0=8.
0
1, 0, 1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9, 9, 11, 10, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 14, 12, 14, 13, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 17, 15, 17, 15, 17, 16, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18
OFFSET
1,4
COMMENTS
Two general types seem to exist:
1) a(n)=a(n-a(n-1))+a(Floor[a0*n/b0]): a0<b0 ( noise-like)
2) a(n)=a(Floor[a0*n/b0])+a(Floor[c0*n/b0]): c0<a0<b0 ( step-like)
FORMULA
a(n)=a(n-a(n-1))+a(Floor[a0*n/b0]): a0<b0:a0=1;b0=8
MATHEMATICA
a[0] = 1; a[1] = 0; a[2] = 1; a[n_] := a[n] = a[n - a[n - 1]] + a[Floor[n/8]] b = Table[a[n], {n, 0, 200}]
CROSSREFS
Cf. A004001.
Sequence in context: A063510 A156878 A214454 * A091195 A280617 A072375
KEYWORD
nonn
AUTHOR
STATUS
approved