A140474 Fractional noise-like sequence: a(n)=a(n-a(n-1))+a(Floor[a0*n/b0]): a0<b0:a0=1;b0=8.

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)

Links

Table of n, a(n) for n=1..83.

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

Adjacent sequences: A140471 A140472 A140473 * A140475 A140476 A140477

Keyword

nonn

Author

Roger L. Bagula and Gary W. Adamson, Jun 28 2008

Status

approved