A140474 - OEIS

%I #2 Oct 12 2012 14:54:50

%S 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,

%T 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,

%U 15,15,15,15,15,15,15,15,17,15,17,15,17,16,17,17,17,18,18,18,18,18,18,18

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

%C Two general types seem to exist:

%C 1) a(n)=a(n-a(n-1))+a(Floor[a0*n/b0]): a0<b0 ( noise-like)

%C 2) a(n)=a(Floor[a0*n/b0])+a(Floor[c0*n/b0]): c0<a0<b0 ( step-like)

%F a(n)=a(n-a(n-1))+a(Floor[a0*n/b0]): a0<b0:a0=1;b0=8

%t 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}]

%Y Cf. A004001.

%K nonn

%O 1,4

%A _Roger L. Bagula_ and _Gary W. Adamson_, Jun 28 2008