A160381 Number of 1's in base-4 representation of n.

0, 1, 0, 0, 1, 2, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 2, 1, 1, 2, 3, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 0, 1, 0, 0, 1, 2, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 2, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 2, 1, 1, 2, 3, 2, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 3, 2, 2, 3, 4, 3, 3, 2, 3, 2, 2, 2, 3, 2, 2, 1, 2, 1, 1, 2, 3, 2, 2, 1

Offset: 0

Author

Frank Ruskey, Jun 05 2009

Keywords

• nonn
• base
• easy

Links

• F. T. Adams-Watters, F. Ruskey, Generating Functions for the Digital Sum and Other Digit Counting Sequences, JIS 12 (2009) 09.5.6

Programs

Mathematica

DigitCount[Range[0,120],4,1] (* Harvey P. Dale, Aug 28 2018 *)

Formula

Recurrence relation: a(0) = 0, a(4m+1) = 1+a(m), a(4m) = a(4m+2) = a(4m+3) = a(m).

Generating function: (1/(1-z))*Sum_{m>=0} (z^(4^m)*(1 - z^(4^m))/(1 - z^(4^(m+1)))).

Morphism: 0, j -> j,j+1,j,j; e.g., 0 -> 0100 -> 0100121101000100 -> ...