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

0,6

Links

Table of n, a(n) for n=0..104.

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

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 -> ...

Mathematica

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

Crossrefs

Sequence in context: A293119 A293133 A178471 * A089311 A086784 A104162

Adjacent sequences: A160378 A160379 A160380 * A160382 A160383 A160384

Keyword

nonn,base,easy

Author

Frank Ruskey, Jun 05 2009

Status

approved