A160382 Number of 2's in base-4 representation of n.

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

Offset: 0

Author

Frank Ruskey, Jun 05 2009

Keywords

• nonn
• base
• easy

Links

• Dominic McCarty, Table of n, a(n) for n = 0..10000
• Franklin T. Adams-Watters and Frank Ruskey, Generating Functions for the Digital Sum and Other Digit Counting Sequences, JIS 12 (2009) 09.5.6.

Crossrefs

Cf. A007090.

Programs

Mathematica

DigitCount[Range[0,110],4,2] (* Harvey P. Dale, Sep 09 2024 *)

PARI

a(n) = #select(x->(x==2), digits(n, 4)); \\ Michel Marcus, Mar 24 2020

Formula

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

G.f.: (1/(1-z))*Sum_{m>=0} (z^(2*4^m)*(1 - z^(4^m))/(1 - z^(4^(m+1)))).

Morphism: 0, j -> j,j,j+1,j; e.g., 0 -> 0010 -> 0010110111210010 -> ...