A071295 Product of numbers of 0's and 1's in binary representation of n.

0, 0, 1, 0, 2, 2, 2, 0, 3, 4, 4, 3, 4, 3, 3, 0, 4, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 4, 6, 4, 4, 0, 5, 8, 8, 9, 8, 9, 9, 8, 8, 9, 9, 8, 9, 8, 8, 5, 8, 9, 9, 8, 9, 8, 8, 5, 9, 8, 8, 5, 8, 5, 5, 0, 6, 10, 10, 12, 10, 12, 12, 12, 10, 12, 12, 12, 12, 12, 12, 10, 10, 12, 12, 12, 12, 12, 12, 10, 12, 12, 12

Offset: 0

Author

Reinhard Zumkeller, Jun 20 2002

Keywords

• nonn
• nice
• base

Comments

a(n) = A023416(n)*A000120(n);

a(1)=0, a(2*n)=(A023416(n)+1)*A000120(n), a(2*n+1)=(A000120(n)+1)*A023416(n);

a(n) = 0 iff n=2^k-1 for some k.

a(A059011(n)) mod 2 = 1. - Reinhard Zumkeller, Aug 09 2014

Examples

			a(14)=3 because 14 is 1110 in binary and has 3 ones and 1 zero.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..1023
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A007088.

Cf. A000120, A023416, A059011.

Programs

Haskell

a071295 n = a000120 n * a023416 n  -- Reinhard Zumkeller, Aug 09 2014

Mathematica

f[n_] := Block[{s = IntegerDigits[n, 2]}, Count[s, 0] Count[s, 1]]; Table[ f[n], {n, 0, 90}]
Table[DigitCount[n,2,1]DigitCount[n,2,0],{n,0,100}] (* Harvey P. Dale, Sep 19 2019 *)

Python

def A071295(n):
    return bin(n)[1:].count('0')*bin(n).count('1') # Chai Wah Wu, Dec 23 2019

Formula

a(n) = a(floor(n/2)) + (1 - n mod 2) * A000120(floor(n/2)) + (n mod 2)*A023416(floor(n/2)).

Extensions

Edited by N. J. A. Sloane and Robert G. Wilson v, Oct 11 2002