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

0,5

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

Links

T. D. Noe, Table of n, a(n) for n = 0..1023

Index entries for sequences related to binary expansion of n

Formula

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

Example

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

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 *)

Prog

(Haskell)
a071295 n = a000120 n * a023416 n  -- Reinhard Zumkeller, Aug 09 2014
(Python)
def A071295(n):
    return bin(n)[1:].count('0')*bin(n).count('1') # Chai Wah Wu, Dec 23 2019

Crossrefs

Cf. A007088.

Cf. A000120, A023416, A059011.

Sequence in context: A071442 A174740 A124759 * A296062 A214178 A117652

Adjacent sequences: A071292 A071293 A071294 * A071296 A071297 A071298

Keyword

nonn,nice,base

Author

Reinhard Zumkeller, Jun 20 2002

Extensions

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

Status

approved