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A071295
Product of numbers of 0's and 1's in binary representation of n.
6
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
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
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