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

%I A071295 #23 Aug 25 2020 12:32:37
%S A071295 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,
%T A071295 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,
%U A071295 12,10,12,12,12,10,12,12,12,12,12,12,10,10,12,12,12,12,12,12,10,12,12,12
%N A071295 Product of numbers of 0's and 1's in binary representation of n.
%C A071295 a(n) = A023416(n)*A000120(n);
%C A071295 a(1)=0, a(2*n)=(A023416(n)+1)*A000120(n), a(2*n+1)=(A000120(n)+1)*A023416(n);
%C A071295 a(n) = 0 iff n=2^k-1 for some k.
%C A071295 a(A059011(n)) mod 2 = 1. - _Reinhard Zumkeller_, Aug 09 2014
%H A071295 T. D. Noe, <a href="/A071295/b071295.txt">Table of n, a(n) for n = 0..1023</a>
%H A071295 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A071295 a(n) = a(floor(n/2)) + (1 - n mod 2) * A000120(floor(n/2)) + (n mod 2)*A023416(floor(n/2)).
%e A071295 a(14)=3 because 14 is 1110 in binary and has 3 ones and 1 zero.
%t A071295 f[n_] := Block[{s = IntegerDigits[n, 2]}, Count[s, 0] Count[s, 1]]; Table[ f[n], {n, 0, 90}]
%t A071295 Table[DigitCount[n,2,1]DigitCount[n,2,0],{n,0,100}] (* _Harvey P. Dale_, Sep 19 2019 *)
%o A071295 (Haskell)
%o A071295 a071295 n = a000120 n * a023416 n  -- _Reinhard Zumkeller_, Aug 09 2014
%o A071295 (Python)
%o A071295 def A071295(n):
%o A071295     return bin(n)[1:].count('0')*bin(n).count('1') # _Chai Wah Wu_, Dec 23 2019
%Y A071295 Cf. A007088.
%Y A071295 Cf. A000120, A023416, A059011.
%K A071295 nonn,nice,base
%O A071295 0,5
%A A071295 _Reinhard Zumkeller_, Jun 20 2002
%E A071295 Edited by _N. J. A. Sloane_ and _Robert G. Wilson v_, Oct 11 2002