Search: id:A071295
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%I A071295
%S A071295 0,0,1,0,2,2,2,0,3,4,4,3,4,3,3,0,4,6,6,6,6,6,6,4,6,6,6,4,6,4,4,0,5,8,8,
%T A071295 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,
%U A071295 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' 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.
%H A071295 T. D. Noe, <a href="b071295.txt">Table of n, a(n) for n=0..1023</a>
%F A071295 a(n)=a(n\2)+(1 - n mod 2)*A000120(n\2)+(n mod 2)*A023416(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}]
%Y A071295 Cf. A007088.
%Y A071295 Sequence in context: A134577 A071442 A124759 this_sequence A103223 A091399 
               A000091
%Y A071295 Adjacent sequences: A071292 A071293 A071294 this_sequence A071296 A071297 
               A071298
%K A071295 nonn,nice,base
%O A071295 0,5
%A A071295 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 20 2002
%E A071295 Edited by N. J. A. Sloane (njas(AT)research.att.com) and Robert G. Wilson 
               v (rgwv(AT)rgwv.com), Oct 11 2002

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