%I #3 Jul 14 2012 11:32:32
%S 0,2,2,7,8,9,9,19,21,23,24,26,27,28,28,47,50,53,55,58,60,62,63,66,68,
%T 70,71,73,74,75,75,111,115,119,122,126,129,132,134,138,141,144,146,
%U 149,151,153,154,158,161,164,166,169,171,173,174,177,179,181,182,184,185,186
%N Number of 0's in the matrix whose lines are the binary expansion of the numbers 1,...,n.
%C The matrix is to be taken of minimal size, i.e., have n lines and the number of columns needed to write n in base 2 in the last line, A070939(n). Otherwise said, there is no zero column.
%C The number of zeros in the last line of the matrix is given by A023416(n).
%C One has a(n)=a(n-1) iff n = 2^k-1 for some k.
%F A168160(n)=n*A070939(n)-A000788(n).
%e a(4)=7 is the number of zeros in the matrix
%e [001] /* = 1 in binary */
%e [010] /* = 2 in binary */
%e [011] /* = 3 in binary */
%e [100] /* = 4 in binary */
%o (PARI) A168160(n)=n*#binary(n)-sum(i=1,n,norml2(binary(i)))
%Y Cf. A059015.
%K base,nonn
%O 1,2
%A _M. F. Hasler_, Nov 22 2009
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