

A168160


Number of 0's in the matrix whose lines are the binary expansion of the numbers 1,...,n.


1



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, 70, 71, 73, 74, 75, 75, 111, 115, 119, 122, 126, 129, 132, 134, 138, 141, 144, 146, 149, 151, 153, 154, 158, 161, 164, 166, 169, 171, 173, 174, 177, 179, 181, 182, 184, 185, 186
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OFFSET

1,2


COMMENTS

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.
The number of zeros in the last line of the matrix is given by A023416(n).
One has a(n)=a(n1) iff n = 2^k1 for some k.


LINKS

Table of n, a(n) for n=1..62.


FORMULA

A168160(n)=n*A070939(n)A000788(n).


EXAMPLE

a(4)=7 is the number of zeros in the matrix
[001] /* = 1 in binary */
[010] /* = 2 in binary */
[011] /* = 3 in binary */
[100] /* = 4 in binary */


PROG

(PARI) A168160(n)=n*#binary(n)sum(i=1, n, norml2(binary(i)))


CROSSREFS

Cf. A059015.
Sequence in context: A151864 A019732 A199467 * A005300 A019087 A293607
Adjacent sequences: A168157 A168158 A168159 * A168161 A168162 A168163


KEYWORD

base,nonn


AUTHOR

M. F. Hasler, Nov 22 2009


STATUS

approved



