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A059451 Number of ways n can be written as the sum of two numbers whose binary expansions have even numbers of zeros; also number of ways n can be written as the sum of two numbers whose binary expansions have odd numbers of zeros. 0
0, 1, 0, 1, 1, 1, 1, 2, 0, 2, 2, 1, 3, 2, 1, 3, 2, 2, 4, 3, 1, 4, 3, 3, 4, 4, 2, 4, 5, 3, 5, 5, 2, 5, 6, 3, 7, 6, 1, 7, 6, 4, 8, 6, 3, 7, 7, 5, 8, 7, 4, 9, 5, 6, 11, 6, 6, 9, 6, 7, 11, 8, 5, 10, 8, 7, 12, 8, 7, 11, 7, 9, 12, 10, 6, 12, 9, 7, 17, 9, 6, 13, 10, 9, 15, 12, 5, 14, 12, 9, 16, 11, 9, 14, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

COMMENTS

The only place where the two sequences differ is a(0) which is 1 for the odds and 0 for the evens.

LINKS

Table of n, a(n) for n=1..95.

IBM Ponder This, Feb. 2001

EXAMPLE

a(16)=3 since 16=2+14=5+11=8+8 (in binary 10+1110=101+1011=1000+1000 where each term has an odd number of zeros) and since 16=1+15=4+12=7+9 (in binary 1+1111=100+1100=111+1001 where each term has an even number of zeros).

CROSSREFS

Cf. A059009 and A059010 for the odd and even binary zeros sequences.

Sequence in context: A268755 A128664 A003823 * A083817 A286222 A029273

Adjacent sequences:  A059448 A059449 A059450 * A059452 A059453 A059454

KEYWORD

nonn

AUTHOR

Henry Bottomley, Feb 02 2001

STATUS

approved

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Last modified April 20 08:32 EDT 2019. Contains 322306 sequences. (Running on oeis4.)