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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
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
IBM Ponder This, Feb. 2001
Y.-G. Chen and B. Wang, On additive properties of two special sequences, Acta Arith. 110 (3) (2003), 299-303.
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
KEYWORD
nonn
AUTHOR
Henry Bottomley, Feb 02 2001
STATUS
approved