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.

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.