Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 4500 articles have referenced us, often saying "we would not have discovered this result without the OEIS".
A178244
Number of distinct transpositions of binary digits (0s and 1s) in n.
a(0)=1 because 0 (or 0 written in base 2), a(1)=1 because 1 (or 1 written in base 2), a(3)= 2 (or 10 written in base 2) and (01,10)=distinct transpositions.