Quote from  A000045:

F(n) = number of compositions of n into odd parts; 
e.g. F(6) counts 1+1+1+1+1+1, 1+1+1+3, 1+1+3+1, 1+3+1+1, 1+5, 3+1+1+1, 3+3, 5+1.

Due to the bijection between compositions

this can be expressed in terms of binary numbers:

Odd composition addends:

• 1s match the space between binary 0s, the space left of leftmost 0s, the space right of rightmost 0s
• 3s, 5s, 7s, 9s ... match blocks of binary 1s of length 2, 4, 6, 8 ...

These blocks, corresponding to odd composition addends, are marked in strong red.

Columns without even composition addents (i.e. without light red squares) are marked by a black dot.