Problem 728

Solution:

This is the same as the number of ways 8 nonnegative even integers sum to 12 (we subtract 1 from each integer in the above sum). All 11 possibilities are (leaving out 0s): $12$, $10+2$, $8+4$, $8+2+2$, $6+6$, $6+4+2$, $6+2+2+2+2$, $4+4+4$, $4+4+2+2$, $4+2+2+2+2$, $2+2+2+2+2+2$.