I did something wrong in the calculations, but I can't find the error. I've recalculated it many times and checked it in many different ways. Here're the calculations: http://pastebin.com/yUvnmKTm But, in the nutshell, the task:
$x_1 + x_2 + x_3 + x_4 + x_5 + x_6 = 29$
But, there must be exactly 3 odd $x_i$, every $x_i$ must be greater then 1.
If I solve this using generating function, as in:
$(k^2 + k^4 + \dots + k^{18})^3(k^3 + k^5 + \dots + k^{17})^3$
The coefficient in front of $k^{29}$ is 792. But this number doesn't correspond to anything. Neither the number of sequences of summands, nor the number of sets of summands. In particular, if solutions such as $(2, 3, 4, 6, 7, 7)$ and $(2, 3, 4, 7, 6, 7)$ are considered distinct, then there are 15840 such sequences. 74 otherwise.
What did I miss?
PS. I'm sorry for the probably vague formulation of the task, ironically, neither the language of the task, nor English are my native tongue. And I really don't know whether it is asking to find all possible summands, or all permutations of all possible summands.