I am interested in partitions of an integer n which do not have 1 and 2 as its part. That is, I am looking to write 
$$n=3^{n\_3}4^{n\_4}\cdots.$$ 


Now, I want to count this. And any other information about generating function or recursive formula will be helpful.



Restricted partitions without 1s and 2s
This is easy with generating functions. Let $a(n)$ be such a count. Then,
$$\sum\_{n=0}^{\infty}a(n)q^n=\prod\_{k=3}^{\infty}\frac1{1-x^k}.$$
For more information, you may like to [explore this](http://oeis.org/search?q=0%2C+0%2C+1%2C+1%2C+1%2C+2%2C+2%2C+3%2C+4%2C+5%2C+6%2C+9%2C+10%2C+13%2C+17%2C+21%2C+25&language=english&go=Search).


