Given the four arithmetic operators {+, -, *, /} and four times the number 4, that is {4,4,4,4}, I would like to find a way to count how many arithmetic formula I am able to construct.

I find difficult to express my thoughts, but I would like to build an algorithm in order to find every formulas as in that page :

http://gery.huvent.pagesperso-orange.fr/

Please look at the upper right corner : la page 4 (c'est fini)

My goal is to find a way to generalize this, that is :

To find all the natural numbers we can build by combining those arithemtic operators and given 1, 2, 3, 4, ..., n times the number n.

Many thanks for any help...