Valid combinations of a 3 letter alphabet

Hi there,

I was hoping one could tell me how to calculate the following problem in the generic form.

3 possible values A,B,C.

where the following constraint states that, "A" must always exist in a combination.

N is the number of columns in a grid that one of the values will be placed.

For example:

if N = 2, then the following are valid combinations:

A A

A B

B A

A C

C A

Invalid combinations are

BB

CC

BC

CB

as these do not have at least one A.

How would you calculate this for N = 3 or N = 4 etc ?

In another example, I can see how the binary alphabet of A,B for N columns can work without the restriction on A.

That is, it is 2^n where n is the number of columns or input number. For example, a 4-input truth table would be 2^4 and 10-input truth table would be 2^10.

However the above scenario has me stumped.

thanks,

Paddy.