MathDB

Let

n

be a positive integer. Compute the number of words

w

that satisfy the following three properties.
1.

w

consists of

n

letters from the alphabet

\{a,b,c,d\}.

w

contains an even number of

a

's
3.

w

contains an even number of

b

's.
For example, for

n=2

there are

6

such words:

aa, bb, cc, dd, cd, dc.

1