Is the number of patterns that can be formed with N bits greater than the number of bits?

Yes ― much greater. This simple fact is of profound importance to computer science.

There is a standard method for listing all of the patterns that can be formed with a given number of bits. First, list all of the patterns that can be formed with one bit:

0 1

To increase the number of bits (from one to two) make two copies of the list:

0 1 0 1

Within each __copy__, each row is unique.
Now, make each row in the __combined__ list unique.
Do this by putting a "0" in front
of each line of the first copy,
and a "1" in front of each
line of the second copy:

0 0 0 1 1 0 1 1

Now each line is unique and you have a complete list of the possible patterns of two bits. The number of unique patterns with 2 bits is double that with 1 bit.

For additional bits, repeat the trick for each new bit.

How many patterns can be formed from three bits?