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:
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?