A single term in the sequence below does not conform to the established mathematical rule. Identify the incorrect number.

4, 12, 30, 68, 148, 304, 622

The correct option is 148.

Let us analyze the pattern followed by the numbers in the given sequence:
4, 12, 30, 68, 148, 304, 622

We can look at the relationship between consecutive terms (multiplying by 2 and adding an increasing even number or successive powers/offsets):

$4\times 2+4=8+4=12$

$12\times 2+6=24+6=30$

$30\times 2+8=60+8=68$

Following this established rule, the next addition term should be 10:

$68\times 2+10=136+10=146$

However, the given sequence lists 148 instead of 146.

Let us verify the remaining terms using 146:

$146\times 2+12=292+12=304$

$304\times 2+14=608+14=622$

Since replacing 148 with 146 makes the entire sequence consistent with the mathematical rule, the incorrect term in the sequence is 148.