If you look at the first problem in the sequence as hinted by Gamer (pid=249) and the hints provided by Dustin, the reasoning behind this sequence is similar to the prior problem combined with a "look back" not just of the previous term but all the prior terms.
For each pair of digits, the first is the number of occurrences of the second digit in all of the lines above. The even digits are listed in increasing order. If no instances of a digit have occurred then rather than a zero followed by that digit, these digits are skipped.
Only every other term is being shown.
The entire sequence is as follows:
Posted by Larry
on 2013-08-03 21:10:58