Given the following sequence, find the next term in the series: 0, 1, 2, 13,…

When a number series does not follow one single obvious rule, check whether two series have been interleaved together. Split the given terms into their odd-position and even-position sub-sequences and look for a consistent pattern - such as a constant or steadily growing gap - within each sub-sequence separately.

1. List the terms by position: 0 (1st), 1 (2nd), 2 (3rd), 13 (4th), 6 (5th), 33 (6th), 12 (7th), 63 (8th), 20 (9th), 103 (10th), and the blank at the 11th position.

2. Since the blank is at an odd position, isolate the odd-position sub-series: 0, 2, 6, 12, 20, __.

3. Find the gaps between consecutive terms of this sub-series: 2 - 0 = 2, 6 - 2 = 4, 12 - 6 = 6, 20 - 12 = 8.

4. The gaps themselves form an arithmetic progression increasing by 2 each time (2, 4, 6, 8, ...), so the next gap is 8 + 2 = 10.

5. Add this gap to the last known odd-position term: 20 + 10 = 30.

This matches the general form k(k - 1) for the odd-position sub-series (k = 1, 2, 3, ..., 6): 0, 2, 6, 12, 20, 30 - confirming the missing term is 30. (The even-position sub-series 1, 13, 33, 63, 103 is not involved, since the blank falls in the odd-position sub-series.)