I was just wondering how you determined the amount of XP needed for a new level for each of the advancement speeds?
No - I can see the chart. What formula was used to determine how much XP is needed for the next level?
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The OGL does not contain the XP chart. Oddly, this implies that WotC believes that it's possible to make the product of 1000 and the sum of the first k positive integers a secret. Sadly for them, this sequence is one of the most well known, often being used to teach math induction and the subject of a famous anecdote involving Gauss. However, copyright law probably allows them to restrict people from using it, which is why they excluded it. But I suspect the OP already knows this.
For a look at the many other representations of this sequence, you can look up A000217 at ATT's online sequence bestiary.
For the designers, let me second the request that at least one of the XP tables not be a lookup table, but instead be a recognized mathematical sequence, or some scalar multiple of one. I like 1000*A000330, the sum of the first n squares (A000330 = n(n+1)(2n+1)/6)):
1st 0
2nd 1,000
3rd 5,000
4th 14,000
5th 30,000
6th 55,000
7th 91,000
8th 140,000
9th 204,000
10th 285,000
11th 385,000
12th 506,000
13th 650,000
14th 819,000
15th 1,015,000
16th 1,240,000
17th 1,496,000
18th 1,785,000
19th 2,109,000
20th 2,470.000
For the designers, let me second the request that at least one of the XP tables not be a lookup table, but instead be a recognized mathematical sequence, or some scalar multiple of one.
Yes, this is what my question was trying to ask - thank you!