This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
The beginning state is missing the peg just above the center, as an initial state with the center peg removed does not yield any valid solutions where 1 peg is remaining.
* * *
* * * * *
* * * O * * *
* * * * * * *
* * * * * * *
* * * * *
* * *
The next move yields the next 4 states:
* * * * * * * O * * * *
* * * * * * * * * * * * O * * * * * * *
* O O * * * * * * * * * * * * * * * * * * * * * * O O *
* * * * * * * * * * O * * * * * * * * * * * * * * * * *
* * * * * * * * * * O * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * *