A355295 - OEIS

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A355295

Number of distinct board states reachable in n jumps in European Peg Solitaire.

1, 4, 17, 92, 495, 2475, 11771, 52226, 212527, 789228, 2640323, 7870055, 20730606, 47916748, 96715832, 170154214, 260956703, 349541944, 410294786, 423631649, 385887175, 310724581, 221398196, 139580751, 77748102, 38162987, 16445627, 6178002, 2007607, 559163, 131269, 25378, 4012, 481, 36, 4

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

LINKS

Table of n, a(n) for n=0..35.

Sander G. Huisman, Mathematica program for this sequence

EXAMPLE

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 * * * * * * * * * * * * * * * * *

* * * * * * * * * * * * * * * * * * * *