A335656
Number of distinct board states reachable in n jumps, in English Peg Solitaire.
Original entry on oeis.org
1, 4, 12, 60, 296, 1338, 5648, 21842, 77559, 249690, 717788, 1834379, 4138302, 8171208, 14020166, 20773236, 26482824, 28994876, 27286330, 22106348, 15425572, 9274496, 4792664, 2120101, 800152, 255544, 68236, 14727, 2529, 334, 32, 5
Offset: 0
Example: for n=1 the four states are:
*** *** *** ***
*.* *** *** ***
***.*** ******* ******* *******
******* ****..* ******* *..****
******* ******* ***.*** *******
*** *** *.* ***
*** *** *** ***
Identifying positions that are related by a symmetry of the board gives
A112737.
A355295
Number of distinct board states reachable in n jumps in European Peg Solitaire.
Original entry on oeis.org
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
Offset: 0
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 * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * *
A112738
On the standard 33-hole cross-shaped peg solitaire board, the number of distinct board positions after n jumps that can still be reduced to one peg at the center (starting with the center vacant).
Original entry on oeis.org
1, 1, 2, 8, 38, 164, 635, 2089, 6174, 16020, 35749, 68326, 112788, 162319, 204992, 230230, 230230, 204992, 162319, 112788, 68326, 35749, 16020, 6174, 2089, 635, 164, 38, 8, 2, 1, 1, 0
Offset: 0
George Bell (gibell(AT)comcast.net), Sep 16 2005
There are four possible first jumps, but they all lead to the same board position (rotationally equivalent), thus a(1)=1.
Showing 1-3 of 3 results.
Comments