A350561
a(n) is the number of ways of making n moves in English Peg Solitaire.
Original entry on oeis.org
1, 4, 12, 60, 400, 2960, 24600, 221072, 2076744, 20123080, 197757768, 1937125160, 18687793880, 175793675328, 1594744777464, 13794351556920, 112576101214496, 857945953884624, 6037935953538456, 38729529837059648, 222984258240522544, 1133096911619304064, 4985812137371331624
Offset: 0
Given the positions marked thus:
a b c
d e f
g h i j k l m
n o p q r s t
u v w x y z 0
1 2 3
4 5 6
there are 12 ways to make two moves, viz.,
(1) e jumps over j, then h jumps over i;
(2) e jumps over j, then x jumps over q;
(3) e jumps over j, then l jumps over k;
(4) o jumps over p, then d jumps over i;
(5) o jumps over p, then 1 jumps over w;
(6) o jumps over p, then r jumps over q;
(7) 2 jumps over x, then j jumps over q;
(8) 2 jumps over x, then v jumps over w;
(9) 2 jumps over x, then z jumps over y;
(10) s jumps over r, then f jumps over k;
(11) s jumps over r, then p jumps over q;
(12) s jumps over r, then 3 jumps over y.
A350998
a(n) is the number of boards in English Peg Solitaire, reached after n moves, for which no more moves are possible.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 4, 0, 28, 66, 40, 176, 302, 816, 2675, 6890, 15122, 25846, 33891, 33051, 23722, 13142, 4987, 1295, 254, 28, 5
Offset: 0
A351286
a(n) is the number of boards in English Peg Solitaire after n moves from which the winning position can be reached.
Original entry on oeis.org
1, 4, 12, 60, 292, 1292, 5012, 16628, 49236, 127964, 285740, 546308, 902056, 1298248, 1639652, 1841556, 1841556, 1639652, 1298248, 902056, 546308, 285740, 127964, 49236, 16628, 5012, 1292, 292, 60, 12, 4, 1
Offset: 0
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 * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * *
Showing 1-4 of 4 results.
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