A112737
On the standard 33-hole cross-shaped peg solitaire board, the number of distinct board positions after n jumps (starting with the center vacant).
Original entry on oeis.org
1, 1, 2, 8, 39, 171, 719, 2757, 9751, 31312, 89927, 229614, 517854, 1022224, 1753737, 2598215, 3312423, 3626632, 3413313, 2765623, 1930324, 1160977, 600372, 265865, 100565, 32250, 8688, 1917, 348, 50, 7, 2, 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.
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.
A125730
Minimal number of initial pieces needed to reach level n in the Solitaire Army game when diagonal jumps are allowed.
Original entry on oeis.org
1, 2, 3, 5, 8, 13, 23, 46, 123
Offset: 0
George I. Bell (gibell(AT)comcast.net), Feb 02 2007
a(1)=2 because it takes 2 men to go one step or level forward.
- E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 715.
- M. Aigner, Moving into the desert with Fibonacci, Mathematics Magazine, 70 (1997), 11-21.
- G. I. Bell, The peg solitaire army.
- G. I. Bell, D. S. Hirschberg and P. Guerrero-Garcia, The minimum size required of a solitaire army, arXiv:math/0612612 [math.CO], 2006-2007.
- N. Eriksen, H. Eriksson and K. Eriksson, Diagonal checker-jumping and Eulerian numbers for color-signed permutations, Electron. J. Combin., 7 (2000), #R3.
- Eric Weisstein's World of Mathematics, Conway's Soldiers.
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