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).

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

Author

George Bell (gibell(AT)comcast.net), Sep 16 2005

Keywords

• full
• nonn
• fini

Comments

If symmetry is not taken into account, these numbers are approximately 8 times larger (except for those at the start). The sum of this (finite) sequence is 23475688, the total number of distinct board positions that can be reached from the central vacancy on the 33-hole peg solitaire board.

Examples

			There are four possible first jumps, but they all lead to the same board position (rotationally equivalent), thus a(1)=1.
		

Links

• George I. Bell, English Peg Solitaire
• Bill Butler, Durango Bill's 33-hole Peg Solitaire

Crossrefs

Cf. A014225, A014227.