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).

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

Author

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

Keywords

• full
• nonn
• fini

Comments

The reason the sequence is palindromic is because playing the game backward is the same as playing it forward, with the notions of "hole" and "peg" interchanged.

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, A112737.

Formula

Satisfies a(n)=a(31-n) for 0<=n<=31 (sequence is a palindrome).