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

0,3

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.

Links

Table of n, a(n) for n=0..32.

George I. Bell, English Peg Solitaire

Bill Butler, Durango Bill's 33-hole Peg Solitaire

Formula

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

Example

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

Crossrefs

Cf. A014225, A014227, A112737.

Sequence in context: A159051 A053520 A202744 * A220806 A192529 A155609

Adjacent sequences: A112735 A112736 A112737 * A112739 A112740 A112741

Keyword

full,nonn,fini

Author

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

Status

approved