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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).
0
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.
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
KEYWORD
full,nonn,fini
AUTHOR
George Bell (gibell(AT)comcast.net), Sep 16 2005
STATUS
approved