A112738 - OEIS

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).

%I #6 Dec 11 2013 07:21:20

%S 1,1,2,8,38,164,635,2089,6174,16020,35749,68326,112788,162319,204992,

%T 230230,230230,204992,162319,112788,68326,35749,16020,6174,2089,635,

%U 164,38,8,2,1,1,0

%N 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).

%C 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.

%H George I. Bell, <a href="http://home.comcast.net/~gibell/pegsolitaire/">English Peg Solitaire</a>

%H Bill Butler, <a href="http://www.durangobill.com/Peg33.html">Durango Bill's 33-hole Peg Solitaire</a>

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

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

%Y Cf. A014225, A014227, A112737.

%K full,nonn,fini

%O 0,3

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