

A112737


On the standard 33hole crossshaped peg solitaire board, the number of distinct board positions after n jumps (starting with the center vacant).


1



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
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OFFSET

0,3


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 33hole peg solitaire board.


LINKS

Table of n, a(n) for n=0..32.
George I. Bell, English Peg Solitaire
Bill Butler, Durango Bill's 33hole Peg Solitaire


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.
Sequence in context: A082014 A154133 A077324 * A206901 A162476 A218321
Adjacent sequences: A112734 A112735 A112736 * A112738 A112739 A112740


KEYWORD

full,nonn,fini


AUTHOR

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


STATUS

approved



