A112737 - OEIS

A112737

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

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

(list; graph; refs; listen; history; text; internal format)

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 33-hole peg solitaire board.

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

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 A366049

Adjacent sequences: A112734 A112735 A112736 * A112738 A112739 A112740

KEYWORD

full,nonn,fini

AUTHOR

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

STATUS

approved