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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). 3
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
George I. Bell, English 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
Sequence in context: A082014 A154133 A077324 * A206901 A162476 A366049
KEYWORD
full,nonn,fini
AUTHOR
George Bell (gibell(AT)comcast.net), Sep 16 2005
STATUS
approved

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Last modified March 18 22:47 EDT 2024. Contains 370951 sequences. (Running on oeis4.)