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Search: id:A112737
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| A112737 |
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On the standard 33-hole cross-shaped peg solitaire board, the number of distinct board positions after n jumps (starting with the center vacant). |
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+0
2
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| 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; listen)
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OFFSET
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0,3
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COMMENT
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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.
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LINKS
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George I. Bell, English Peg Solitaire
Bill Butler, Durango Bill's 33-hole Peg Solitaire
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EXAMPLE
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There are four possible first jumps, but they all lead to the same board position (rotationally equivalent), thus a(1)=1.
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CROSSREFS
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Cf. A014225, A014227.
Adjacent sequences: A112734 A112735 A112736 this_sequence A112738 A112739 A112740
Sequence in context: A082014 A154133 A077324 this_sequence A162476 A059275 A020047
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KEYWORD
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full,nonn,fini
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AUTHOR
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George Bell (gibell(AT)comcast.net), Sep 16 2005
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