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Search: id:A112738
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| A112738 |
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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). |
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+0
1
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| 1, 1, 2, 8, 38, 164, 635, 2089, 6174, 16020, 35749, 68326, 112788, 162319, 204992, 230230, 230230, 204992, 162319, 112788, 68326, 35749, 16020, 6174, 2089, 635, 164, 38, 8, 2, 1, 1, 0
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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.
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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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FORMULA
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Satisfies a(n)=a(31-n) for 0<=n<=31 (sequence is a palindrome).
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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, A112737.
Sequence in context: A020130 A159051 A053520 this_sequence A155609 A123164 A002003
Adjacent sequences: A112735 A112736 A112737 this_sequence A112739 A112740 A112741
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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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