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Search: id:A122158
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| A122158 |
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Smallest positive number of "triangular" shuffles of n(n+1)/2 cards needed to restore them to their original order. |
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+0
2
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| 1, 2, 4, 20, 18, 12, 126, 33, 204, 1638, 1968, 2010, 504, 17043, 240, 222870
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Lay out cards in a triangular array from left to right in rows, with 1 card in row 1 (the top row), 2 cards in row 2, etc., then pick up by columns, in order from the bottom of the column to the top, first from column 1, then column 2, etc. See A048782 for analogous results for a different triangular shuffle.
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EXAMPLE
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For n=3, successive shuffles give:
1.......4.......5.......3.......1
2.3.....2.1.....2.4.....2.5.....2.3
4.5.6...5.3.6...3.1.6...1.4.6...4.5.6
returning the deck of 6 cards to its original order in 4 shuffles. Thus a(3)=4.
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CROSSREFS
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Cf. A121052, A048782.
Sequence in context: A063458 A132530 A133521 this_sequence A033180 A069535 A108866
Adjacent sequences: A122155 A122156 A122157 this_sequence A122159 A122160 A122161
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Aug 22 2006
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