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Search: id:A048782
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| A048782 |
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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, 1, 2, 6, 10, 84, 70, 24, 36, 330, 210, 288, 1428, 252, 10080, 13680, 1260, 19320, 2160, 22440, 1692152, 50400, 140760, 3071880, 284088, 608753236, 617760, 15600, 35287560, 214138080, 30240, 1866600, 58333800, 8637552, 4034916600
(list; graph; listen)
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OFFSET
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1,3
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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 top of the column to the bottom, first from column 1, then column 2, etc. See A122158 for analogous results for a different triangular shuffle.
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EXAMPLE
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For n=3, successive shuffles give:
1.......1.......1
2.3.....2.4.....2.3
4.5.6...3.5.6...4.5.6,
returning the deck of 6 cards to its original order in 2 shuffles. Thus a(3)=2.
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CROSSREFS
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Cf. A121052, A122158.
Adjacent sequences: A048779 A048780 A048781 this_sequence A048783 A048784 A048785
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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), Jul 14 1999, Aug 22 2006
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EXTENSIONS
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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 02 2008
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