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Search: id:A054357
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| A054357 |
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Number of unlabeled 2-ary cacti having n polygons. Also number of bi-colored plane trees with n edges. |
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+0
12
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| 1, 1, 2, 3, 6, 10, 28, 63, 190, 546, 1708, 5346, 17428, 57148, 191280, 646363, 2210670, 7626166, 26538292, 93013854, 328215300, 1165060668, 4158330416, 14915635378, 53746119972, 194477856100, 706437056648, 2575316704200, 9419571138368
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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a(n) = the number of inequivalent non-crossing partitions of n points (equally spaced) on a circle, under rotations of the circle. This may be considered the number of non-crossing partitions of n unlabeled points on a circle, so this sequence has the same relation to the Catalan numbers (A000108) as the number of partitions of an integer (A000041) has to the Bell numbers (A000110). - Len Smiley (smiley(AT)math.uaa.alaska.edu), Sep 06 2005
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LINKS
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Miklos Bona, Michel Bousquet, Gilbert Labelle and Pierre Leroux, Enumeration of m-ary cacti, Advances in Applied Mathematics, 24 (2000), 22-56 (pdf, dvi).
Index entries for sequences related to cacti
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CROSSREFS
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Sequence in context: A124345 A123256 A111275 this_sequence A056606 A062527 A038752
Adjacent sequences: A054354 A054355 A054356 this_sequence A054358 A054359 A054360
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KEYWORD
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nonn
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AUTHOR
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Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
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More terms from Len Smiley (smiley(AT)math.uaa.alaska.edu), Sep 06 2005
More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 04 2007
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