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Search: id:A067142
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| A067142 |
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One half of the number of Young tableaux with n cells whose shape is asymmetric. |
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+0
2
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| 0, 0, 1, 1, 4, 10, 30, 106, 316, 1254, 4140, 17128, 63856, 271492, 1126216, 4936608, 22278712, 101330506, 487735440, 2313734596, 11706759352, 58073844300, 305941244576, 1587272257096, 8656011151184, 46886237603400
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Equivalently, the row lengths are a non-self-conjugate partition of n.
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FORMULA
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a(n) = (A000085(n) - A067136(n))/2.
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EXAMPLE
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a(4) = 4 = 8/2; the 8 tableaux are:
1..1234..123..124..134..14..12..13
2........4....3....2....2...3...2.
3.......................3...4...4.
4.................................
The two tableaux of size 4 with symmetric shape are excluded:
12..13
34..24
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CROSSREFS
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Cf. A000085, A000701, A067136.
Sequence in context: A047088 A114946 A001551 this_sequence A034730 A095127 A006342
Adjacent sequences: A067139 A067140 A067141 this_sequence A067143 A067144 A067145
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KEYWORD
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nonn
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AUTHOR
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Naohiro Nomoto (n_nomoto(AT)yabumi.com), Feb 19 2002
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EXTENSIONS
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Edited by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 07 2006
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