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A330644
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Number of non-self-conjugate partitions of n.
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23
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0, 0, 2, 2, 4, 6, 10, 14, 20, 28, 40, 54, 74, 98, 132, 172, 226, 292, 380, 484, 620, 784, 994, 1246, 1564, 1946, 2424, 2996, 3702, 4548, 5586, 6822, 8326, 10118, 12284, 14854, 17944, 21602, 25978, 31144, 37292, 44534, 53122, 63204, 75112, 89066, 105486, 124676, 147186, 173432
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OFFSET
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0,3
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COMMENTS
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Also number of asymmetric Ferrers graphs with n nodes.
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LINKS
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Table of n, a(n) for n=0..49.
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FORMULA
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a(n) = A000041(n) - A000700(n).
a(n) = 2*A000701(n).
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EXAMPLE
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For n = 5 the partitions of 5 and their respective Ferrers graphs are as follows:
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5 * * * * * 4 * * * * 3 * * * 3 * * * 2 * * 2 * * 1 *
1 * 2 * * 1 * 2 * * 1 * 1 *
1 * 1 * 1 * 1 *
1 * 1 *
1 *
The number 5 has seven partitions, and one of them [3, 1, 1] is a self-conjugate partition, hence the number of non-self-conjugate partitions of 5 is 7 - 1 = 6, so a(5) = 6.
On the other hand there are six asymmetric Ferrers graphs with n nodes, they are the graphs associated to the partitions [5], [4, 1], [3, 2], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1], so a(5) = 6.
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CROSSREFS
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Cf. A000041, A000700, A000701, A046682.
Sequence in context: A098330 A240310 A083848 * A278297 A139582 A300415
Adjacent sequences: A330641 A330642 A330643 * A330645 A330646 A330647
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KEYWORD
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nonn
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AUTHOR
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Omar E. Pol, Jan 10 2020
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STATUS
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approved
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