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Search: id:A108962
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| A108962 |
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Number of partitions that are "3-close" to being self-conjugate. |
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+0
2
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| 1, 1, 2, 3, 5, 5, 9, 11, 16, 20, 28, 34, 47, 57, 75, 92, 119, 143, 183, 220, 277, 332, 412, 491, 605, 718, 874, 1036, 1252, 1475, 1772, 2082, 2483, 2909, 3450, 4027, 4755, 5533, 6499, 7545, 8826, 10213, 11904, 13741, 15955, 18372, 21262, 24422
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OFFSET
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0,3
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COMMENT
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Let (a1,a2,a3,...ad:b1,b2,b3,...bd) be the Frobenius symbol for a partition pi of n. Then pi is m-close to being self-conjugate if for all k, |ak-bk| <= m.
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FORMULA
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Define the Dedekind eta function = q^1/24. Product(1-q^k), k >=1. Then the number of m-close partitions is q^(1/24).(m+2)^2/(1.(2m+4)) (where m denotes eta(q^m)).
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CROSSREFS
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Cf. A000700 for m=0 (self-conjugate), A070047 for m=1, A108961 for m=2.
Adjacent sequences: A108959 A108960 A108961 this_sequence A108963 A108964 A108965
Sequence in context: A128188 A139127 A131319 this_sequence A091608 A088887 A066911
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KEYWORD
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nonn
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AUTHOR
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John McKay (mckay(AT)cs.concordia.ca), Jul 22 2005
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