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Search: id:A131139
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| A131139 |
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Counts 2-wild partitions. In general p-wild partitions of n are defined so that they are in bijection with geometric equivalence classes of degree n algebra extensions of the p-adic field Q_p. Here two algebra extensions are equivalent if they become isomorphic after tensoring with the maximal unramified extension of Q_p. |
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2
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| 1, 1, 4, 5, 36, 40, 145, 180, 1572, 1712, 6181, 7712, 43860, 49856, 171844, 213953, 1634448, 1798404, 6362336, 7945252, 43391232, 49532049, 169120448, 210664996, 1310330112, 1471297572
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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In general, the number of p-wild partitions of n is equal to the number of partitions of n if and only if n<p. From n=p onward, there are many more p-wild partitions.
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LINKS
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David P. Roberts, Wild Partitions and Number Theory Journal of Integer Sequences, Volume 10, Issue 6, Article 07.6.6, (2007)
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FORMULA
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The generating function is prod_{j=0}^infinity theta_2(2^(2^j-1) x)^(2^j) where theta_2(y) is the generating function for 2-cores A010054
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EXAMPLE
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a(2) = 4, since there are four quadratic algebras over Q_2 up to geometric equivalence, namely Q_2 times Q_2, Q_2(sqrt{-1}), Q_2(sqrt{2}), and Q_2(sqrt{-2})
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CROSSREFS
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Cf. A000041, A010054, A131140.
Adjacent sequences: A131136 A131137 A131138 this_sequence A131140 A131141 A131142
Sequence in context: A128867 A013468 A041907 this_sequence A041557 A123304 A041037
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KEYWORD
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nonn
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AUTHOR
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David P. Roberts (roberts(AT)morris.umn.edu), Jun 19 2007
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