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A131139 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. 1
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; refs; listen; history; text; internal format)



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.


Table of n, a(n) for n=0..25.

David P. Roberts, Wild Partitions and Number Theory Journal of Integer Sequences, Volume 10, Issue 6, Article 07.6.6, (2007)


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  (this appears to be incorrect Joerg Arndt, Apr 06 2013)


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})


Cf. A000041, A010054, A131140.

Sequence in context: A243772 A243275 A269782 * A152291 A228798 A041557

Adjacent sequences:  A131136 A131137 A131138 * A131140 A131141 A131142




David P. Roberts (roberts(AT)morris.umn.edu), Jun 19 2007



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Last modified January 29 04:46 EST 2020. Contains 331335 sequences. (Running on oeis4.)