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, 4, 5, 36, 40, 145, 180, 1572, 1712, 6181, 7712, 43860, 49856, 171844, 213953, 1634448, 1798404, 6362336, 7945252, 43391232, 49532049, 169120448, 210664996, 1310330112, 1471297572

Offset

0,3

Comments

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.

Links

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).

Formula

The generating function is Product_{j>=0} 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)

Example

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})

Crossrefs

Cf. A000041, A010054, A131140.

Sequence in context: A332316 A243275 A269782 * A152291 A336024 A228798

Adjacent sequences: A131136 A131137 A131138 * A131140 A131141 A131142

Keyword

nonn,more

Author

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

Status

approved