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
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_3(2^((3^j-1)/2)*x)^(3^j) where theta_3(y) is the generating function for 3-cores A033687. [This appears to be incorrect - Joerg Arndt, Apr 06 2013]
EXAMPLE
a(3) = 9, since there are four quadratic algebras over Q_3 up to geometric equivalence, namely the unramified algebra Q_3 times Q_3 times Q_3, the tamely ramified algebras Q_3 times Q_3[x]/(x^2-3) and two, two and three wildly ramified algebras with discriminants 3^3, 3^4 and 3^5 respectively.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
David P. Roberts (roberts(AT)morris.umn.edu), Jun 19 2007
STATUS
approved