strong law (mutatis mutandis)

[wouter meeussen]

the count of plane partitions of n+1 that can be shrunk in exactly 1 way to a plane partition of
n by removing one element
equals again (the beheaded)
Anum=A007425 = (1,)  3,3,6,3,9,3,10,6,9,3,18,3,9,9,15 ..
or
Inverse Moebius transform applied twice to all 1's sequence.
or
tau_3(n)

***

the count of solid partitions of n that can be shrunk in exactly 1 way to a solid partition of
n by removing one element
equals again (the beheaded)
Anum=A007426 = (1,)  4,4,10,4,16,4,20,10,16 ..
or
Inverse Moebius transform applied thrice to all 1's sequence
or
tau_4(n)

***

?? sigh.

all this must be particularly boring to the many who dislike partitions in more than one part (Rick
Shepherd's sheep dog for one).

W.