login
A248476
Number of pairs (not necessarily successors) of partitions of n that are incomparable in dominance (natural, majorization) ordering.
4
0, 0, 0, 0, 0, 4, 8, 30, 70, 170, 340, 770, 1424, 2810, 5166, 9542, 16614, 29596, 49952, 85610, 141604, 234622, 379218, 616008, 976134, 1549134, 2418768, 3771252, 5795300, 8903306, 13497384, 20438432, 30630108, 45789134, 67857566, 100346480, 147170162, 215341690
OFFSET
1,6
COMMENTS
a(n) is always even since each incomparable pair (p1,p2) has a distinct companion (p2,p1).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..200 (first 55 terms from Wouter Meeussen)
Wikipedia, Dominance Order
FORMULA
a(n) = p(n)^2 - A182988(n), where p(n) denotes the number of partitions of n, A000041(n).
MATHEMATICA
Table[Count[ Flatten[Outer[dominant , Partitions[n], Partitions[n], 1]], 0], {n, 24}] (* see A248475 for definition of 'dominant' *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Wouter Meeussen, Oct 07 2014
STATUS
approved