A248476 Number of pairs (not necessarily successors) of partitions of n that are incomparable in dominance (natural, majorization) ordering.

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

Author

Wouter Meeussen, Oct 07 2014

Keywords

• nonn

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

Crossrefs

Cf. A000041, A001255, A182988, A248475, A265508.

Programs

Mathematica

Table[Count[ Flatten[Outer[dominant , Partitions[n], Partitions[n], 1]], 0], {n, 24}] (* see A248475 for definition of 'dominant' *)

Formula

a(n) = p(n)^2 - A182988(n), where p(n) denotes the number of partitions of n, A000041(n).