A265506 Number of pairs (p,q) of partitions of n into distinct parts such that p majorizes q in the dominance order.

1, 1, 1, 3, 3, 6, 10, 15, 21, 35, 54, 75, 115, 161, 238, 349, 486, 673, 972, 1323, 1840, 2562, 3478, 4711, 6407, 8624, 11533, 15502, 20574, 27194, 36030, 47320, 61833, 81139, 105286, 136845, 177369, 228563, 293787, 377803, 483090, 616546, 785925, 997987

Offset: 0

Author

Alois P. Heinz, Dec 09 2015

Keywords

• nonn

Examples

			a(3) = 3: (21,21), (3,21), (3,3).
a(4) = 3: (31,31), (4,31), (4,4).
a(5) = 6: (32,32), (41,32), (41,41), (5,32), (5,41), (5,5).
a(6) = 10: (321,321), (42,321), (42,42), (51,321), (51,42), (51,51), (6,321), (6,42), (6,51), (6,6).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..250
• Wikipedia, Dominance Order

Crossrefs

Cf. A000009, A182988, A265508.

Programs

Maple

b:= proc(n, m, i, j, t) option remember; `if`(n0, b(n, m, i, j-1, true), 0)+
      b(n, m, i-1, j, false)+b(n-i, m-j, max(0, min(n-i, i-1)),
      max(0, min(m-j, j-1)), true))))
    end:
a:= n-> b(n$4, true):
seq(a(n), n=0..40);

Mathematica

b[n_, m_, i_, j_, t_] := b[n, m, i, j, t] = If[n < m, 0, If[n == 0, 1, If[i < 1, 0, If[t && j > 0, b[n, m, i, j-1, True], 0] + b[n, m, i-1, j, False] + b[n-i, m-j, Max[0, Min[n-i, i-1]], Max[0, Min[m-j, j-1]], True]]]]; a[n_] := b[n, n, n, n, True]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 05 2017, translated from Maple *)