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

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..250

Wikipedia, Dominance Order

Example

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).

Maple

b:= proc(n, m, i, j, t) option remember; `if`(n<m, 0, `if`(n=0, 1,
      `if`(i<1, 0, `if`(t and 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))))
    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 *)

Crossrefs

Cf. A000009, A182988, A265508.

Sequence in context: A212991 A226642 A266137 * A366317 A300301 A031504

Adjacent sequences: A265503 A265504 A265505 * A265507 A265508 A265509

Keyword

nonn

Author

Alois P. Heinz, Dec 09 2015

Status

approved