A306319 Number of length-rectangular twice-partitions of n.

1, 1, 3, 5, 10, 14, 26, 35, 60, 82, 131, 177, 286, 376, 582, 793, 1202, 1610, 2450, 3274, 4906, 6665, 9770, 13274, 19690, 26506, 38596, 53006, 76432, 104189, 150844, 205282, 294304, 404146, 573140, 786169, 1119457, 1527554, 2155953, 2965567, 4163955, 5701816

Offset

0,3

Comments

A twice partition of n is a sequence of integer partitions, one of each part in an integer partition of n. It is length-rectangular if all parts have the same number of parts.

Links

Table of n, a(n) for n=0..41.

Example

The a(5) = 14 length-rectangular twice-partitions:
  [5] [4 1] [3 2] [3 1 1] [2 2 1] [2 1 1 1] [1 1 1 1 1]
.
  [4] [3] [2 1]
  [1] [2] [1 1]
.
  [3] [2]
  [1] [2]
  [1] [1]
.
  [2]
  [1]
  [1]
  [1]
.
  [1]
  [1]
  [1]
  [1]
  [1]

Mathematica

Table[Length[Join@@Table[Select[Tuples[IntegerPartitions/@ptn], SameQ@@Length/@#&], {ptn, IntegerPartitions[n]}]], {n, 20}]

Crossrefs

Dominates A319066 (rectangular partitions of partitions), which dominates A323429 (rectangular plane partitions).

Cf. A000219, A001970, A063834 (twice-partitions), A089299, A271619, A279787 (sum-rectangular twice-partitions), A305551, A306017, A306318 (square case), A323531.

Sequence in context: A092269 A323429 A319066 * A182722 A365379 A089483

Adjacent sequences: A306316 A306317 A306318 * A306320 A306321 A306322

Keyword

nonn

Author

Gus Wiseman, Feb 07 2019

Status

approved