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A306319
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Number of length-rectangular twice-partitions of n.
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8
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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
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..41.
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EXAMPLE
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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]
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MATHEMATICA
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Table[Length[Join@@Table[Select[Tuples[IntegerPartitions/@ptn], SameQ@@Length/@#&], {ptn, IntegerPartitions[n]}]], {n, 20}]
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CROSSREFS
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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 A089483 A323858
Adjacent sequences: A306316 A306317 A306318 * A306320 A306321 A306322
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Feb 07 2019
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STATUS
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approved
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