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%I #10 Feb 08 2019 22:19:28
%S 1,1,3,5,10,14,26,35,60,82,131,177,286,376,582,793,1202,1610,2450,
%T 3274,4906,6665,9770,13274,19690,26506,38596,53006,76432,104189,
%U 150844,205282,294304,404146,573140,786169,1119457,1527554,2155953,2965567,4163955,5701816
%N Number of length-rectangular twice-partitions of n.
%C 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.
%e The a(5) = 14 length-rectangular twice-partitions:
%e [5] [4 1] [3 2] [3 1 1] [2 2 1] [2 1 1 1] [1 1 1 1 1]
%e .
%e [4] [3] [2 1]
%e [1] [2] [1 1]
%e .
%e [3] [2]
%e [1] [2]
%e [1] [1]
%e .
%e [2]
%e [1]
%e [1]
%e [1]
%e .
%e [1]
%e [1]
%e [1]
%e [1]
%e [1]
%t Table[Length[Join@@Table[Select[Tuples[IntegerPartitions/@ptn],SameQ@@Length/@#&],{ptn,IntegerPartitions[n]}]],{n,20}]
%Y Dominates A319066 (rectangular partitions of partitions), which dominates A323429 (rectangular plane partitions).
%Y Cf. A000219, A001970, A063834 (twice-partitions), A089299, A271619, A279787 (sum-rectangular twice-partitions), A305551, A306017, A306318 (square case), A323531.
%K nonn
%O 0,3
%A _Gus Wiseman_, Feb 07 2019
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