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 A323429 Number of rectangular plane partitions of n. 15
 1, 1, 3, 5, 10, 14, 26, 35, 58, 81, 124, 169, 257, 345, 501, 684, 968, 1304, 1830, 2452, 3387, 4541, 6188, 8257, 11193, 14865, 19968, 26481, 35341, 46674, 62007, 81611, 107860, 141602, 186292, 243800, 319610, 416984, 544601, 708690, 922472, 1197018, 1553442 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Number of ways to fill a (not necessarily square) matrix with the parts of an integer partition of n so that the rows and columns are weakly decreasing. LINKS EXAMPLE The a(5) = 14 matrices:   [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[Sum[Length[Select[Union[Sort/@Tuples[IntegerPartitions[#, {k}]&/@ptn]], And@@OrderedQ/@Transpose[#]&]], {ptn, IntegerPartitions[n]}, {k, Min[ptn]}], {n, 30}] CROSSREFS Cf. A000219, A003293, A047966, A101509, A114736, A117433, A299968, A319066. Cf. A323301, A323307, A323430, A323431, A323432, A323435, A323436, A323438. Sequence in context: A220489 A229915 A092269 * A319066 A306319 A182722 Adjacent sequences:  A323426 A323427 A323428 * A323430 A323431 A323432 KEYWORD nonn AUTHOR Gus Wiseman, Jan 15 2019 STATUS approved

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Last modified January 24 01:05 EST 2020. Contains 331178 sequences. (Running on oeis4.)