A323432 - OEIS

%I #4 Jan 17 2019 09:57:38

%S 1,1,2,4,6,9,15,20,30,42,59,79,112,146,199,264,350,455,603,774,1010,

%T 1297,1668,2124,2724,3441,4372,5513,6955,8718,10960,13670,17091,21264,

%U 26454,32786,40667,50215,62048,76435,94126

%N Number of semistandard rectangular plane partitions of n.

%C Number of ways to fill a (not necessarily square) matrix with the parts of an integer partition of n so that the rows are weakly decreasing and the columns are strictly decreasing.

%e The a(6) = 15 matrices:

%e   [6] [51] [42] [411] [33] [321] [3111] [222] [2211] [21111] [111111]

%e .

%e   [5] [4] [22]

%e   [1] [2] [11]

%e .

%e   [3]

%e   [2]

%e   [1]

%t Table[Sum[Length[Select[Union[Tuples[IntegerPartitions[#,{k}]&/@ptn]],And@@(OrderedQ[#,Greater]&/@Transpose[#])&]],{ptn,IntegerPartitions[n]},{k,Min[ptn]}],{n,30}]

%Y Cf. A000219, A003293, A047966, A089299, A101509, A114736, A117433, A299968, A319066.

%Y Cf. A323301, A323307, A323429, A323430, A323431, A323435, A323436, A323438.

%K nonn

%O 0,3

%A _Gus Wiseman_, Jan 16 2019