A323431 - OEIS

%I #5 Jan 17 2019 09:57:30

%S 1,1,1,3,3,5,7,9,11,15,21,25,33,41,53,65,81,97,121,143,173,215,255,

%T 305,367,441,527,637,751,899,1067,1269,1491,1775,2071,2439,2875,3357,

%U 3911,4577,5309,6177,7171,8305,9609,11151

%N Number of strict rectangular plane partitions of n.

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

%e The a(10) = 21 matrices:

%e   [10] [9 1] [8 2] [7 3] [7 2 1] [6 4] [6 3 1] [5 4 1] [5 3 2] [4 3 2 1]

%e .

%e   [9] [8] [7] [6] [4 2] [4 3]

%e   [1] [2] [3] [4] [3 1] [2 1]

%e .

%e   [7] [6] [5] [5]

%e   [2] [3] [4] [3]

%e   [1] [1] [1] [2]

%e .

%e   [4]

%e   [3]

%e   [2]

%e   [1]

%t Table[Sum[Length[Select[Union[Sort/@Tuples[IntegerPartitions[#,{k}]&/@ptn]],UnsameQ@@Join@@#&&And@@OrderedQ/@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, A323432, A323435, A323436, A323438.

%K nonn

%O 0,4

%A _Gus Wiseman_, Jan 16 2019