cp's OEIS Frontend

A323429 Number of rectangular plane partitions of n.

%I A323429 #6 Jan 15 2019 09:24:28
%S A323429 1,1,3,5,10,14,26,35,58,81,124,169,257,345,501,684,968,1304,1830,2452,
%T A323429 3387,4541,6188,8257,11193,14865,19968,26481,35341,46674,62007,81611,
%U A323429 107860,141602,186292,243800,319610,416984,544601,708690,922472,1197018,1553442
%N A323429 Number of rectangular plane partitions of n.
%C A323429 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.
%e A323429 The a(5) = 14 matrices:
%e A323429   [5] [4 1] [3 2] [3 1 1] [2 2 1] [2 1 1 1] [1 1 1 1 1]
%e A323429 .
%e A323429   [4] [3] [2 1]
%e A323429   [1] [2] [1 1]
%e A323429 .
%e A323429   [3] [2]
%e A323429   [1] [2]
%e A323429   [1] [1]
%e A323429 .
%e A323429   [2]
%e A323429   [1]
%e A323429   [1]
%e A323429   [1]
%e A323429 .
%e A323429   [1]
%e A323429   [1]
%e A323429   [1]
%e A323429   [1]
%e A323429   [1]
%t A323429 Table[Sum[Length[Select[Union[Sort/@Tuples[IntegerPartitions[#,{k}]&/@ptn]],And@@OrderedQ/@Transpose[#]&]],{ptn,IntegerPartitions[n]},{k,Min[ptn]}],{n,30}]
%Y A323429 Cf. A000219, A003293, A047966, A101509, A114736, A117433, A299968, A319066.
%Y A323429 Cf. A323301, A323307, A323430, A323431, A323432, A323435, A323436, A323438.
%K A323429 nonn
%O A323429 0,3
%A A323429 _Gus Wiseman_, Jan 15 2019