A323530 - OEIS

%I #10 Feb 23 2019 10:10:59

%S 1,1,1,1,1,1,1,1,2,2,4,5,8,10,15,18,25,30,39,46,58,67,82,94,112,127,

%T 149,168,194,218,251,282,324,368,425,489,573,670,797,952,1148,1392,

%U 1703,2086,2568,3168,3908,4823,5947,7318,8986,11012,13443,16371,19866

%N Number of square plane partitions of n with strictly decreasing rows and columns.

%e The a(12) = 8 plane partitions:

%e   [12]

%e .

%e   [5 4] [6 3] [7 2] [5 3] [6 2] [4 3] [5 2]

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

%t Table[Sum[Length[Select[Tuples[IntegerPartitions[#,{Length[ptn]}]&/@ptn],And@@Greater@@@#&&And@@Greater@@@Transpose[#]&]],{ptn,IntegerPartitions[n]}],{n,30}]

%Y Cf. A000219, A089299, A306320, A323429, A323434, A323439, A323522, A323529, A323530, A323531.

%K nonn

%O 0,9

%A _Gus Wiseman_, Jan 17 2019