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Number of square plane partitions of n with distinct row sums and distinct column sums.
1

%I #8 Feb 09 2019 08:49:02

%S 1,1,1,1,1,2,2,5,5,10,11,18,21,31,37,56,70,97,134,180,247,343,462,623,

%T 850,1128,1509,2004,2649,3467,4590,5958,7814,10161,13287,17208,22495,

%U 29129,37997,49229,64098,82940,107868,139390,180737,233214,301527,388018,500058

%N Number of square plane partitions of n with distinct row sums and distinct column sums.

%e The a(12) = 21 square plane partitions with distinct row sums and distinct column sums:

%e [twelve]

%e .

%e [64][73][82][91][54][63][72][81][44][53][53][62][62][71][43][43][52][52][61]

%e [11][11][11][11][21][21][21][21][31][22][31][22][31][31][32][41][32][41][41]

%e .

%e [221]

%e [211]

%e [111]

%t Table[Sum[Length[Select[Union[Reverse/@Sort/@Tuples[IntegerPartitions[#,{Length[ptn]}]&/@ptn]],UnsameQ@@Total/@#&&UnsameQ@@Total/@If[#=={},{},Transpose[#]]&&And@@OrderedQ/@Reverse/@If[#=={},{},Transpose[#]]&]],{ptn,IntegerPartitions[n]}],{n,0,20}]

%Y Cf. A000219, A089299 (square plane partitions), A101509, A271619, A279785, A306318, A323429, A323529, A323530, A323531.

%K nonn

%O 0,6

%A _Gus Wiseman_, Feb 07 2019