cp's OEIS Frontend

A306320 Number of square plane partitions of n with distinct row sums and distinct column sums.

%I A306320 #8 Feb 09 2019 08:49:02
%S A306320 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 A306320 850,1128,1509,2004,2649,3467,4590,5958,7814,10161,13287,17208,22495,
%U A306320 29129,37997,49229,64098,82940,107868,139390,180737,233214,301527,388018,500058
%N A306320 Number of square plane partitions of n with distinct row sums and distinct column sums.
%e A306320 The a(12) = 21 square plane partitions with distinct row sums and distinct column sums:
%e A306320 [twelve]
%e A306320 .
%e A306320 [64][73][82][91][54][63][72][81][44][53][53][62][62][71][43][43][52][52][61]
%e A306320 [11][11][11][11][21][21][21][21][31][22][31][22][31][31][32][41][32][41][41]
%e A306320 .
%e A306320 [221]
%e A306320 [211]
%e A306320 [111]
%t A306320 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 A306320 Cf. A000219, A089299 (square plane partitions), A101509, A271619, A279785, A306318, A323429, A323529, A323530, A323531.
%K A306320 nonn
%O A306320 0,6
%A A306320 _Gus Wiseman_, Feb 07 2019