cp's OEIS Frontend

A323586 Number of plane partitions of n with no repeated rows (or, equivalently, no repeated columns).

%I A323586 #5 Jan 20 2019 23:19:38
%S A323586 1,1,2,5,8,16,30,53,89,158,265,443,735,1197
%N A323586 Number of plane partitions of n with no repeated rows (or, equivalently, no repeated columns).
%e A323586 The a(4) = 8 plane partitions with no repeated rows:
%e A323586   4   31   22   211   1111
%e A323586 .
%e A323586   3   21   111
%e A323586   1   1    1
%e A323586 The a(6) = 30 plane partitions with no repeated columns:
%e A323586   6   51   42   321
%e A323586 .
%e A323586   5   4   41   3   31   32   31   22   21   221   211
%e A323586   1   2   1    3   2    1    11   2    21   1     11
%e A323586 .
%e A323586   4   3   31   2   21   22   21   111
%e A323586   1   2   1    2   2    1    11   11
%e A323586   1   1   1    2   1    1    1    1
%e A323586 .
%e A323586   3   2   21   11
%e A323586   1   2   1    11
%e A323586   1   1   1    1
%e A323586   1   1   1    1
%e A323586 .
%e A323586   2   11
%e A323586   1   1
%e A323586   1   1
%e A323586   1   1
%e A323586   1   1
%e A323586 .
%e A323586   1
%e A323586   1
%e A323586   1
%e A323586   1
%e A323586   1
%e A323586   1
%t A323586 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A323586 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A323586 ptnplane[n_]:=Union[Map[Reverse@*primeMS,Join@@Permutations/@facs[n],{2}]];
%t A323586 Table[Sum[Length[Select[ptnplane[Times@@Prime/@y],And[UnsameQ@@#,And@@GreaterEqual@@@#,And@@(GreaterEqual@@@Transpose[PadRight[#]])]&]],{y,IntegerPartitions[n]}],{n,10}]
%Y A323586 Cf. A000219, A003293 (strict rows), A114736 (strict rows and columns), A117433 (distinct entries), A299968, A319646 (no repeated rows or columns), A323429, A323436 (plane partitions of type), A323580, A323587.
%K A323586 nonn,more
%O A323586 0,3
%A A323586 _Gus Wiseman_, Jan 20 2019