This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A323586 Number of plane partitions of n with no repeated rows (or, equivalently, no repeated columns). 0
 1, 1, 2, 5, 8, 16, 30, 53, 89, 158, 265, 443, 735, 1197 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS EXAMPLE The a(4) = 8 plane partitions with no repeated rows:   4   31   22   211   1111 .   3   21   111   1   1    1 The a(6) = 30 plane partitions with no repeated columns:   6   51   42   321 .   5   4   41   3   31   32   31   22   21   221   211   1   2   1    3   2    1    11   2    21   1     11 .   4   3   31   2   21   22   21   111   1   2   1    2   2    1    11   11   1   1   1    2   1    1    1    1 .   3   2   21   11   1   2   1    11   1   1   1    1   1   1   1    1 .   2   11   1   1   1   1   1   1   1   1 .   1   1   1   1   1   1 MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]]; ptnplane[n_]:=Union[Map[Reverse@*primeMS, Join@@Permutations/@facs[n], {2}]]; Table[Sum[Length[Select[ptnplane[Times@@Prime/@y], And[UnsameQ@@#, And@@GreaterEqual@@@#, And@@(GreaterEqual@@@Transpose[PadRight[#]])]&]], {y, IntegerPartitions[n]}], {n, 10}] CROSSREFS 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. Sequence in context: A032233 A026530 A032254 * A048237 A048139 A071085 Adjacent sequences:  A323583 A323584 A323585 * A323587 A323588 A323589 KEYWORD nonn,more AUTHOR Gus Wiseman, Jan 20 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 12 20:12 EST 2019. Contains 329961 sequences. (Running on oeis4.)