OFFSET
1,2
COMMENTS
Last column equals the partition numbers, corresponding to the 'single column' solid partitions.
FORMULA
Finding a GF for the solid partitions is an open problem.
EXAMPLE
Table starts {1}, {2,2},{3,4,3},{4,11,6,5},..
T[4,3]=6 since these 6 solid partitions with trace 3 are:
[{{3,1}}], [{{3},{1}}], [{{2,1}},{{1}}], [{{2},{1}},{{1}}], [{{1,1}},{{1}},{{1}}], [{{1},{1}},{{1}},{{1}}]
MATHEMATICA
uses functions defined in A090984, A089924. solidform[q_?PartitionQ]:=Module[{}, Select[Flatten[Outer[z, Sequence@@(planepartitions/@q), 1]], And@@Apply[coversplaneQ, Partition[ #/.z->List, 2, 1], {1}]&]]; tomatrix[par_]:=Block[{l=Max[Length/@ par]}, Map[PadRight[ #, l]&, par]]; Table[Length/@Split[Sort[Plus@@@Map[Tr[tomatrix[ # ]]&, Flatten[solidform/ @Partitions[n]], {2}]]], {n, 12}]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Wouter Meeussen, Jun 05 2004
STATUS
approved