|
| |
|
|
A094504
|
|
T[n,m] equals number of solid partitions of n containing m plane partitions.
|
|
9
| |
|
|
1, 3, 1, 6, 3, 1, 13, 9, 3, 1, 24, 22, 9, 3, 1, 48, 54, 25, 9, 3, 1, 86, 120, 63, 25, 9, 3, 1, 160, 267, 153, 66, 25, 9, 3, 1, 282, 559, 357, 162, 66, 25, 9, 3, 1, 500, 1158, 805, 390, 165, 66, 25, 9, 3, 1, 859, 2314, 1761, 898, 399, 165, 66, 25, 9, 3, 1, 1479, 4559, 3761, 2025
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| First column equals the number of plane partitions of n, corresponding to the 'single layer' solid partitions. Rows read backward tend to limiting sequence 1,3,9,25,66,165,402...
|
|
|
FORMULA
| Finding a GF for the solid partitions is an open problem.
|
|
|
EXAMPLE
| T[5,3]=9 since these 9 solid partitions are [{{3}},{{1}},{{1}}], [{{2,1}},{{1}},{{1}}], [{{1,1,1}},{{1}},{{1}}], [{{2},{1}},{{1}},{{1}}],
[{{1,1},{1}},{{1}},{{1}}], [{{1},{1},{1}},{{1}},{{1}}], [{{2}},{{2}},{{1}}], [{{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}]&]]; Table[Length/@Split[Sort[Length/@Flatten[solidform/@Partitions[n]]]], {n, 10}]
|
|
|
CROSSREFS
| Cf. A000293, A090984, A089924.
Sequence in context: A130452 A133085 A039805 * A107884 A185628 A158822
Adjacent sequences: A094501 A094502 A094503 * A094505 A094506 A094507
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jun 05 2004
|
| |
|
|
