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Search: id:A094504
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| A094504 |
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T[n,m] equals number of solid partitions of n containing m plane partitions. |
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+0
10
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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first column equals the 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...
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FORMULA
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Finding a GF for the solid partitions is an open problem.
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EXAMPLE
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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}}]
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A000293, A090984, A089924.
Sequence in context: A130452 A133085 A039805 this_sequence A107884 A158822 A121443
Adjacent sequences: A094501 A094502 A094503 this_sequence A094505 A094506 A094507
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KEYWORD
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nonn,tabl
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jun 05 2004
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