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A098530
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T(n,k) counts solid partitions of n+1 that can be 'shrunk' in k ways to a solid partition of n by removing 1 element from it. Equivalently, it counts how many solid partitions of n+1 have k different solid partitions of n it just covers.
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0
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4, 4, 6, 10, 12, 4, 4, 42, 12, 1, 16, 60, 60, 4, 4, 105, 164, 34, 20, 162, 316, 180, 6, 10, 202, 672, 484, 96
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Sequence starts 4; 4,6; 10,12,4; 4,42,12,1; 16,60,60,4; 4,105,164,34; Row sums are A000293= the solid partitions of n+1 apart from offset. First column conjectured to be the (beheaded) A007426.
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EXAMPLE
| T(3,3)=4 because the only solid partitions of 3+1=4 that can be shrunk in exactly 3 ways to plane partitions of 3 are
[{{2,1},{1}}], [{{2,1}},{{1}}], [{{2},{1}},{{1}}] and [{{1,1},{1}},{{1}}].
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MATHEMATICA
| (* functions 'solidform' and 'coverssolidQ', see A098052 *) Table[Frequencies[Count[Flatten[solidform / @ Partitions[n+1]], q_/; coverssolidQ[q, # ]]&/ @ Flatten[solidform / @ Partitions[n]]], {n, 1, 8}]
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CROSSREFS
| Cf. A000293, A007426, A098529.
Sequence in context: A102414 A127799 A098052 * A163976 A054223 A160643
Adjacent sequences: A098527 A098528 A098529 * A098531 A098532 A098533
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KEYWORD
| more,nonn,tabf
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AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be), Sep 12 2004
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