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A097994
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T(n,k) counts plane partitions of n that can be 'extended' in (k+2) ways to a plane partition of n+1 by adding 1 element to it. Equivalently, it counts how many partitions of n have (k+2) different partitions of n+1 just covering it.
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1, 3, 0, 3, 3, 0, 6, 6, 0, 1, 3, 15, 3, 3, 0, 9, 21, 6, 12, 0, 0, 3, 34, 21, 25, 3, 0, 0, 10, 45, 36, 54, 15, 0, 0, 0, 6, 54, 72, 108, 36, 6, 0, 0, 0, 9, 84, 102, 172, 117, 15, 0, 1, 0, 0, 3, 84, 174, 306, 228, 54, 7, 3, 0, 0, 0, 18, 114, 225, 483, 447, 162, 18, 12, 0, 0, 0, 0, 3, 114
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The first column starts a t k=3 since all plane partitions can be extended in at least 3 ways. Row sums are A000219 by definition. Sum T(n,k) (k+2) =A090984.
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EXAMPLE
| T(4,4)=1 because {{2,1},{1}} is the only plane partition of 4 that can be extended in 4+2 = 6 ways to a plane partition of 5.
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MATHEMATICA
| (* functions 'planepartitions' and 'coversplaneQ', see A096574 *) Table[Frequencies[Count[planepartitions[n+1], q_/; coversplaneQ[q, # ]]&/@ planepartitions[n]], {n, 1, 16}]
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CROSSREFS
| Cf. A000219, A090984.
Sequence in context: A115379 A127801 A096597 * A053604 A066958 A066851
Adjacent sequences: A097991 A097992 A097993 * A097995 A097996 A097997
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KEYWORD
| hard,nonn,tabl
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AUTHOR
| Wouter Meeussen (wouter.meeussen(AT)pandora.be), Sep 07 2004
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