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Search: id:A090984
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| A090984 |
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a(n)= number of pairs (x,y) where x is plane partition of n+1, and y is a plane partition of n, and x 'covers' y. x= (x_1_1 .. x_1_u1)(x_2_1 .. x_2_u2) .. (x_k_1 .. x_k_uk) y= (y_1_1 .. y_1_v1)(y_2_1 .. y-2_v2) .. (y_m_1 .. y_m_vm) x covers y iff ui>=vi, k>=m, x_i_j >= y_i_j, or, the 3-dimensional Ferrers plot of y falls within that of x. |
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+0
6
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| 1, 3, 9, 21, 48, 102, 213, 421, 819, 1542, 2854, 5172
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The analogue for ordinary partitions and 2D-Ferrers plots gives A000070.
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MATHEMATICA
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coversplaneQ[parent_?planepartitionQ, child_?planepartitionQ] := Block[{dif=Length[parent]-Length[child], p=Length/@ parent, c=PadRight[Length/@ child, Length[parent], 0]}, And[dif>=0, Min[p-c]>=0, Min[parent-MapThread[PadRight[ #1, #2, 0]&, { PadRight[child, Length[parent], {{0}}], p}]]>=0]]; Table[Count[Outer[coversplaneQ, planepartitions[k], planepartitions[k-1], 1], True, -1], {k, 12}]
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CROSSREFS
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Cf. A000070, A090539.
Sequence in context: A141156 A014286 A000714 this_sequence A006813 A056823 A105544
Adjacent sequences: A090981 A090982 A090983 this_sequence A090985 A090986 A090987
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KEYWORD
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more,nonn
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be), Feb 28 2004
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