A090984 - OEIS

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A090984

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.

1, 3, 9, 21, 48, 102, 213, 421, 819, 1542, 2854, 5172 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,2`
	COMMENTS	`The analogue for ordinary partitions and 2D-Ferrers plots gives A000070.`
	MATHEMATICA	`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}]`
	CROSSREFS	`Cf. A000070, A090539.` `Sequence in context: A141156 A014286 A000714 * A006813 A056823 A105544` `Adjacent sequences: A090981 A090982 A090983 * A090985 A090986 A090987`
	KEYWORD	`more,nonn`
	AUTHOR	`Wouter Meeussen (wouter.meeussen(AT)pandora.be), Feb 28 2004`

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Last modified February 16 07:10 EST 2012. Contains 205874 sequences.