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A090984 a(n) is the 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. 7
1, 3, 9, 21, 48, 102, 213, 421, 819, 1542, 2854, 5172, 9240, 16233, 28182, 48288, 81862, 137295, 228153, 375658, 613554, 994155, 1599309, 2554932, 4055406, 6397160, 10032907, 15647277, 24275455, 37471066, 57562533, 88018488, 133996590, 203126712, 306671525, 461184246, 690935892, 1031379271 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
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.
The analog for ordinary partitions and 2D-Ferrers plots gives A000070.
LINKS
Suresh Govindarajan, Table of n, a(n) for n = 0..40
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
Sequence in context: A000714 A267226 A273845 * A319781 A006813 A274230
KEYWORD
nonn
AUTHOR
Wouter Meeussen, Feb 28 2004
STATUS
approved

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Last modified July 24 20:30 EDT 2024. Contains 374585 sequences. (Running on oeis4.)