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.

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

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

Cf. A000070, A090539.

Sequence in context: A000714 A267226 A273845 * A319781 A006813 A274230

Adjacent sequences: A090981 A090982 A090983 * A090985 A090986 A090987

Keyword

nonn

Author

Wouter Meeussen, Feb 28 2004

Status

approved