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

Author

Wouter Meeussen, Feb 28 2004

Keywords

• nonn

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

Crossrefs

Cf. A000070, A090539.

Programs

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}]