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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. 7

%I

%S 1,3,9,21,48,102,213,421,819,1542,2854,5172,9240,16233,28182,48288,

%T 81862,137295,228153,375658,613554,994155,1599309,2554932,4055406,

%U 6397160,10032907,15647277,24275455,37471066,57562533,88018488,133996590,203126712,306671525,461184246,690935892,1031379271

%N 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.

%C The analog for ordinary partitions and 2D-Ferrers plots gives A000070.

%H Suresh Govindarajan, <a href="/A090984/b090984.txt">Table of n, a(n) for n = 0..40</a>

%t 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}]

%Y Cf. A000070, A090539.

%K nonn

%O 0,2

%A _Wouter Meeussen_, Feb 28 2004

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Last modified August 15 16:02 EDT 2020. Contains 336505 sequences. (Running on oeis4.)