A098530 T(n,k) counts solid partitions of n+1 that can be 'shrunk' in k ways to a solid partition of n by removing 1 element from it. Equivalently, it counts how many solid partitions of n+1 have k different solid partitions of n it just covers.

4, 4, 6, 10, 12, 4, 4, 42, 12, 1, 16, 60, 60, 4, 4, 105, 164, 34, 20, 162, 316, 180, 6, 10, 202, 672, 484, 96

Offset

1,1

Comments

Sequence starts 4; 4,6; 10,12,4; 4,42,12,1; 16,60,60,4; 4,105,164,34; Row sums are A000293= the solid partitions of n+1 apart from offset. First column conjectured to be the (beheaded) A007426.

Links

Table of n, a(n) for n=1..28.

Example

T(3,3)=4 because the only solid partitions of 3+1=4 that can be shrunk in exactly 3 ways to plane partitions of 3 are
[{{2,1},{1}}], [{{2,1}},{{1}}], [{{2},{1}},{{1}}] and [{{1,1},{1}},{{1}}].

Mathematica

(* functions 'solidform' and 'coverssolidQ', see A098052 *) Table[Frequencies[Count[Flatten[solidform / @ Partitions[n+1]], q_/; coverssolidQ[q, # ]]&/ @ Flatten[solidform / @ Partitions[n]]], {n, 1, 8}]

Crossrefs

Cf. A000293, A007426, A098529.

Sequence in context: A213375 A226834 A098052 * A213379 A163976 A213383

Adjacent sequences: A098527 A098528 A098529 * A098531 A098532 A098533

Keyword

more,nonn,tabf

Author

Wouter Meeussen, Sep 12 2004

Status

approved