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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 18 12:34 EST 2020. Contains 332018 sequences. (Running on oeis4.)