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A094508 Triangle read by rows: T[n,m] = number of solid partitions of n with trace m, where the trace of a solid partitions is defined as the sum of the traces of the constituent plane partitions. 9
1, 2, 2, 3, 4, 3, 4, 11, 6, 5, 5, 18, 19, 10, 7, 6, 33, 42, 34, 14, 11, 7, 48, 85, 80, 50, 22, 15, 8, 74, 156, 186, 128, 80, 30, 22, 9, 100, 275, 368, 318, 208, 112, 44, 30, 10, 140, 446, 725, 696, 534, 304, 165, 60, 42, 11, 180, 705, 1300, 1464, 1214, 808, 450, 228, 84, 56 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Last column equals the partition numbers, corresponding to the 'single column' solid partitions.

LINKS

Table of n, a(n) for n=1..66.

FORMULA

Finding a GF for the solid partitions is an open problem.

EXAMPLE

Table starts {1}, {2,2},{3,4,3},{4,11,6,5},..

T[4,3]=6 since these 6 solid partitions with trace 3 are:

[{{3,1}}], [{{3},{1}}], [{{2,1}},{{1}}], [{{2},{1}},{{1}}], [{{1,1}},{{1}},{{1}}], [{{1},{1}},{{1}},{{1}}]

MATHEMATICA

uses functions defined in A090984, A089924. solidform[q_?PartitionQ]:=Module[{}, Select[Flatten[Outer[z, Sequence@@(planepartitions/@q), 1]], And@@Apply[coversplaneQ, Partition[ #/.z->List, 2, 1], {1}]&]]; tomatrix[par_]:=Block[{l=Max[Length/@ par]}, Map[PadRight[ #, l]&, par]]; Table[Length/@Split[Sort[Plus@@@Map[Tr[tomatrix[ # ]]&, Flatten[solidform/ @Partitions[n]], {2}]]], {n, 12}]

CROSSREFS

Cf. A000293, A090984, A089924.

Sequence in context: A049787 A084192 A129595 * A183517 A080046 A047675

Adjacent sequences:  A094505 A094506 A094507 * A094509 A094510 A094511

KEYWORD

nonn,tabl

AUTHOR

Wouter Meeussen, Jun 05 2004

STATUS

approved

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Last modified April 18 01:48 EDT 2021. Contains 343072 sequences. (Running on oeis4.)