OFFSET
4,2
COMMENTS
LINKS
Wouter Meeussen, SolidPartitions.xls
EXAMPLE
T(5,7)=1 because there is only 1 solid partition of 5 [{{2, 1}, {1}}, {{1}}] that can be extended to a solid partition of 6 in exactly (7+3 =10) ways:
[{{2,1},{2}},{{1}}], [{{2,1},{1,1}},{{1}}], [{{2,2},{1}},{{1}}],
[{{3,1},{1}},{{1}}], [{{2,1,1},{1}},{{1}}], [{{2,1},{1},{1}},{{1}}],
[{{2,1},{1}},{{2}}], [{{2,1},{1}},{{1,1}}], [{{2,1},{1}},{{1},{1}}],
[{{2,1},{1}},{{1}},{{1}}].
Table starts
1;
4;
4,6;
10,12,0,4;
4,30,12,12,0,0,1;
...
MATHEMATICA
(* functions 'solidform' and 'coversplaneQ', see A096574 *) coverssolidQ[par_z, chi_z]:=Module[{p, c}, p=Length[par]; c=Length[chi]; And[p>=c, And@@MapThread[coversplaneQ, {List@@Take[par, c], List@@chi}]]]; Table[Frequencies[Count[Flatten[solidform/@Partitions[n+1]], q_/; coverssolidQ[q, # ]]&/ @ Flatten[solidform/@Partitions[n]]], {n, 1, 5}]
CROSSREFS
KEYWORD
nonn,tabf,hard,more
AUTHOR
Wouter Meeussen, Sep 11 2004
STATUS
approved