OFFSET
1,3
COMMENTS
Solid partitions of n that fit inside a 4-dimensional k X k X k X k box. Regard solid partitions as safe pilings of boxes in a corner, stacking height does not increase away from the corner and each box contains an integer and this integer too does not increase away from the corner.
If k > 1+(n/2) then T(n,k) = T(n-1,k-1). For large n and k, each row ends as the reverse of 4, 12, 36, 100, 264, 660, 1608, 3772, 8652, 19340, 42392, 91140, 192860, 401880, 836480, ... = 4*A096322(i), i>=1.
LINKS
Wouter Meeussen, SolidPartitions.txt
EXAMPLE
Triangle T(n,k) begins:
1;
0, 4;
0, 6, 4;
0, 10, 12, 4;
0, 13, 30, 12, 4;
0, 18, 70, 36, 12, 4;
...
T(16,2) = 1 because only { {{2,2},{2,2}}, {{2,2},{2,2}} } has only two planes, each plane has no more than 2 columns, each column no more than 2 rows and each element is no larger than 2.
MATHEMATICA
Max[ Max @(Flatten@(List @@ #)), Max @@ Map[Length, #, {-2}], Length /@ List @@ #, Length[ # ]] & /@ Flatten[solidformBTK /@ Partitions[n]]]], {n, 12}]; (* see link for function definition *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Wouter Meeussen, Jun 22 2004, Sep 21 2008
STATUS
approved