A096272 Triangle read by rows: T(n,k) counts solid partitions of n such that the maximum of planes, rows, columns and values is k.

1, 0, 4, 0, 6, 4, 0, 10, 12, 4, 0, 13, 30, 12, 4, 0, 18, 70, 36, 12, 4, 0, 19, 142, 94, 36, 12, 4, 0, 24, 274, 234, 100, 36, 12, 4, 0, 19, 501, 534, 258, 100, 36, 12, 4, 0, 18, 872, 1186, 630, 264, 100, 36, 12, 4, 0, 13, 1449, 2486, 1482, 654, 264, 100, 36, 12, 4, 0, 10, 2336

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

Table of n, a(n) for n=1..69.

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

Cf. A000293, A007760, A094504, A094508, A096322.

Sequence in context: A338682 A305731 A279433 * A340949 A021715 A327278

Adjacent sequences: A096269 A096270 A096271 * A096273 A096274 A096275

Keyword

nonn,tabl

Author

Wouter Meeussen, Jun 22 2004, Sep 21 2008

Status

approved