|
Search: id:A096272
|
|
|
| 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. |
|
+0
11
|
|
| 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
(list; table; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
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, ...
|
|
LINKS
|
Wouter Meeussen, SolidPartitions.txt
|
|
EXAMPLE
|
{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 not 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. A094508, A007760, A094504, A000293.
Sequence in context: A085968 A010637 A127447 this_sequence A021715 A075443 A021250
Adjacent sequences: A096269 A096270 A096271 this_sequence A096273 A096274 A096275
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Wouter Meeussen (wouter.meeussen(AT)pandora.be), Jun 22 2004, Sep 21 2008
|
|
|
Search completed in 0.002 seconds
|
