|
| |
|
|
A228747
|
|
Number T(n,k,r,c) of partitions of an n X k X r rectangular cuboid into c integer-sided cubes, considering only the list of parts; irregular triangle T(n,k,r,c), n >= k >= r >= 1, s >= 1, read by rows.
|
|
1
|
|
|
|
1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1
|
|
|
COMMENTS
|
Row length = n*k*r.
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
T(2,2,2,1) = 1 because there is 1 partition of a 2 X 2 X 2 rectangular cuboid (in this case a cube) comprising one 2 X 2 X 2 cube.
T(2,2,2,8) = 1 because there is 1 partition of a 2 X 2 X 2 rectangular cuboid comprising eight 1 X 1 X 1 cubes.
The irregular triangle begins:
. c 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...
n k r
1,1,1 1
2,1,1 0 1
2,2,1 0 0 0 1
2,2,2 1 0 0 0 0 0 0 1
3,1,1 0 0 1
3,2,1 0 0 0 0 0 1
3,2,2 0 0 0 0 1 0 0 0 0 0 0 1
3,3,1 0 0 0 0 0 0 0 0 1
3,3,2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1
3,3,3 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1
4,1,1 0 0 0 1
4,2,1 0 0 0 0 0 0 0 1
4,2,2 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1
4,3,1 0 0 0 0 0 0 0 0 0 0 0 1
4,3,2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1
4,3,3 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ...
4,4,1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
4,4,2 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 ...
4,4,3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 ...
4,4,4 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 ...
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,tabf
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
