|
| |
|
|
A227796
|
|
T(n,k,r,s) is the number of partitions in the s-th run of strictly increasing numbers of 2 X 2 X 2 cubes in the list of partitions of an n X k X r rectangular cuboid into integer sided cubes, considering only the list of parts; irregular triangle T(n,k,r,s), n>=k>=r>=1, s>=1. The sorting order for the list of partitions is ascending with larger squares taking higher precedence.
|
|
1
|
|
|
|
1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 3, 1, 3, 3, 1, 1, 5, 5, 1, 9, 1, 1, 1, 1, 3, 1, 3, 3, 2, 1, 5, 5, 3, 9, 5, 1, 1, 5, 5, 4, 9, 7, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,4
|
|
|
COMMENTS
|
The irregular triangle begins:
s 1 2 3
n k r
1,1,1 1
2,1,1 1
2,2,1 1
2,2,2 2
3,1,1 1
3,2,1 1
3,2,2 2
3,3,1 1
3,3,2 2
3,3,3 2 1
4,1,1 1
4,2,1 1
4,2,2 3
4,3,1 1
4,3,2 3
4,3,3 3 1
4,4,1 1
4,4,2 5
4,4,3 5 1
4,4,4 9 1 1
5,1,1 1
5,2,1 1
5,2,2 3
5,3,1 1
5,3,2 3
5,3,3 3 2
5,4,1 1
5,4,2 5
5,4,3 5 3
5,4,4 9 5 1
5,5,1 1
5,5,2 5
5,5,3 5 4
5,5,4 9 7 1
|
|
|
LINKS
|
Table of n, a(n) for n=1..46.
Christopher Hunt Gribble, C++ program
|
|
|
EXAMPLE
|
T(3,3,2,1) = 2 because their are 2 partitions in the 1st run of strictly increasing numbers of 2 X 2 X 2 cubes in the list of partitions of a 3 X 3 X 2 rectangular cuboid into integer sided cubes. The 2 partitions are (18 1 X 1 X 1 cubes and 0 2 X 2 X 2 cubes) and (10 1 X 1 X 1 cubes and 1 2 X 2 X 2 cube).
|
|
|
CROSSREFS
|
Row sums = A228202(n,k,r)
Cf. A228106
Sequence in context: A240545 A091591 A337633 * A109374 A079706 A250005
Adjacent sequences: A227793 A227794 A227795 * A227797 A227798 A227799
|
|
|
KEYWORD
|
nonn,tabf
|
|
|
AUTHOR
|
Christopher Hunt Gribble, Sep 03 2013
|
|
|
STATUS
|
approved
|
| |
|
|
