OFFSET
1,63
COMMENTS
Row lengths are specified in A228726.
LINKS
Christopher Hunt Gribble, Rows 1..34 flattened
Christopher Hunt Gribble, C++ program
EXAMPLE
T(4,4,4,8) = 2 because the 4 X 4 X 4 rectangular cuboid (in this case a cube) has 2 partitions in which there are 8 nodes unconnected to any of their neighbors. The partitions are (8 2 X 2 X 2 cubes) and (37 1 X 1 X 1 cubes and 1 3 X 3 X 3 cube). The partitions and isolated nodes can be illustrated by expanding into 2 dimensions:
._______. ._______. ._______. ._______. ._______.
| | | | . | . | | | | | . | . | | | |
|___|___| |___|___| |___|___| |___|___| |___|___|
| | | | . | . | | | | | . | . | | | |
|___|___| |___|___| |___|___| |___|___| |___|___|
._______. ._______. ._______. ._______. ._______.
| |_| | . . |_| | . . |_| | |_| |_|_|_|_|
| |_| | . . |_| | . . |_| | |_| |_|_|_|_|
|_____|_| |_____|_| |_____|_| |_____|_| |_|_|_|_|
|_|_|_|_| |_|_|_|_| |_|_|_|_| |_|_|_|_| |_|_|_|_|
.
The irregular triangle begins:
u 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 ...
n k r
1,1,1 1
2,1,1 1
2,2,1 1
2,2,2 1 1
3,1,1 1
3,2,1 1
3,2,2 1 1
3,3,1 1
3,3,2 1 1
3,3,3 1 1 0 0 0 0 0 0 1
4,1,1 1
4,2,1 1
4,2,2 1 1 1
4,3,1 1
4,3,2 1 1 1
4,3,3 1 1 1 0 0 0 0 0 1
4,4,1 1
4,4,2 1 1 1 1 1
4,4,3 1 1 1 1 1 0 0 0 1
4,4,4 1 1 1 1 1 1 1 1 2 0 0 0 0 0 0 0 0 ...
5,1,1 1
5,2,1 1
5,2,2 1 1 1
5,3,1 1
5,3,2 1 1 1
5,3,3 1 1 1 0 0 0 0 0 1 1
5,4,1 1
5,4,2 1 1 1 1 1
5,4,3 1 1 1 1 1 0 0 0 1 1 1
5,4,4 1 1 1 1 1 1 1 1 2 1 1 1 1 0 0 0 0 ...
5,5,1 1
5,5,2 1 1 1 1 1
5,5,3 1 1 1 1 1 0 0 0 1 1 1 1
5,5,4 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 0 0 ...
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Christopher Hunt Gribble, Aug 27 2013
STATUS
approved