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, 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

Offset

1

Comments

Row length = n*k*r.

Links

Christopher Hunt Gribble, Rows 1..34 flattened

Christopher Hunt Gribble, C++ program

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

Row sums = A228202(n,k,r).

Cf. A227998.

Sequence in context: A014669 A185276 A266282 * A285162 A074381 A179560

Adjacent sequences: A228744 A228745 A228746 * A228748 A228749 A228750

Keyword

nonn,tabf

Author

Christopher Hunt Gribble, Sep 02 2013

Status

approved