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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 = nkr.

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 ...

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 1 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 8 1 X 1 X 1 cubes.

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

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Last modified June 24 12:30 EDT 2021. Contains 345416 sequences. (Running on oeis4.)