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A228202 Number T(n,k,r) 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), n>=k>=r>=1 read by rows. 4
1, 1, 1, 2, 1, 1, 2, 1, 2, 3, 1, 1, 3, 1, 3, 4, 1, 5, 6, 11, 1, 1, 3, 1, 3, 5, 1, 5, 8, 15, 1, 5, 9, 17, 19, 1, 1, 4, 1, 4, 7, 1, 7, 11, 24, 1, 7, 16, 34, 40, 1, 10, 23, 52, 80, 121 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The irregular triangle begins:

   r  1   2   3   4 ...

n,k

1,1   1

2,1   1

2,2   1   2

3,1   1

3,2   1   2

3,3   1   2   3

4,1   1

4,2   1   3

4,3   1   3   4

4,4   1   5   6  11

5,1   1

5,2   1   3

5,3   1   3   5

5,4   1   5   8  15

5,5   1   5   9  17  19

LINKS

Christopher Hunt Gribble and Alois P. Heinz, Rows n = 1..6, flattened (rows n=1..5 from Christopher Hunt Gribble)

Christopher Hunt Gribble, C++ program

EXAMPLE

T(4,4,3) = 6 because there are 6 partitions of a 4 X 4 X 3 rectangular cuboid into integer sided cubes.  The partitions are:

48 1X1X1 cubes

40 1X1X1 cubes and 1 2X2X2 cube

32 1X1X1 cubes and 2 2X2X2 cubes

24 1X1X1 cubes and 3 2X2X2 cubes

16 1X1X1 cubes and 4 2X2X2 cubes

21 1X1X1 cubes and 1 3X3X3 cube

CROSSREFS

T(n,n,n) = A129668(n).

Cf. A224697.

Sequence in context: A317685 A257540 A333516 * A308972 A137900 A025837

Adjacent sequences:  A228199 A228200 A228201 * A228203 A228204 A228205

KEYWORD

nonn,tabf

AUTHOR

Christopher Hunt Gribble, Aug 17 2013

EXTENSIONS

21 more terms (row 6) from Alois P. Heinz, Aug 18 2013

STATUS

approved

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Last modified February 26 16:54 EST 2021. Contains 341632 sequences. (Running on oeis4.)