login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 


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
OFFSET
1,4
LINKS
Alois P. Heinz, Rows n = 1..6, flattened (rows n=1..5 from Christopher Hunt Gribble)
Christopher Hunt Gribble, C++ program
EXAMPLE
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
...
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 1 X 1 X 1 cubes,
40 1 X 1 X 1 cubes and 1 2 X 2 X 2 cube,
32 1 X 1 X 1 cubes and 2 2 X 2 X 2 cubes,
24 1 X 1 X 1 cubes and 3 2 X 2 X 2 cubes,
16 1 X 1 X 1 cubes and 4 2 X 2 X 2 cubes,
21 1 X 1 X 1 cubes and 1 3 X 3 X 3 cube.
CROSSREFS
T(n,n,n) = A129668(n).
Cf. A224697.
Sequence in context: A317685 A257540 A333516 * A308972 A137900 A025837
KEYWORD
nonn,tabf
AUTHOR
EXTENSIONS
21 more terms (row 6) from Alois P. Heinz, Aug 18 2013
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 19 21:59 EDT 2024. Contains 376015 sequences. (Running on oeis4.)