A227796 T(n,k,r,s) is the number of partitions in the s-th run of strictly increasing numbers of 2 X 2 X 2 cubes in the list 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,s), n >= k >= r >= 1, s >= 1. The sorting order for the list of partitions is ascending with larger squares taking higher precedence.

1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 3, 1, 3, 3, 1, 1, 5, 5, 1, 9, 1, 1, 1, 1, 3, 1, 3, 3, 2, 1, 5, 5, 3, 9, 5, 1, 1, 5, 5, 4, 9, 7, 1

Offset

1,4

Links

Table of n, a(n) for n=1..46.

Christopher Hunt Gribble, C++ program

Example

The irregular triangle begins:
      s   1   2   3
n k r
1,1,1     1
2,1,1     1
2,2,1     1
2,2,2     2
3,1,1     1
3,2,1     1
3,2,2     2
3,3,1     1
3,3,2     2
3,3,3     2   1
4,1,1     1
4,2,1     1
4,2,2     3
4,3,1     1
4,3,2     3
4,3,3     3   1
4,4,1     1
4,4,2     5
4,4,3     5   1
4,4,4     9   1   1
5,1,1     1
5,2,1     1
5,2,2     3
5,3,1     1
5,3,2     3
5,3,3     3   2
5,4,1     1
5,4,2     5
5,4,3     5   3
5,4,4     9   5   1
5,5,1     1
5,5,2     5
5,5,3     5   4
5,5,4     9   7   1
...
T(3,3,2,1) = 2 because there are 2 partitions in the 1st run of strictly increasing numbers of 2 X 2 X 2 cubes in the list of partitions of a 3 X 3 X 2 rectangular cuboid into integer-sided cubes. The 2 partitions are (18 1 X 1 X 1 cubes and 0 2 X 2 X 2 cubes) and (10 1 X 1 X 1 cubes and 1 2 X 2 X 2 cube).

Crossrefs

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

Cf. A228106.

Sequence in context: A091591 A337633 A358492 * A109374 A079706 A250005

Adjacent sequences: A227793 A227794 A227795 * A227797 A227798 A227799

Keyword

nonn,tabf

Author

Christopher Hunt Gribble, Sep 03 2013

Status

approved