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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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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

LINKS

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

Christopher Hunt Gribble, C++ program

EXAMPLE

T(3,3,2,1) = 2 because their 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: A240545 A091591 A337633 * A109374 A079706 A250005

Adjacent sequences:  A227793 A227794 A227795 * A227797 A227798 A227799

KEYWORD

nonn,tabf

AUTHOR

Christopher Hunt Gribble, Sep 03 2013

STATUS

approved

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Last modified January 22 13:57 EST 2021. Contains 340362 sequences. (Running on oeis4.)