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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 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.)