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A227796
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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.
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1
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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
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OFFSET
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1,4
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LINKS
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EXAMPLE
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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).
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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