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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

%I

%S 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,

%T 5,3,9,5,1,1,5,5,4,9,7,1

%N 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.

%C The irregular triangle begins:

%C s 1 2 3

%C n k r

%C 1,1,1 1

%C 2,1,1 1

%C 2,2,1 1

%C 2,2,2 2

%C 3,1,1 1

%C 3,2,1 1

%C 3,2,2 2

%C 3,3,1 1

%C 3,3,2 2

%C 3,3,3 2 1

%C 4,1,1 1

%C 4,2,1 1

%C 4,2,2 3

%C 4,3,1 1

%C 4,3,2 3

%C 4,3,3 3 1

%C 4,4,1 1

%C 4,4,2 5

%C 4,4,3 5 1

%C 4,4,4 9 1 1

%C 5,1,1 1

%C 5,2,1 1

%C 5,2,2 3

%C 5,3,1 1

%C 5,3,2 3

%C 5,3,3 3 2

%C 5,4,1 1

%C 5,4,2 5

%C 5,4,3 5 3

%C 5,4,4 9 5 1

%C 5,5,1 1

%C 5,5,2 5

%C 5,5,3 5 4

%C 5,5,4 9 7 1

%H Christopher Hunt Gribble, <a href="/A227796/a227796.cpp.txt">C++ program</a>

%e 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).

%Y Row sums = A228202(n,k,r)

%Y Cf. A228106

%K nonn,tabf

%O 1,4

%A _Christopher Hunt Gribble_, Sep 03 2013

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Last modified February 26 16:40 EST 2021. Contains 341632 sequences. (Running on oeis4.)