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A227272 T(n,k,r) is the total number of parts in the set 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), n >= k >= r >= 1, read by rows. 1
1, 2, 4, 9, 3, 6, 17, 9, 29, 48, 4, 8, 27, 12, 51, 97, 16, 90, 192, 363, 5, 10, 39, 15, 69, 145, 20, 130, 311, 685, 25, 180, 459, 1056 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Christopher Hunt Gribble, C++ program
FORMULA
T(n,k,1) = n*k.
T(n,2,2) = (n+1)(n+2) - 3.
EXAMPLE
The irregular triangle begins:
. r 1 2 3 4 ...
n,k
1,1 1
2,1 2
2,2 4 9
3,1 3
3,2 6 17
3,3 9 29 48
4,1 4
4,2 8 27
4,3 12 51 97
4,4 16 90 192 363
5,1 5
5,2 10 39
5,3 15 69 145
5,4 20 130 311 685
5,5 25 180 459 1056 ...
...
T(2,2,2) = 9 because a 2 X 2 X 2 rectangular cuboid has 2 partitions, (8 1 X 1 X 1 squares) and (1 2 X 2 X 2 square) with 9 parts in total.
CROSSREFS
Cf. A225622.
Sequence in context: A019912 A354903 A081344 * A021405 A201946 A341352
KEYWORD
nonn,tabf
AUTHOR
STATUS
approved

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)