A227272 - OEIS

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, 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

Table of n, a(n) for n=1..34.

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

Adjacent sequences: A227269 A227270 A227271 * A227273 A227274 A227275

KEYWORD

nonn,tabf

AUTHOR

Christopher Hunt Gribble, Sep 02 2013

STATUS

approved