OFFSET
1,2
COMMENTS
For the construction of the diagram see A225600.
EXAMPLE
For n = 5 and k = 3 the diagram of regions of the set of partitions of 5 contains three parts that start in the third column: two parts of size 1 and one part of size 2, therefore the sum of all parts that start in column 3 is 1 + 1 + 2 = 4, so T(5,3) = 4.
.
. Illustration of the parts
. Diagram that start in column k:
. for n=5 k=1 k=2 k=3 k=4 k=5
. _ _ _ _ _ _ _ _ _ _
. |_ _ _ | |_ _ _ _ _| _ _
. |_ _ _|_ | |_ _ _|_ |_ _| _
. |_ _ | | |_ _ _ _| _ _ |_|
. |_ _|_ | | |_ _|_ |_ _| _ |_|
. |_ _ | | | |_ _ _| _ |_| |_|
. |_ | | | | |_ _| _ |_| |_| |_|
. |_|_|_|_|_| |_| |_| |_| |_| |_|
.
k = 1 2 3 4 5
.
The 5th row lists: 20 1 4 5 5
.
Triangle begins:
1;
3, 1;
6, 1, 2;
12, 1, 4, 3;
20, 1, 4, 5, 5;
35, 1, 6, 8, 9, 7;
54, 1, 6, 10, 12, 11, 11;
86, 1, 8, 13, 20, 14, 19, 15;
128, 1, 8, 18, 23, 22, 25, 23, 22;
192, 1, 10, 21, 34, 30, 37, 29, 36, 30;
275, 1, 10, 26, 41, 41, 48, 41, 45, 46, 42;
399, 1, 12, 32, 56, 53, 72, 52, 67, 58, 66, 56;
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Aug 02 2013
STATUS
approved