OFFSET
1,3
COMMENTS
EXAMPLE
Illustration (using the colexicograpical order of compositions A228525) of the four sections of the set of compositions of 4:
.
. 1 2 3 4
. _ _ _ _
. |_| _| | | | | |
. |_ _| _ _| | | |
. |_| | | |
. |_ _ _| _ _ _| |
. |_| | |
. |_ _| |
. |_| |
. |_ _ _ _|
.
For n = 4 and k = 2, T(4,2) = 6 because there are 3 parts of size 2 in the last section of the set of compositions of 4, so T(4,2) = 3*2 = 6, see below:
--------------------------------------------------------
. The last section Sum of
. Composition of 4 of the set of parts of
. compositions of 4 size k
. -------------------- -------------------
. Diagram Diagram k = 1 2 3 4
. ------------------------------------------------------
. _ _ _ _ _
. 1+1+1+1 |_| | | | 1 | | 1 0 0 0
. 2+1+1 |_ _| | | 1 | | 1 0 0 0
. 1+2+1 |_| | | 1 | | 1 0 0 0
. 3+1 |_ _ _| | 1 _ _ _| | 1 0 0 0
. 1+1+2 |_| | | 1+1+2 |_| | | 2 2 0 0
. 2+2 |_ _| | 2+2 |_ _| | 0 4 0 0
. 1+3 |_| | 1+3 |_| | 1 0 3 0
. 4 |_ _ _ _| 4 |_ _ _ _| 0 0 0 4
. ---------
. Column sums give row 4: 7,6,3,4
.
Triangle begins:
1;
1, 2;
3, 2, 3;
7, 6, 3, 4;
16, 14, 9, 4, 5;
36, 32, 21, 12, 5, 6;
80, 72, 48, 28, 15, 6, 7;
176, 160, 108, 64, 35, 18, 7, 8;
384, 352, 240, 144, 80, 42, 21, 8, 9;
832, 768, 528, 320, 180, 96, 49, 24, 9, 10;
1792, 1664, 1152, 704, 400, 216, 112, 56, 27, 10, 11;
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Omar E. Pol, Sep 01 2013
STATUS
approved