|
|
A208482
|
|
Triangle read by rows: T(n,k) = sum of positive k-th ranks of all partitions of n.
|
|
10
|
|
|
0, 1, 1, 2, 1, 1, 4, 1, 2, 1, 7, 1, 3, 2, 1, 12, 2, 5, 4, 2, 1, 18, 3, 6, 6, 4, 2, 1, 29, 6, 9, 10, 7, 4, 2, 1, 42, 9, 11, 13, 11, 7, 4, 2, 1, 63, 16, 15, 19, 17, 12, 7, 4, 2, 1, 89, 24, 18, 25, 24, 18, 12, 7, 4, 2, 1, 128, 39, 24, 36, 34, 28, 19, 12, 7, 4, 2, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
COMMENTS
|
For the definition of the k-th rank see A208478.
It appears that the sum of the k-th ranks of all partitions of n is equal to zero.
It appears that reversed rows converge to A000070, the same as A208478. - Omar E. Pol, Mar 10 2012
|
|
LINKS
|
|
|
EXAMPLE
|
For n = 4 the partitions of 4 and the four types of ranks of the partitions of 4 are
----------------------------------------------------------
Partitions First Second Third Fourth
of 4 rank rank rank rank
----------------------------------------------------------
4 4-1 = 3 0-1 = -1 0-1 = -1 0-1 = -1
3+1 3-2 = 1 1-1 = 0 0-1 = -1 0-0 = 0
2+2 2-2 = 0 2-2 = 0 0-0 = 0 0-0 = 0
2+1+1 2-3 = -1 1-1 = 0 1-0 = 1 0-0 = 0
1+1+1+1 1-4 = -3 1-0 = 1 1-0 = 1 1-0 = 1
----------------------------------------------------------
The sums of positive k-th ranks of the partitions of 4 are 4, 1, 2, 1 so row 4 lists 4, 1, 2, 1.
Triangle begins:
0;
1, 1;
2, 1, 1;
4, 1, 2, 1;
7, 1, 3, 2, 1;
12, 2, 5, 4, 2, 1;
18, 3, 6, 6, 4, 2, 1;
29, 6, 9, 10, 7, 4, 2, 1;
42, 9, 11, 13, 11, 7, 4, 2, 1;
63, 16, 15, 19, 17, 12, 7, 4, 2, 1;
89, 24, 18, 25, 24, 18, 12, 7, 4, 2, 1;
128, 39, 24, 36, 34, 28, 19, 12, 7, 4, 2, 1;
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Terms a(1)-a(22) confirmed and additional terms added by John W. Layman, Mar 10 2012
|
|
STATUS
|
approved
|
|
|
|