|
|
A340525
|
|
Triangle read by rows: T(n,k) = A006218(n-k+1)*A002865(k-1), 1 <= k <= n.
|
|
3
|
|
|
1, 3, 0, 5, 0, 1, 8, 0, 3, 1, 10, 0, 5, 3, 2, 14, 0, 8, 5, 6, 2, 16, 0, 10, 8, 10, 6, 4, 20, 0, 14, 10, 16, 10, 12, 4, 23, 0, 16, 14, 20, 16, 20, 12, 7, 27, 0, 20, 16, 28, 20, 32, 20, 21, 8, 29, 0, 23, 20, 32, 28, 40, 32, 35, 24, 12, 35, 0, 27, 23, 40, 32, 56, 40, 56, 40, 36, 14
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Conjecture: the sum of row n equals A006128(n), the total number of parts in all partitions of n.
|
|
LINKS
|
|
|
EXAMPLE
|
Triangle begins:
1;
3, 0;
5, 0, 1;
8, 0, 3, 1;
10, 0, 5, 3, 2;
14, 0, 8, 5, 6, 2;
16, 0, 10, 8, 10, 6, 4;
20, 0, 14, 10, 16, 10, 12, 4;
23, 0, 16, 14, 20, 16, 20, 12, 7;
27, 0, 20, 16, 28, 20, 32, 20, 21, 8;
29, 0, 23, 20, 32, 28, 40, 32, 35, 24, 12;
35, 0, 27, 23, 40, 32, 56, 40, 56, 40, 36, 14;
...
For n = 6 the calculation of every term of row 6 is as follows:
--------------------------
--------------------------
1 1 * 14 = 14
2 0 * 10 = 0
3 1 * 8 = 8
4 1 * 5 = 5
5 2 * 3 = 6
6 2 * 1 = 2
--------------------------
The sum of row 6 is 14 + 0 + 8 + 5 + 6 + 2 = 35, equaling A006128(6).
|
|
CROSSREFS
|
Row sums give A006128 (conjectured).
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|