|
|
A352460
|
|
Triangle read by rows: T(n,k), 2 <= k < n is the number of n-element k-ary unlabeled rooted trees where a subtree consisting of h + 1 nodes has exactly min{h,k} subtrees.
|
|
0
|
|
|
1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 4, 3, 2, 1, 1, 5, 4, 3, 2, 1, 1, 9, 6, 5, 3, 2, 1, 1, 13, 10, 6, 5, 3, 2, 1, 1, 23, 15, 10, 7, 5, 3, 2, 1, 1, 35, 24, 14, 10, 7, 5, 3, 2, 1, 1, 61, 39, 23, 14, 11, 7, 5, 3, 2, 1, 1, 98, 63, 34, 21, 14, 11, 7, 5, 3, 2, 1, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
3,4
|
|
LINKS
|
|
|
EXAMPLE
|
Triangle begins:
1;
1, 1;
2, 1, 1;
2, 2, 1, 1;
4, 3, 2, 1, 1;
5, 4, 3, 2, 1, 1;
9, 6, 5, 3, 2, 1, 1;
13, 10, 6, 5, 3, 2, 1, 1;
23, 15, 10, 7, 5, 3, 2, 1, 1;
35, 24, 14, 10, 7, 5, 3, 2, 1, 1;
61, 39, 23, 14, 11, 7, 5, 3, 2, 1, 1;
98, 63, 34, 21, 14, 11, 7, 5, 3, 2, 1, 1;
In particular, the rooted trees counted in the first three rows of the triangle are shown by using the Hasse diagram as follows:
---------
o o
\ /
o
----------------------
o |
| |
o o | o o o
\ / | \ | /
o | o
------------------------------------------------------
o o o o | o |
\ / | | | | |
o o o o | o o o | o o o o
\ / \ / | \ | / | \ \ / /
o o | o | o
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|