|
|
A003227
|
|
Endpoints (leaves) in rooted trees with n nodes.
(Formerly M2744)
|
|
7
|
|
|
1, 1, 3, 8, 22, 58, 160, 434, 1204, 3341, 9363, 26308, 74376, 210823, 599832, 1710803, 4891876, 14015505, 40231632, 115669419, 333052242, 960219982, 2771707332, 8009222307, 23166563032, 67069289457, 194332834601
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Number of unlabeled rooted trees with n nodes and a distinguished leaf. - Gus Wiseman, Jul 31 2018
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
|
|
LINKS
|
Eric Weisstein's World of Mathematics, Tree Leaf.
|
|
FORMULA
|
a(n) = Sum_{k=1..n} k*A055277(n, k).
|
|
EXAMPLE
|
The a(4) = 8 rooted trees with a distinguished leaf are (((O))), ((Oo)), ((oO)), (O(o)), (o(O)), (Ooo), (oOo), (ooO). - Gus Wiseman, Jul 31 2018
|
|
MATHEMATICA
|
urt[n_]:=Join@@Table[Union[Sort/@Tuples[urt/@ptn]], {ptn, IntegerPartitions[n-1]}];
Table[Sum[Length[Flatten[{t/.{}->1}]], {t, urt[n]}], {n, 15}] (* Gus Wiseman, Jul 31 2018 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|