|
Search: id:A035010
|
|
|
| A035010 |
|
Prime binary rooted trees with n external nodes. |
|
+0
3
|
|
| 1, 2, 4, 14, 38, 132, 420, 1426, 4834, 16796, 58688, 208012, 742636, 2674384, 9693976, 35357670, 129641774, 477638700, 1767253368, 6564119892, 24466233428, 91482563640, 343059494120, 1289904147128, 4861945985428
(list; graph; listen)
|
|
|
OFFSET
|
2,2
|
|
|
COMMENT
|
If a,b are binary trees, a.b is equal to tree b where a copy of a is put on each of b's external node. This is non-commutative but associative. A binary tree a is prime if it is different from the 1 node tree and if a=b.c implies that b or c is equal to the 1 node tree.
|
|
REFERENCES
|
B. Amerlynck, Ite're'es d'exponentielles: aspects combinatoires et arithme'tiques, Me'moire de licence, Univ. Libre de Bruxelles (1998).
V. Blondel, Structured numbers: properties of a hierarchy of operations on binary trees, Acta Informatica, vol. 35 (1998), pp. 1-15.
V. Blondel, Operations on binary trees, Comptes Rendus de l'Acad. des Sciences de Paris - Ser. I, 321, pp. 491-494, 1995.
|
|
LINKS
|
Index entries for sequences related to rooted trees
|
|
FORMULA
|
a(n)=Cat_{n-1} - sum_{d_1.d_2=n and 1<d_1<n}a(d_1).Cat_{d_2-1} where Cat_n = n-th Catalan number (A000108).
|
|
EXAMPLE
|
a(4) = Cat_3 - sum_{d_1.d_2=4}a(d_1)Cat_{d_2-1} = 5 - a(2)Cat_1 = 5 - 1 = 4
|
|
CROSSREFS
|
Cf. A035102.
Sequence in context: A006611 A007462 A053623 this_sequence A055540 A006252 A079995
Adjacent sequences: A035007 A035008 A035009 this_sequence A035011 A035012 A035013
|
|
KEYWORD
|
nice,easy,nonn
|
|
AUTHOR
|
Bernard Amerlynck (B.Amerlynck(AT)ulg.ac.be)
|
|
EXTENSIONS
|
More terms from Christian G. Bower (bowerc(AT)usa.net)
|
|
|
Search completed in 0.002 seconds
|
