|
Search: id:A072638
|
|
|
| A072638 |
|
Number of unary-binary rooted trees of height at most n. |
|
+0
9
|
|
| 0, 1, 3, 10, 66, 2278, 2598060, 3374961778891, 5695183504492614029263278, 16217557574922386301420536972254869595782763547560, 13150458684796123568718187457806311711432940989761518850409171616252222583493212\ 2128288032336298141
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
A unary-binary tree is one in which the degree of every node is <= 3.
a(n+1) = (a(n)+1) th triangular numbers = A000217(a(n)+1). a(n+1) = (a(n) + 1) * (a(n) + 2) / 2. a(n+1) = A006894(n+2) - 1. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Sep 11 2009]
|
|
LINKS
|
Index entries for sequences related to rooted trees
|
|
FORMULA
|
a(n+1)=1+(a(n)*(a(n)+3))/2.
Conjecture: a(n)=A006894(n+1)-1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 23 2007
a(n):=C(a(n-1)+2,2),n>=-1. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 08 2007
|
|
MAPLE
|
a[ -1]:=0:a[0]:=1:for n from 1 to 50 do a[n]:=binomial(a[n-1]+2, 2) od: seq(a[n], n=-1..9); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 08 2007
|
|
CROSSREFS
|
Maximal position in A071673 where the value n occurs.
Binary width of each term: A072641. Cf. A072639, A072640, A072654.
Sequence in context: A041014 A009400 A004102 this_sequence A080526 A143083 A002499
Adjacent sequences: A072635 A072636 A072637 this_sequence A072639 A072640 A072641
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Antti Karttunen Jun 02 2002
|
|
EXTENSIONS
|
Edited by Christian G. Bower (bowerc(AT)usa.net), Oct 23 2002
|
|
|
Search completed in 0.002 seconds
|
