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A072638
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Number of unary-binary rooted trees of height at most n.
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9
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OFFSET
| 0,3
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COMMENTS
| 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]
a(n) is the smallest integer that is the sum of n distinct members of the complete sequence A000124. See A204009 for the binary vectors that select the terms from A000124. [Frank M Jackson, Jan 09 2012]
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LINKS
| Index entries for sequences related to rooted trees
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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
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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
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CROSSREFS
| Maximal position in A071673 where the value n occurs.
Binary width of each term: A072641. Cf. A072639, A072640, A072654.
Sequence in context: A206724 A009400 A004102 * A080526 A143083 A002499
Adjacent sequences: A072635 A072636 A072637 * A072639 A072640 A072641
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen Jun 02 2002
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EXTENSIONS
| Edited by Christian G. Bower (bowerc(AT)usa.net), Oct 23 2002
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