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A072638
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Number of unary-binary rooted trees of height at most n.
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14
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OFFSET
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0,3
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COMMENTS
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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. - Jaroslav Krizek, 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
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Table of n, a(n) for n=0..9.
Index entries for sequences related to rooted trees
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FORMULA
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a(n+1) = 1 + (a(n)*(a(n)+3))/2.
Conjecture: a(n) = A006894(n+1) - 1. - R. J. Mathar, Apr 23 2007
a(n) := C(a(n-1) + 2, 2), n >= -1. - Zerinvary Lajos, Jun 08 2007
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MAPLE
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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, Jun 08 2007
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MATHEMATICA
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Clear[a]; a[0] = 0; a[n_] := a[n] = 1 + (a[n-1]*(a[n-1]+3))/2; Table[a[n], {n, 0, 9}] (* Jean-François Alcover, Jan 31 2013 *)
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CROSSREFS
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Maximal position in A071673 where the value n occurs.
Binary width of each term: A072641. Cf. A072639, A072640, A072654.
Sequence in context: A009400 A217388 A004102 * A262843 A080526 A359701
Adjacent sequences: A072635 A072636 A072637 * A072639 A072640 A072641
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, Jun 02 2002
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EXTENSIONS
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Edited by Christian G. Bower, Oct 23 2002
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STATUS
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approved
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