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A072638 Number of unary-binary rooted trees of height at most n. 13
0, 1, 3, 10, 66, 2278, 2598060, 3374961778891, 5695183504492614029263278, 16217557574922386301420536972254869595782763547560 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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, 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]

LINKS

Table of n, a(n) for n=0..9.

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, Apr 23 2007

a(n):=C(a(n-1)+2,2),n>=-1. - Zerinvary Lajos, 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, Jun 08 2007

MATHEMATICA

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-Fran├žois Alcover, Jan 31 2013 *)

CROSSREFS

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 A232213

Adjacent sequences:  A072635 A072636 A072637 * A072639 A072640 A072641

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 02 2002

EXTENSIONS

Edited by Christian G. Bower, Oct 23 2002

STATUS

approved

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Last modified June 28 16:56 EDT 2017. Contains 288839 sequences.