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A072638

Number of unary-binary rooted trees of height at most n.

0, 1, 3, 10, 66, 2278, 2598060, 3374961778891, 5695183504492614029263278, 16217557574922386301420536972254869595782763547560

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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. - 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-François Alcover, Jan 31 2013 *)

CROSSREFS