OFFSET
0,2
COMMENTS
From a posting by Antreas P. Hatzipolakis to the Yahoo news group "Hyacinthos", circa Jun 10 2005.
The next term has 99 digits. - Harvey P. Dale, Jun 09 2011
a(n) for n>0 gives the rank of the unlabeled binary rooted tree, among those with n+1 leaves, that has the largest rank according to the bijection of Colijn and Plazzotta (2018) between unlabeled binary rooted trees and positive integers. - Noah A Rosenberg, Jun 03 2022
LINKS
Robert Israel, Table of n, a(n) for n = 0..14
C. Colijn and G. Plazzotta, A metric on phylogenetic tree shapes, Syst. Biol., 67 (2018), 113-126.
Luc Devroye, Michael R. Doboli, Noah A. Rosenberg, and Stephan Wagner, Tree height and the asymptotic mean of the Colijn-Plazzotta rank of unlabeled binary rooted trees, arXiv:2409.18956 [math.CO], 2024. See p. 3.
Luc Devroye, Michael R. Doboli, Noah A. Rosenberg, and Stephan Wagner, Tree height and the asymptotic mean of the Colijn-Plazzotta rank of unlabeled binary rooted trees, Bull. Math. Biol. 87 (2025), 172. See p. 3.
N. A. Rosenberg, On the Colijn-Plazzotta numbering scheme for unlabeled binary rooted trees, Discr. Appl. Math., 291 (2021), 88-98.
J.S. Seneschal, Iteration of Semi-Complete Graphs
FORMULA
Conjecture: a(n) = A006894(n) + 1. - R. J. Mathar, Apr 23 2007
From J.S. Seneschal, Jul 17 2025 (Start)
a(n) = A002658(n-1) + a(n-1) for n > 1. (End)
MAPLE
F:=proc(n) option remember; if n <= 1 then RETURN(2*n) fi; (F(n-1)+F(n-2))*(F(n-1)-F(n-2)+1)/2; end;
a[ -2]:=-2: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]+2, n=-2..8); # Zerinvary Lajos, Jun 08 2007
MATHEMATICA
RecurrenceTable[{a[0]==0, a[1]==2, a[n]==(a[n-1]+a[n-2])(a[n-1]- a[n-2]+1)/2}, a[n], {n, 15}] (* Harvey P. Dale, Jun 09 2011 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 16 2005
STATUS
approved