The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A108225 a(0) = 0, a(1) = 2; for n >= 2, a(n) = (a(n-1) + a(n-2))*(a(n-1) - a(n-2) + 1)/2. 2
 0, 2, 3, 5, 12, 68, 2280, 2598062, 3374961778893, 5695183504492614029263280, 16217557574922386301420536972254869595782763547562 (list; graph; refs; listen; history; text; internal format)
 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 Table of n, a(n) for n=0..10. C. Colijn and G. Plazzotta, A metric on phylogenetic tree shapes, Syst. Biol., 67 (2018), 113-126. N. A. Rosenberg, On the Colijn-Plazzotta numbering scheme for unlabeled binary rooted trees, Discr. Appl. Math., 291 (2021), 88-98. FORMULA Conjecture: a(n) = A006894(n) + 1. - R. J. Mathar, Apr 23 2007 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 First differences give A103410. Cf. A006894. Sequence in context: A266541 A301929 A107475 * A259503 A193064 A133832 Adjacent sequences: A108222 A108223 A108224 * A108226 A108227 A108228 KEYWORD nonn AUTHOR N. J. A. Sloane, Jun 16 2005 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 23 07:28 EDT 2024. Contains 372760 sequences. (Running on oeis4.)