This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A108225 #41 Jul 22 2025 00:42:26
%S A108225 0,2,3,5,12,68,2280,2598062,3374961778893,5695183504492614029263280,
%T A108225 16217557574922386301420536972254869595782763547562
%N 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.
%C A108225 From a posting by Antreas P. Hatzipolakis to the Yahoo news group "Hyacinthos", circa Jun 10 2005.
%C A108225 The next term has 99 digits. - _Harvey P. Dale_, Jun 09 2011
%C A108225 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
%H A108225 Robert Israel, <a href="/A108225/b108225.txt">Table of n, a(n) for n = 0..14</a>
%H A108225 C. Colijn and G. Plazzotta, <a href="https://doi.org/10.1093/sysbio/syx046">A metric on phylogenetic tree shapes</a>, Syst. Biol., 67 (2018), 113-126.
%H A108225 Luc Devroye, Michael R. Doboli, Noah A. Rosenberg, and Stephan Wagner, <a href="https://arxiv.org/abs/2409.18956">Tree height and the asymptotic mean of the Colijn-Plazzotta rank of unlabeled binary rooted trees</a>, arXiv:2409.18956 [math.CO], 2024. See p. 3.
%H A108225 N. A. Rosenberg, <a href="https://doi.org/10.1016/j.dam.2020.11.021">On the Colijn-Plazzotta numbering scheme for unlabeled binary rooted trees</a>, Discr. Appl. Math., 291 (2021), 88-98.
%H A108225 J.S. Seneschal, <a href="/A108225/a108225.jpg">Iteration of Semi-Complete Graphs</a>
%F A108225 Conjecture: a(n) = A006894(n) + 1. - _R. J. Mathar_, Apr 23 2007
%F A108225 From _J.S. Seneschal_, Jul 17 2025 (Start)
%F A108225 a(n) = A000217(a(n)) - A072638(n) = A072638(n-1) + 2.
%F A108225 a(n) = A002658(n-1) + a(n-1) for n > 1. (End)
%p A108225 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;
%p A108225 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
%t A108225 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 *)
%Y A108225 First differences give A103410.
%Y A108225 Cf. A006894.
%Y A108225 Cf. A000217, A007501, A002658, A072638.
%K A108225 nonn
%O A108225 0,2
%A A108225 _N. J. A. Sloane_, Jun 16 2005