cp's OEIS Frontend

A214204 Number of rooted planar binary unlabeled trees with n leaves and caterpillar index >= 5.

%I A214204 #19 Jun 18 2017 13:52:33
%S A214204 0,0,0,0,0,8,16,48,160,560,1952,7008,25536,94000,348640,1301664,
%T A214204 4884928,18410208,69632320,264176320,1004907904,3831461936,
%U A214204 14638340960,56028848160,214804352960,824741125536,3170860158656,12205939334976,47038828816512,181465889281760,700734291793600,2708333654394432,10476476693939584,40557325959684032
%N A214204 Number of rooted planar binary unlabeled trees with n leaves and caterpillar index >= 5.
%H A214204 Filippo Disanto, <a href="http://arxiv.org/abs/1202.5668">The size of the biggest Caterpillar subtree in binary rooted planar trees</a>, arXiv preprint arXiv:1202.5668 [math.CO], 2012.
%H A214204 Filippo Disanto, <a href="http://www.kurims.kyoto-u.ac.jp/EMIS/journals/SLC/wpapers/s68disanto.html">Unbalanced subtrees in binary rooted ordered and un-ordered trees</a>, Séminaire Lotharingien de Combinatoire, 68 (2013), Article B68b.
%p A214204 C:=(1-sqrt(1-4*x))/2; # A000108 with a different offset
%p A214204 # F-(k): gives A025266, A025271, A214200, A214203
%p A214204 Fm:=k->(1/2)*(1-sqrt(1-4*x+2^(k+1)*x^(k+1)));
%p A214204 Sm:=k->seriestolist(series(Fm(k),x,50));
%p A214204 # F+(k): gives A000108, A214198, A214201, A214204
%p A214204 Fp:=k->C-Fm(k-1);
%p A214204 Sp:=k->seriestolist(series(Fp(k),x,50));
%p A214204 # F(k): gives A025266, A214199, A214202, A214205
%p A214204 F:=k->Fm(k)-Fm(k-1);
%p A214204 S:=k->seriestolist(series(F(k),x,50));
%t A214204 (1/2)*(Sqrt[1-4*x+32*x^5] - Sqrt[1-4*x]) + O[x]^34 //CoefficientList[#, x]& (* _Jean-François Alcover_, Nov 07 2016, after Maple *)
%Y A214204 Cf. A025266, A000108, A025271, A214198-A214205.
%K A214204 nonn
%O A214204 0,6
%A A214204 _N. J. A. Sloane_, Jul 07 2012