cp's OEIS Frontend

A214205 Number of rooted planar binary unlabeled trees with n leaves and caterpillar index = 5.

%I A214205 #18 Jun 18 2017 13:52:19
%S A214205 0,0,0,0,0,8,0,16,64,240,832,2976,11008,40624,150400,559584,2090112,
%T A214205 7832928,29432704,110863680,418479104,1582628656,5995379456,
%U A214205 22746329952,86417102720,328720669216,1251831214976,4772155518656,18209463672320,69544295350240,265814912973056,1016776398337728,3892040452165888,14907843267549376
%N A214205 Number of rooted planar binary unlabeled trees with n leaves and caterpillar index = 5.
%H A214205 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 A214205 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 A214205 C:=(1-sqrt(1-4*x))/2; # A000108 with a different offset
%p A214205 # F-(k): gives A025266, A025271, A214200, A214203
%p A214205 Fm:=k->(1/2)*(1-sqrt(1-4*x+2^(k+1)*x^(k+1)));
%p A214205 Sm:=k->seriestolist(series(Fm(k),x,50));
%p A214205 # F+(k): gives A000108, A214198, A214201, A214204
%p A214205 Fp:=k->C-Fm(k-1);
%p A214205 Sp:=k->seriestolist(series(Fp(k),x,50));
%p A214205 # F(k): gives A025266, A214199, A214202, A214205
%p A214205 F:=k->Fm(k)-Fm(k-1);
%p A214205 S:=k->seriestolist(series(F(k),x,50));
%t A214205 (1/2)*(Sqrt[1 - 4*x + 32*x^5] - Sqrt[1 - 4*x + 64*x^6]) + O[x]^34 // CoefficientList[#, x]& (* _Jean-François Alcover_, Nov 07 2016, after Maple *)
%Y A214205 Cf. A025266, A000108, A025271, A214198-A214205.
%K A214205 nonn
%O A214205 0,6
%A A214205 _N. J. A. Sloane_, Jul 07 2012