cp's OEIS Frontend

A214200 Number of rooted planar binary unlabeled trees with n leaves and caterpillar index <= 4.

%I A214200 #16 Jun 18 2017 13:53:29
%S A214200 0,1,1,2,5,6,26,84,269,870,2910,9788,33250,114012,394260,1372776,
%T A214200 4809917,16947462,60012470,213462380,762355286,2732658484,9827926060,
%U A214200 35453715480,128255260690,465163021788,1691086242796,6161413737176,22494722099492,82282062468600,301507924857768,1106652847697872,4068159345287325,14976738917364166
%N A214200 Number of rooted planar binary unlabeled trees with n leaves and caterpillar index <= 4.
%H A214200 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.
%p A214200 C:=(1-sqrt(1-4*x))/2; # A000108 with a different offset
%p A214200 # F-(k): gives A025266, A025271, A214200, A214203
%p A214200 Fm:=k->(1/2)*(1-sqrt(1-4*x+2^(k+1)*x^(k+1)));
%p A214200 Sm:=k->seriestolist(series(Fm(k),x,50));
%p A214200 # F+(k): gives A000108, A214198, A214201, A214204
%p A214200 Fp:=k->C-Fm(k-1);
%p A214200 Sp:=k->seriestolist(series(Fp(k),x,50));
%p A214200 # F(k): gives A025266, A214199, A214202, A214205
%p A214200 F:=k->Fm(k)-Fm(k-1);
%p A214200 S:=k->seriestolist(series(F(k),x,50));
%t A214200 (1/2)*(1 - Sqrt[1 - 4*x + 32*x^5]) + O[x]^34 // CoefficientList[#, x]& (* _Jean-François Alcover_, Nov 07 2016, after Maple *)
%Y A214200 Cf. A025266, A000108, A025271, A214198-A214205.
%K A214200 nonn
%O A214200 0,4
%A A214200 _N. J. A. Sloane_, Jul 07 2012