cp's OEIS Frontend

A214198 Number of rooted planar binary unlabeled trees with n leaves and caterpillar index >= 3.

%I A214198 #18 Jun 18 2017 13:53:58
%S A214198 0,0,0,2,4,12,36,116,384,1304,4504,15772,55832,199432,717816,2600680,
%T A214198 9476800,34710000,127712560,471851180,1749864920,6511643720,
%U A214198 24307501720,91000873560,341594374400,1285436348112,4848292800336,18325541062936,69405260675824,263353613108944,1001028051476656,3811242180811728,14533071892504448
%N A214198 Number of rooted planar binary unlabeled trees with n leaves and caterpillar index >= 3.
%H A214198 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 A214198 C:=(1-sqrt(1-4*x))/2; # A000108 with a different offset
%p A214198 # F-(k): gives A025266, A025271, A214200, A214203
%p A214198 Fm:=k->(1/2)*(1-sqrt(1-4*x+2^(k+1)*x^(k+1)));
%p A214198 Sm:=k->seriestolist(series(Fm(k),x,50));
%p A214198 # F+(k): gives A000108, A214198, A214201, A214204
%p A214198 Fp:=k->C-Fm(k-1);
%p A214198 Sp:=k->seriestolist(series(Fp(k),x,50));
%p A214198 # F(k): gives A025266, A214199, A214202, A214205
%p A214198 F:=k->Fm(k)-Fm(k-1);
%p A214198 S:=k->seriestolist(series(F(k),x,50));
%t A214198 (1/2)*(Sqrt[1-4*x+8*x^3] - Sqrt[1-4*x]) + O[x]^33 // CoefficientList[#, x]& (* _Jean-François Alcover_, Nov 07 2016, after Maple *)
%Y A214198 Cf. A025266, A000108, A025271, A214198-A214205.
%K A214198 nonn
%O A214198 0,4
%A A214198 _N. J. A. Sloane_, Jul 07 2012