cp's OEIS Frontend

A214201 Number of rooted planar binary unlabeled trees with n leaves and caterpillar index >= 4.

%I A214201 #18 Jun 18 2017 13:53:10
%S A214201 0,0,0,0,4,8,24,80,264,912,3216,11488,41528,151408,555792,2051808,
%T A214201 7610384,28341536,105914784,397028544,1492351576,5623204528,
%U A214201 21235347856,80355038176,304630332528,1156851587552,4400205758176,16761475403328,63937267846704,244209062245984,933904716768672,3575584117620416,13704666128328736,52582688861676096
%N A214201 Number of rooted planar binary unlabeled trees with n leaves and caterpillar index >= 4.
%H A214201 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 A214201 C:=(1-sqrt(1-4*x))/2; # A000108 with a different offset
%p A214201 # F-(k): gives A025266, A025271, A214200, A214203
%p A214201 Fm:=k->(1/2)*(1-sqrt(1-4*x+2^(k+1)*x^(k+1)));
%p A214201 Sm:=k->seriestolist(series(Fm(k),x,50));
%p A214201 # F+(k): gives A000108, A214198, A214201, A214204
%p A214201 Fp:=k->C-Fm(k-1);
%p A214201 Sp:=k->seriestolist(series(Fp(k),x,50));
%p A214201 # F(k): gives A025266, A214199, A214202, A214205
%p A214201 F:=k->Fm(k)-Fm(k-1);
%p A214201 S:=k->seriestolist(series(F(k),x,50));
%t A214201 (1/2)*(Sqrt[1-4*x+16*x^4]-Sqrt[1-4*x]) + O[x]^34 // CoefficientList[#, x]& (* _Jean-François Alcover_, Nov 07 2016, after Maple *)
%Y A214201 Cf. A025266, A000108, A025271, A214198-A214205.
%K A214201 nonn
%O A214201 0,5
%A A214201 _N. J. A. Sloane_, Jul 07 2012