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

0, 0, 0, 0, 4, 8, 24, 80, 264, 912, 3216, 11488, 41528, 151408, 555792, 2051808, 7610384, 28341536, 105914784, 397028544, 1492351576, 5623204528, 21235347856, 80355038176, 304630332528, 1156851587552, 4400205758176, 16761475403328, 63937267846704, 244209062245984, 933904716768672, 3575584117620416, 13704666128328736, 52582688861676096

Offset: 0

Author

N. J. A. Sloane, Jul 07 2012

Keywords

• nonn

Links

• Filippo Disanto, The size of the biggest Caterpillar subtree in binary rooted planar trees, arXiv preprint arXiv:1202.5668 [math.CO], 2012.

Crossrefs

Cf. A025266, A000108, A025271, A214198-A214205.

Programs

Maple

C:=(1-sqrt(1-4*x))/2; # A000108 with a different offset
# F-(k): gives A025266, A025271, A214200, A214203
Fm:=k->(1/2)*(1-sqrt(1-4*x+2^(k+1)*x^(k+1)));
Sm:=k->seriestolist(series(Fm(k),x,50));
# F+(k): gives A000108, A214198, A214201, A214204
Fp:=k->C-Fm(k-1);
Sp:=k->seriestolist(series(Fp(k),x,50));
# F(k): gives A025266, A214199, A214202, A214205
F:=k->Fm(k)-Fm(k-1);
S:=k->seriestolist(series(F(k),x,50));

Mathematica

(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 *)