A214204 Number of rooted planar binary unlabeled trees with n leaves and caterpillar index >= 5.

0, 0, 0, 0, 0, 8, 16, 48, 160, 560, 1952, 7008, 25536, 94000, 348640, 1301664, 4884928, 18410208, 69632320, 264176320, 1004907904, 3831461936, 14638340960, 56028848160, 214804352960, 824741125536, 3170860158656, 12205939334976, 47038828816512, 181465889281760, 700734291793600, 2708333654394432, 10476476693939584, 40557325959684032

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.
• Filippo Disanto, Unbalanced subtrees in binary rooted ordered and un-ordered trees, Séminaire Lotharingien de Combinatoire, 68 (2013), Article B68b.

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+32*x^5] - Sqrt[1-4*x]) + O[x]^34 //CoefficientList[#, x]& (* Jean-François Alcover, Nov 07 2016, after Maple *)