A214202 Number of rooted planar binary unlabeled trees with n leaves and caterpillar index = 4.

0, 0, 0, 0, 4, 0, 8, 32, 104, 352, 1264, 4480, 15992, 57408, 207152, 750144, 2725456, 9931328, 36282464, 132852224, 487443672, 1791742592, 6597006896, 24326190016, 89825979568, 332110462016, 1229345599520, 4555536068352, 16898439030192, 62743172964224, 233170424975072, 867250463225984, 3228189434389152, 12025362901992064, 44827564359795392

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 + 32*x^5]) + O[x]^35 // CoefficientList[#, x]& (* Jean-François Alcover, Nov 07 2016, after Maple *)