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

0, 0, 0, 2, 4, 12, 36, 116, 384, 1304, 4504, 15772, 55832, 199432, 717816, 2600680, 9476800, 34710000, 127712560, 471851180, 1749864920, 6511643720, 24307501720, 91000873560, 341594374400, 1285436348112, 4848292800336, 18325541062936, 69405260675824, 263353613108944, 1001028051476656, 3811242180811728, 14533071892504448

Offset

0,4

Links

Table of n, a(n) for n=0..32.

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

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+8*x^3] - Sqrt[1-4*x]) + O[x]^33 // CoefficientList[#, x]& (* Jean-François Alcover, Nov 07 2016, after Maple *)

Crossrefs

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

Sequence in context: A291190 A273955 A054542 * A117757 A009623 A148208

Adjacent sequences: A214195 A214196 A214197 * A214199 A214200 A214201

Keyword

nonn

Author

N. J. A. Sloane, Jul 07 2012

Status

approved