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A214199 Number of rooted planar binary unlabeled trees with n leaves and caterpillar index = 3. 8
0, 0, 0, 2, 0, 4, 12, 36, 120, 392, 1288, 4284, 14304, 48024, 162024, 548872, 1866416, 6368464, 21797776, 74822636, 257513344, 888439192, 3072153864, 10645835384, 36964041872, 128584760560, 448087042160, 1564065659608, 5467992829120, 19144550862960, 67123334707984, 235658063191312, 828405764175712, 2915610778184352, 10273466501139232, 36239527330228044 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..35.

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+16*x^4])+O[x]^36 // CoefficientList[#, x]& (* Jean-Fran├žois Alcover, Nov 07 2016, after Maple *)

CROSSREFS

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

Sequence in context: A224822 A246928 A167341 * A320491 A295907 A317364

Adjacent sequences:  A214196 A214197 A214198 * A214200 A214201 A214202

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 07 2012

STATUS

approved

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Last modified January 18 13:30 EST 2020. Contains 331007 sequences. (Running on oeis4.)