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A214200 Number of rooted planar binary unlabeled trees with n leaves and caterpillar index <= 4. 8
0, 1, 1, 2, 5, 6, 26, 84, 269, 870, 2910, 9788, 33250, 114012, 394260, 1372776, 4809917, 16947462, 60012470, 213462380, 762355286, 2732658484, 9827926060, 35453715480, 128255260690, 465163021788, 1691086242796, 6161413737176, 22494722099492, 82282062468600, 301507924857768, 1106652847697872, 4068159345287325, 14976738917364166 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
LINKS
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)*(1 - Sqrt[1 - 4*x + 32*x^5]) + O[x]^34 // CoefficientList[#, x]& (* Jean-François Alcover, Nov 07 2016, after Maple *)
CROSSREFS
Sequence in context: A303659 A250546 A137067 * A273924 A008555 A056441
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 07 2012
STATUS
approved

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Last modified February 28 00:18 EST 2024. Contains 370379 sequences. (Running on oeis4.)