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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 Table of n, a(n) for n=0..33. 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 Cf. A025266, A000108, A025271, A214198-A214205. Sequence in context: A303659 A250546 A137067 * A273924 A008555 A056441 Adjacent sequences: A214197 A214198 A214199 * A214201 A214202 A214203 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.)