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 A214204 Number of rooted planar binary unlabeled trees with n leaves and caterpillar index >= 5. 8
 0, 0, 0, 0, 0, 8, 16, 48, 160, 560, 1952, 7008, 25536, 94000, 348640, 1301664, 4884928, 18410208, 69632320, 264176320, 1004907904, 3831461936, 14638340960, 56028848160, 214804352960, 824741125536, 3170860158656, 12205939334976, 47038828816512, 181465889281760, 700734291793600, 2708333654394432, 10476476693939584, 40557325959684032 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 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. Filippo Disanto, Unbalanced subtrees in binary rooted ordered and un-ordered trees, Séminaire Lotharingien de Combinatoire, 68 (2013), Article B68b. 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+32*x^5] - Sqrt[1-4*x]) + O[x]^34 //CoefficientList[#, x]& (* Jean-François Alcover, Nov 07 2016, after Maple *) CROSSREFS Cf. A025266, A000108, A025271, A214198-A214205. Sequence in context: A089828 A297619 A188825 * A335771 A159038 A235055 Adjacent sequences: A214201 A214202 A214203 * A214205 A214206 A214207 KEYWORD nonn AUTHOR N. J. A. Sloane, Jul 07 2012 STATUS approved

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Last modified April 13 20:16 EDT 2024. Contains 371645 sequences. (Running on oeis4.)