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 A214201 Number of rooted planar binary unlabeled trees with n leaves and caterpillar index >= 4. 8
 0, 0, 0, 0, 4, 8, 24, 80, 264, 912, 3216, 11488, 41528, 151408, 555792, 2051808, 7610384, 28341536, 105914784, 397028544, 1492351576, 5623204528, 21235347856, 80355038176, 304630332528, 1156851587552, 4400205758176, 16761475403328, 63937267846704, 244209062245984, 933904716768672, 3575584117620416, 13704666128328736, 52582688861676096 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 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)*(Sqrt[1-4*x+16*x^4]-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: A010366 A222356 A370158 * A265185 A240530 A303882 Adjacent sequences: A214198 A214199 A214200 * A214202 A214203 A214204 KEYWORD nonn AUTHOR N. J. A. Sloane, Jul 07 2012 STATUS approved

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Last modified August 14 15:29 EDT 2024. Contains 375165 sequences. (Running on oeis4.)