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 A233389 Naturally embedded ternary trees having no internal node of label greater than 1. 2
 1, 1, 3, 11, 46, 209, 1006, 5053, 26227, 139726, 760398, 4211959, 23681987, 134869448, 776657383, 4516117107, 26486641078, 156532100029, 931426814462, 5576590927886, 33574649282538, 203169756237944, 1235156720288767, 7541099028832261, 46222213821431646 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 M. Kuba, A note on naturally embedded ternary trees, Electronic Journal of Combinatorics, Volume 18 (1), paper P142, 2011. M. Kuba, A note on naturally embedded ternary trees, arXiv:0902.2646 [math.CO], 2009. FORMULA G.f.: (T(z)-2)*T^3(z)/(T^2(z)-3*T(z)+1), where T(z)=1+zT^3(z) is the generating function of ternary trees. MAPLE a:= proc(n) option remember; `if`(n<3, 1+n*(n-1),       ((1349*n^2-2738*n+953)*n*a(n-1) -(5567*n^3-20114*n^2        +22439*n-7320)*a(n-2)-(3*(3*n-4))*(19*n-11)*(3*n-5)        *a(n-3))/((2*(2*n-1))*(n+1)*(19*n-30)))     end: seq(a(n), n=0..30);  # Alois P. Heinz, Jul 03 2017 MATHEMATICA a[n_] := a[n] = If[n < 3, 1 + n*(n - 1), ((1349*n^2 - 2738*n + 953)*n*a[n - 1] - (5567*n^3 - 20114*n^2 + 22439*n - 7320)*a[n - 2] - (3*(3*n - 4)) * (19*n - 11)*(3*n - 5)*a[n - 3])/((2*(2*n - 1))*(n + 1)*(19*n - 30))]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Nov 09 2017, after Alois P. Heinz *) PROG (PARI) N=66; x='x+O('x^N); T=serreverse(x-x^3)/x; v=Vec(((T-2)*T^3/(T^2-3*T+1))); vector(#v\2, n, v[2*n-1]) \\ Joerg Arndt, May 26 2016 CROSSREFS Cf. A000139, A001764. Sequence in context: A306822 A193074 A287891 * A281548 A086521 A225293 Adjacent sequences:  A233386 A233387 A233388 * A233390 A233391 A233392 KEYWORD nonn AUTHOR Markus Kuba, Dec 08 2013 EXTENSIONS More terms from F. Chapoton, May 26 2016 STATUS approved

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Last modified May 29 16:43 EDT 2020. Contains 334704 sequences. (Running on oeis4.)