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 A126187 Sum of the levels of the first leaf (in the preorder traversal) over all hex trees with n edges. 1
 3, 19, 96, 453, 2085, 9513, 43323, 197542, 903141, 4142565, 19067202, 88065360, 408108285, 1897265405, 8846769300, 41368049400, 193950461985, 911564782065, 4294230794520, 20273068467725, 95902496669091, 454528832324919 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A hex tree is a rooted tree where each vertex has 0, 1, or 2 children and, when only one child is present, it is either a left child, or a middle child, or a right child (name due to an obvious bijection with certain tree-like polyhexes; see the Harary-Read reference). LINKS Table of n, a(n) for n=1..22. F. Harary and R. C. Read, The enumeration of tree-like polyhexes, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13. FORMULA a(n) = Sum_{k=1..n} k*A126186(n,k). G.f.: 2[1+3z-sqrt(1-6z+5z^2)]/[1-3z+sqrt(1-6z+5z^2)]^2. D-finite with recurrence (n-1)*(3*n-1)*(n+4)*a(n) -n*(18*n^2+21*n-19)*a(n-1) +5*n*(3*n+2)*(n-1)*a(n-2)=0. - R. J. Mathar, Jun 17 2016 MAPLE g:=2*(1+3*z-sqrt(1-6*z+5*z^2))/(1-3*z+sqrt(1-6*z+5*z^2))^2: gser:=series(g, z=0, 28): seq(coeff(gser, z, n), n = 1..25); CROSSREFS Cf. A126186. Sequence in context: A283380 A049153 A074361 * A215420 A303542 A294251 Adjacent sequences: A126184 A126185 A126186 * A126188 A126189 A126190 KEYWORD nonn AUTHOR Emeric Deutsch, Dec 22 2006 STATUS approved

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Last modified July 13 20:40 EDT 2024. Contains 374288 sequences. (Running on oeis4.)