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Search: id:A126187
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| A126187 |
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Sum of the levels of the first leaf (in the preorder traversal) over all hex trees with n edges. 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). |
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+0
2
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| 3, 19, 96, 453, 2085, 9513, 43323, 197542, 903141, 4142565, 19067202, 88065360, 408108285, 1897265405, 8846769300, 41368049400, 193950461985, 911564782065, 4294230794520, 20273068467725, 95902496669091, 454528832324919
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(n)=Sum(k*A126186(n,k),k=1..n).
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REFERENCES
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F. Harary and R. C. Read, The enumeration of tree-like polyhexes, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.
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FORMULA
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G.f.=2[1+3z-sqrt(1-6z+5z^2)]/[1-3z+sqrt(1-6z+5z^2)]^2.
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MAPLE
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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);
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CROSSREFS
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Cf. A126186.
Sequence in context: A050863 A049153 A074361 this_sequence A047029 A095120 A089164
Adjacent sequences: A126184 A126185 A126186 this_sequence A126188 A126189 A126190
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 22 2006
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