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Search: id:A126190
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| A126190 |
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Number of pairs of adjacent vertices of outdegree 2 in 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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| 0, 0, 0, 0, 2, 24, 190, 1260, 7602, 43344, 238308, 1278360, 6739590, 35086392, 180952200, 926583840, 4718481950, 23923888800, 120881319280, 609086170080, 3062089990710, 15365797583400, 76989505040350, 385265732393388
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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a(n)=Sum(k*A126188(n,k),k=0..floor(n/2)-1).
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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=[1-9z+24z^2-18z^3-(1-6z+8z^2)sqrt(1-6z+5z^2)]/[z^2*sqrt(1-6z+5z^2)].
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MAPLE
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G:=(1-9*z+24*z^2-18*z^3-(1-6*z+8*z^2)*sqrt(1-6*z+5*z^2))/z^2/sqrt(1-6*z+5*z^2): Gser:=series(G, z=0, 32): seq(coeff(Gser, z, n), n=0..27);
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CROSSREFS
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Cf. A126188.
Sequence in context: A002736 A131972 A059387 this_sequence A121356 A052780 A121213
Adjacent sequences: A126187 A126188 A126189 this_sequence A126191 A126192 A126193
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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 25 2006
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