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A126184
Number of hex trees with n edges and having no nonroot nodes of outdegree 2.
2
1, 3, 10, 33, 108, 351, 1134, 3645, 11664, 37179, 118098, 373977, 1180980, 3720087, 11691702, 36669429, 114791256, 358722675, 1119214746, 3486784401, 10847773692, 33705582543, 104603532030, 324270949293, 1004193907488
OFFSET
0,2
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
F. Harary and R. C. Read, The enumeration of tree-like polyhexes, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.
FORMULA
a(n) = A126183(n,0).
a(n) = (n+8)*3^(n-2) for n >= 1; a(0)=1.
G.f.: (1-3z+z^2)/(1-3z)^2.
From Paul Curtz, Mar 27 2022: (Start)
a(n+1) = 3*a(n) + A140429(n), for n >= 0; a(0)=1.
Binomial transform of A172481(n) for n >= 0.
Also, with a different offset, the binomial transform of A045891(n+2) for n >= 0. (End)
MAPLE
1, seq(3^(n-2)*(n+8), n=1..28);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Dec 19 2006
STATUS
approved