A126184 Number of hex trees with n edges and having no nonroot nodes of outdegree 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

Author

Emeric Deutsch, Dec 19 2006

Keywords

• nonn

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.
• Index entries for linear recurrences with constant coefficients, signature (6, -9).

Crossrefs

Cf. A126183.

Cf. A045891, A140429, A172481.

Programs

Maple

1,seq(3^(n-2)*(n+8),n=1..28);

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)