A126190 Number of pairs of adjacent vertices of outdegree 2 in all hex trees with n edges.

0, 0, 0, 0, 2, 24, 190, 1260, 7602, 43344, 238308, 1278360, 6739590, 35086392, 180952200, 926583840, 4718481950, 23923888800, 120881319280, 609086170080, 3062089990710, 15365797583400, 76989505040350, 385265732393388

Offset: 0

Author

Emeric Deutsch, Dec 25 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

• Robert Israel, Table of n, a(n) for n = 0..1432
• F. Harary and R. C. Read, The enumeration of tree-like polyhexes, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.

Crossrefs

Cf. A126188.

Programs

Maple

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);

Formula

a(n) = Sum_{k=0..floor(n/2)-1} k*A126188(n,k).

G.f.: [1-9z+24z^2-18z^3-(1-6z+8z^2)sqrt(1-6z+5z^2)]/[z^2*sqrt(1-6z+5z^2)].

90*n*a(n)+(-294-228*n)*a(n+1)+(558+207*n)*a(2+n)+(-345-83*n)*a(n+3)+(84+15*n)*a(n+4)+(-7-n)*a(n+5) = 0. - Robert Israel, Dec 29 2016