A126323 Number of branches of length 1 in all hex trees with n edges.

0, 3, 2, 15, 80, 399, 1956, 9546, 46552, 227100, 1108698, 5417127, 26490312, 129645027, 634978290, 3112277265, 15264984260, 74919716085, 367926876630, 1807912844925, 8888531467360, 43722603214365, 215175747222640

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

Table of n, a(n) for n=0..22.

F. Harary and R. C. Read, The enumeration of tree-like polyhexes, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.

Formula

a(n) = Sum_{k=0..n} k*A126321(n,k).

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

Conjecture: -(n+2)*(1176*n^2+350135*n-2095015)*a(n) +3*(-392*n^3+1110577*n^2-6230546*n-1231580)*a(n-1) +(43512*n^3-9103273*n^2+68264245*n-103131090) *a(n-2) -15*(n-4)*(2744*n^2-398547*n+1917624)*a(n-3)=0. - R. J. Mathar, Jun 17 2016

Maple

g:=(1-3*z)^2*(2-9*z+5*z^2-(2-3*z)*sqrt(1-6*z+5*z^2))/2/z^2/sqrt(1-6*z+5*z^2): gser:=series(g, z=0, 33): seq(coeff(gser, z, n), n=0..27);

Crossrefs

Cf. A126321.

Sequence in context: A334559 A190961 A346059 * A292123 A084886 A275463

Adjacent sequences: A126320 A126321 A126322 * A126324 A126325 A126326

Keyword

nonn

Author

Emeric Deutsch, Dec 25 2006

Status

approved