A119855 Number of equicolorable rooted trees on 2n nodes.

1, 2, 9, 44, 249, 1506, 9687, 64803, 447666, 3169566, 22897260, 168168164, 1252391041, 9437809359, 71850420813, 551876468717, 4272100488830, 33299732401378, 261165251593743, 2059638535690473, 16324255856903830, 129969379170062142, 1039056925387672998

Offset: 1

Author

N. J. A. Sloane, Aug 04 2006

Keywords

• nonn

Comments

For precise definition, recurrence and asymptotics see the Pippenger reference.

An equicolorable tree is a tree which can be colored with two colors with adjacent nodes having different colors and there being an equal number of nodes of each color. - Andrew Howroyd, May 21 2018

References

• N. Pippenger, Enumeration of equicolorable trees, SIAM J. Discrete Math., 14 (2001), 93-115.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A119856, A119857.

Programs

PARI

\\ R is b.g.f of rooted trees x nodes, y in one part
R(n)={my(A=O(x)); for(j=1, 2*n, A = if(j%2,1,y)*x*exp(sum(i=1, j, 1/i * subst(subst(A + x * O(x^(j\i)), x, x^i), y, y^i)))); A};
seq(n)={my(A=Pol(R(n))); my(r(x,y)=substvec(A, ['x,'y], [x,y/x])); Vec(polcoeff(r(x, y/x), 0) + O(y*y^n))} \\ Andrew Howroyd, May 23 2018

Extensions

Terms a(8) and beyond from Andrew Howroyd, May 21 2018