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

1,2

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

Prog

(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

Crossrefs

Cf. A119856, A119857.

Sequence in context: A246812 A365123 A108308 * A047119 A052881 A020071

Adjacent sequences: A119852 A119853 A119854 * A119856 A119857 A119858

Keyword

nonn

Author

N. J. A. Sloane, Aug 04 2006

Extensions

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

Status

approved