A119856 Number of equicolorable (unrooted) trees on 2n nodes.

1, 1, 3, 9, 37, 168, 895, 5097, 30983, 196096, 1283552, 8621364, 59176966, 413613891, 2936303012, 21128390679, 153841228779, 1131941424480, 8406680733066, 62958726953945, 475074493277317, 3609405128045162, 27593870865196624, 212159118489924538, 1639760091688265416

Offset: 1

Author

N. J. A. Sloane, Aug 04 2006

Keywords

• nonn

Comments

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..100
• Austin Mohr, Unlabeled Trees
• N. Pippenger, Enumeration of equicolorable trees, SIAM J. Discrete Math., 14 (2001), 93-115.

Crossrefs

Cf. A000081, A119855, 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) + r(y/x,x) - r(x,y/x)*r(y/x,x)), 0) + O(y*y^n) + r(y,y))/2} \\ Andrew Howroyd, May 23 2018

Formula

a(n) = (A000081(n) + A119857(n))/2. - Andrew Howroyd, May 21 2018

Extensions

a(8)-a(9) from John P. McSorley, Aug 08 2017

Terms a(10) and beyond from Andrew Howroyd, May 21 2018