A122086 Number of unlabeled free bicolored trees with n nodes (the colors are not interchangeable).

2, 1, 2, 3, 6, 10, 22, 42, 94, 203, 470, 1082, 2602, 6270, 15482, 38525, 97258, 247448, 635910, 1645411, 4289010, 11245670, 29656148, 78595028, 209273780, 559574414, 1502130920, 4046853091, 10939133170, 29661655793

Offset: 1

Author

N. J. A. Sloane, Oct 19 2006

Keywords

• nonn

References

• R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..500

Crossrefs

Row sums of A122085.

Antidiagonal sums of A329054.

Same as A125702 except for n = 1.

Cf. A000055, A000081.

Programs

PARI

\\ here TreeGf is A000081 as g.f.
TreeGf(N)={my(A=vector(N, j, 1)); for (n=1, N-1, A[n+1] = 1/n * sum(k=1, n, sumdiv(k, d, d*A[d]) * A[n-k+1] ) ); x*Ser(A)}
seq(n)={Vec(2*TreeGf(n) - TreeGf(n)^2)} \\ Andrew Howroyd, Nov 02 2019

Formula

For n even, a(n) = 2*A000055(n) - A000081(n/2), for n odd, a(n) = 2*A000055(n).

G.f.: 2*f(x) - f(x)^2 where f(x) is the g.f. of A000081. - Andrew Howroyd, Nov 02 2019

Extensions

Edited by Christian G. Bower and Franklin T. Adams-Watters, Jan 05 2007