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

1,1

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

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

Prog

(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

Crossrefs

Row sums of A122085.

Antidiagonal sums of A329054.

Same as A125702 except for n = 1.

Cf. A000055, A000081.

Sequence in context: A277631 A277633 A001037 * A082594 A051850 A077013

Adjacent sequences: A122083 A122084 A122085 * A122087 A122088 A122089

Keyword

nonn

Author

N. J. A. Sloane, Oct 19 2006

Extensions

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

Status

approved