A339835 Number of rooted bicolored trees on n unlabeled nodes such that every white node is adjacent to a black node.

1, 3, 9, 30, 111, 424, 1705, 7024, 29692, 127748, 558219, 2469403, 11039992, 49796803, 226348740, 1035750855, 4767429667, 22058219466, 102534463563, 478602668159, 2242383155726, 10541976883286, 49714185649417, 235109360767014, 1114782699692044, 5298494249055391

Offset

1,2

Links

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

Example

a(1) = 1: B.
a(2) = 4: B(B), B(W), W(B).
a(3) = 9: B(BB), B(BW), B(WW), W(BB), B(B(B)), B(B(W)), B(W(B)), W(B(B)), W(B(W)).

Prog

(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
seq(n)={my(u=v=w=[]); for(n=1, n, my(t1=EulerT(v), t2=EulerT(u+v)); u=concat([1], EulerT(u+v+w)); v=concat([0], t2-t1); w=concat([1], t1)); u+v}

Crossrefs

Cf. A038055 (rooted bicolored trees), A339831, A339834 (unrooted), A339838.

Sequence in context: A151472 A107379 A117428 * A134168 A124427 A350589

Adjacent sequences: A339832 A339833 A339834 * A339836 A339837 A339838

Keyword

nonn

Author

Andrew Howroyd, Dec 19 2020

Status

approved