A339831 Number of rooted bicolored trees on n nodes such that black nodes are not adjacent to each other.

2, 3, 9, 28, 97, 346, 1302, 5014, 19830, 79813, 326344, 1350918, 5652334, 23861787, 101519790, 434827232, 1873491739, 8114411769, 35309142309, 154288183928, 676730773252, 2978405318453, 13149337960554, 58218455727085, 258435947527696, 1149982662789042

Offset

1,1

Links

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

Example

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

Prog

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

Crossrefs

Cf. A038055 (rooted bicolored trees), A339830 (unrooted case), A339835, A339838.

Sequence in context: A057248 A015960 A099079 * A006797 A144239 A320951

Adjacent sequences: A339828 A339829 A339830 * A339832 A339833 A339834

Keyword

nonn

Author

Andrew Howroyd, Dec 19 2020

Status

approved