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A339831
Number of rooted bicolored trees on n nodes such that black nodes are not adjacent to each other.
5
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
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: A015960 A376478 A099079 * A006797 A144239 A320951
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Dec 19 2020
STATUS
approved