login
A355024
Number of unlabeled trees on n nodes with maximum degree three and three vertices of degree three.
1
1, 3, 10, 24, 55, 109, 206, 360, 606, 970, 1508, 2264, 3322, 4750, 6668, 9176, 12439, 16597, 21870, 28448, 36617, 46627, 58842, 73584, 91308, 112420, 137480, 166992, 201636, 242028, 288984, 343248, 405789
OFFSET
8,2
LINKS
FORMULA
G.f.: z^8*(1 - z + 2*z^2)/((1 - z)^7*(1 + z)^3*(1 + z^2)).
Cycle index of edges of Eiffel gadget below is (1/8) (a_1^7 + 2 a_1^5 a_2 + a_1^3 a_2^2 + 2 a_1 a_2^3 + 2 a_1 a_2 a_4).
a(n) ~ n^6/5760. - Stefano Spezia, Jun 16 2022
EXAMPLE
First term counts:
o
|
|
|
|
o
/ \
/ \
o o
/ \ / \
o o o o
MAPLE
gf := z^8*(1 - z + 2*z^2)/((1 - z)^7*(1 + z)^3*(1 + z^2)): ser := series(gf, z, 42): seq(coeff(ser, z, n), n = 8..40); # Peter Luschny, Jun 16 2022
CROSSREFS
Cf. A355023.
Sequence in context: A033811 A062446 A053208 * A338706 A338710 A336516
KEYWORD
nonn,easy
AUTHOR
Marko Riedel, Jun 15 2022
STATUS
approved