A355024 Number of unlabeled trees on n nodes with maximum degree three and three vertices of degree three.

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

Table of n, a(n) for n=8..40.

Marko R. Riedel et al., Mathematics Stack Exchange, Trees with maximum degree three and three vertices of degree three.

Index entries for linear recurrences with constant coefficients, signature (4,-4,-4,11,-8,0,8,-11,4,4,-4,1).

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

Adjacent sequences: A355021 A355022 A355023 * A355025 A355026 A355027

Keyword

nonn,easy

Author

Marko Riedel, Jun 15 2022

Status

approved