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Number of unlabeled trees on n nodes with maximum degree three and three vertices of degree three.
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%I #24 Aug 22 2022 04:49:31

%S 1,3,10,24,55,109,206,360,606,970,1508,2264,3322,4750,6668,9176,12439,

%T 16597,21870,28448,36617,46627,58842,73584,91308,112420,137480,166992,

%U 201636,242028,288984,343248,405789

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

%H Marko R. Riedel et al., Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/4472439/">Trees with maximum degree three and three vertices of degree three</a>.

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-4,11,-8,0,8,-11,4,4,-4,1).

%F G.f.: z^8*(1 - z + 2*z^2)/((1 - z)^7*(1 + z)^3*(1 + z^2)).

%F 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).

%F a(n) ~ n^6/5760. - _Stefano Spezia_, Jun 16 2022

%e First term counts:

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%p 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

%Y Cf. A355023.

%K nonn,easy

%O 8,2

%A _Marko Riedel_, Jun 15 2022