A055357 - OEIS

%I #22 Mar 13 2024 04:41:56

%S 2,18,98,424,1614,5682,19022,61584,194882,607042,1870122,5716680,

%T 17379206,52628898,158934998,479032912,1441816986,4335412050,

%U 13027207250,39125661480,117469258622,352600713298,1058204792478

%N Number of increasing mobiles (circular rooted trees) with n nodes and 3 leaves.

%H Georg Fischer, <a href="/A055357/b055357.txt">Table of n, a(n) for n = 4..250</a>

%H <a href="/index/Mo#mobiles">Index entries for sequences related to mobiles</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (10,-40,82,-91,52,-12).

%F G.f.: x^4*(-2*x^2-2*x+2)/((1-3*x)*(1-2*x)^2*(1-x)^3).

%F For n>0, a(n) = 5*3^(n-1)/4 - 2^n*(n+1)/2 + n^2/2 + 1/4. - _Vaclav Kotesovec_, Mar 15 2022

%t Drop[CoefficientList[Series[x^4*(-2*x^2 - 2*x + 2)/((1 - 3*x)*(1 - 2*x)^2*(1 - x)^3), {x, 0, 30}], x], 4] (* _Vaclav Kotesovec_, Mar 15 2022 *)

%Y Column 3 of A055356.

%K nonn

%O 4,1

%A _Christian G. Bower_, May 15 2000