A055357 Number of increasing mobiles (circular rooted trees) with n nodes and 3 leaves.

2, 18, 98, 424, 1614, 5682, 19022, 61584, 194882, 607042, 1870122, 5716680, 17379206, 52628898, 158934998, 479032912, 1441816986, 4335412050, 13027207250, 39125661480, 117469258622, 352600713298, 1058204792478

Offset: 4

Author

Christian G. Bower, May 15 2000

Keywords

• nonn

Links

• Georg Fischer, Table of n, a(n) for n = 4..250
• Index entries for sequences related to mobiles
• Index entries for linear recurrences with constant coefficients, signature (10,-40,82,-91,52,-12).

Crossrefs

Column 3 of A055356.

Programs

Mathematica

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 *)

Formula

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

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