login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A032171 Number of rooted compound windmills (mobiles) of n nodes with no symmetries. 3
1, 1, 1, 2, 4, 10, 23, 59, 148, 385, 1006, 2678, 7170, 19421, 52933, 145364, 401421, 1114713, 3109710, 8713076, 24506121, 69168705, 195849114, 556165311, 1583601840, 4520226558, 12931917204, 37075154703 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..28.

Index entries for sequences related to mobiles

FORMULA

Shifts left under "CHK" (necklace, identity, unlabeled) transform.

From Petros Hadjicostas, Dec 03 2017: (Start)

a(n+1) = (1/n)*Sum_{d|n} mu(n/d)*c(d), where c(n) = n*a(n) + Sum_{s=1..n-1} c(s)*a(n-s) with a(1) = c(1) = 1.

G.f.: If A(x) = Sum_{n>=1} a(n)*x^n, then Sum_{n>=1} a(n+1)*x^n = -Sum_{n>=1} (mu(n)/n)*log(1-A(x^n)).

The g.f. of the auxiliary sequence (c(n): n>=1) is C(x) = Sum_{n>=1} c(n)*x^n = x*(dA(x)/dx)/(1-A(x)) = x + 3*x^2 + 7*x^3 + 19*x^4 + 51*x^5 + 147*x^6 + 414*x^7 + 1203*x^8 + ...

(End)

MATHEMATICA

T[n_, k_] := Module[{A}, A[_, _] = 0; If[k < 1 || k > n, 0, For[j = 1, j <= n, j++, A[x_, y_] = x*y - x*Sum[MoebiusMu[i]/i * Log[1 -  A [x^i, y^i]] + O[x]^j // Normal , {i, 1, j}]]; Coefficient[Coefficient[A[x, y], x, n], y, k]]];

a[n_] := a[n] = Sum[T[n, k], {k, 1, n}];

Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 28}] (* Jean-Fran├žois Alcover, Jun 30 2017, using Michael Somos' code for A055363 *)

CROSSREFS

Cf. A032200, A055363.

Sequence in context: A137681 A127389 A152173 * A127713 A151256 A205999

Adjacent sequences:  A032168 A032169 A032170 * A032172 A032173 A032174

KEYWORD

nonn,eigen

AUTHOR

Christian G. Bower

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 20 15:02 EST 2018. Contains 299380 sequences. (Running on oeis4.)