A108532 -id:A108532 - cp's OEIS frontend

A108531 Number of mobiles (cycle rooted trees) with n nodes and 2-colored internal (non-leaf) nodes.

1, 2, 6, 18, 60, 206, 770, 2950, 11748, 47746, 197808, 830878, 3532790, 15168294, 65683552, 286504378, 1257693038, 5551978426, 24630911086, 109759215338, 491060888588, 2204938828766, 9933016712348, 44881199711338

Offset: 1

Christian G. Bower, Jun 07 2005

Andrew Howroyd, Table of n, a(n) for n = 1..200
Index entries for sequences related to mobiles
C. G. Bower, Transforms (2)

Cf. A032200, A108530, A108532.

CIK(p,n)={sum(d=1, n, eulerphi(d)/d*log(subst(1/(1+O(x*x^(n\d))-p), x, x^d)))}
seq(n)={my(p=O(1));for(i=1, n, p=1+2*CIK(x*p, i)); Vec(p)} \\ Andrew Howroyd, Jun 20 2018

Shifts left and halves under CIK transform.

A108530 Number of rooted identity trees with n internal (non-leaf) nodes.

Original entry on oeis.org

1, 1, 2, 4, 12, 34, 110, 364, 1248, 4356, 15520, 56022, 204726, 755472, 2812004, 10543718, 39791070, 151022006, 576090250, 2207493080, 8493196536, 32797115398, 127071214442, 493831241234, 1924504466246, 7519182311366, 29447430754182, 115577336981932

Offset: 0

Christian G. Bower, Jun 07 2005

Also for n>0, rooted trees with n nodes and 2-colored internal nodes. Black nodes correspond to nodes with a leaf child; white nodes correspond to those without one.

Alois P. Heinz, Table of n, a(n) for n = 0..1000
N. J. A. Sloane, Transforms
Index entries for sequences related to rooted trees

Cf. A004111, A004113, A108531, A108532.

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(binomial(a(i$2), j)*b(n-i*j, i-1), j=0..n/i)))
    end:
a:= n-> `if`(n<2, 1, 2*b(n-1,n-1)):
seq(a(n), n=0..30);  # Alois P. Heinz, May 20 2013

b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[Binomial[a[i], j]*b[n - i*j, i-1], {j, 0, n/i}]]];
a[n_] := If[n<2, 1, 2*b[n-1, n-1]];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Mar 01 2016, after Alois P. Heinz *)

Shifts left and halves under WEIGH transform.

a(n) ~ c * d^n / n^(3/2), where d = 4.1516890102085520777311008746639624... and c = 0.3329810927479684511418598248... - Vaclav Kotesovec, Feb 28 2014

cp's OEIS Frontend

A108531 Number of mobiles (cycle rooted trees) with n nodes and 2-colored internal (non-leaf) nodes.

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