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A052301 Number of asymmetric rooted Greg trees. 6
1, 1, 2, 5, 14, 43, 138, 455, 1540, 5305, 18546, 65616, 234546, 845683, 3072350, 11235393, 41326470, 152793376, 567518950, 2116666670, 7924062430, 29765741831, 112157686170, 423809991041, 1605622028100, 6097575361683, 23207825593664, 88512641860558 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A rooted Greg tree can be described as a rooted tree with 2-colored nodes where only the black nodes are counted and the white nodes have at least 2 children.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000

N. J. A. Sloane, Transforms

Index entries for sequences related to rooted trees

FORMULA

Satisfies a = WEIGH(a) + SHIFT_RIGHT(WEIGH(a)) - a.

a(n) ~ c * d^n / n^(3/2), where d = 4.0278584853545190803008179085023154..., c = 0.14959176868229550510957320468... . - Vaclav Kotesovec, Sep 12 2014

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

      add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))

    end:

a:= n-> `if`(n<1, 1, b(n-1$2)) +b(n, n-1):

seq(a(n), n=1..40);  # Alois P. Heinz, Jul 06 2014

MATHEMATICA

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<1, 1, b[n-1, n-1]] + b[n, n-1];

Table[a[n], {n, 1, 40}] (* Jean-Fran├žois Alcover, Mar 01 2016, after Alois P. Heinz *)

CROSSREFS

Essentially the same as A031148. Cf. A005263, A005264, A048159, A048160, A052300-A052303.

Sequence in context: A071743 A071747 A071751 * A071755 A149879 A149880

Adjacent sequences:  A052298 A052299 A052300 * A052302 A052303 A052304

KEYWORD

nonn,eigen

AUTHOR

Christian G. Bower, Nov 15 1999

STATUS

approved

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Last modified December 12 07:00 EST 2019. Contains 329948 sequences. (Running on oeis4.)