

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
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OFFSET

1,3


COMMENTS

A rooted Greg tree can be described as a rooted tree with 2colored 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(ni*j, i1), j=0..n/i)))
end:
a:= n> `if`(n<1, 1, b(n1$2)) +b(n, n1):
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, i1], {j, 0, n/i}]]];
a[n_] := If[n<1, 1, b[n1, n1]] + b[n, n1];
Table[a[n], {n, 1, 40}] (* JeanFrançois Alcover, Mar 01 2016, after Alois P. Heinz *)


CROSSREFS

Essentially the same as A031148. Cf. A005263, A005264, A048159, A048160, A052300A052303.
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



