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A052303 Number of asymmetric Greg trees. 8
1, 1, 0, 0, 0, 0, 1, 4, 12, 42, 137, 452, 1491, 4994, 16831, 57408, 197400, 685008, 2395310, 8437830, 29917709, 106724174, 382807427, 1380058180, 4998370015, 18181067670, 66393725289, 243347195594, 894959868983, 3301849331598, 12217869541117, 45335177297876 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

A Greg tree can be described as a tree with 2-colored nodes where only the black nodes are counted and the white nodes are of degree at least 3.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1668

Index entries for sequences related to trees

FORMULA

G.f.: 1+B(x)-B(x)^2 where B(x) is g.f. of A052301.

MAPLE

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

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

    end:

g:= n-> `if`(n<1, 0, b(n-1$2)+b(n, n-1)) :

a:= n-> `if`(n=0, 1, g(n)-add(g(j)*g(n-j), j=0..n)):

seq(a(n), n=0..40);  # Alois P. Heinz, Jun 22 2018

CROSSREFS

Cf. A005263, A005264, A048159, A048160, A052300-A052302.

Sequence in context: A237501 A300124 A308371 * A017942 A149344 A178078

Adjacent sequences:  A052300 A052301 A052302 * A052304 A052305 A052306

KEYWORD

nonn

AUTHOR

Christian G. Bower, Nov 15 1999.

STATUS

approved

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Last modified December 12 15:11 EST 2019. Contains 329960 sequences. (Running on oeis4.)