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A052302 Number of Greg trees. 4
1, 1, 1, 2, 5, 12, 37, 116, 412, 1526, 5995, 24284, 101619, 434402, 1893983, 8385952, 37637803, 170871486, 783611214, 3625508762, 16906577279, 79395295122, 375217952457, 1783447124452, 8521191260092, 40907997006020, 197248252895597, 954915026282162 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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..1000

Index entries for sequences related to trees

FORMULA

G.f.: 1 + B(x) - B(x)^2 where B(x) is g.f. of A052300.

MAPLE

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

      add(binomial(g(i)+j-1, 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-A052303.

Sequence in context: A267398 A267399 A267400 * A280275 A009598 A002216

Adjacent sequences:  A052299 A052300 A052301 * A052303 A052304 A052305

KEYWORD

nonn

AUTHOR

Christian G. Bower, Nov 15 1999

STATUS

approved

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Last modified November 15 01:20 EST 2019. Contains 329142 sequences. (Running on oeis4.)