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A052303
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Number of asymmetric Greg trees.
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8
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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
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OFFSET
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0,8
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COMMENTS
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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.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..1668
Index entries for sequences related to trees
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FORMULA
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G.f.: 1+B(x)-B(x)^2 where B(x) is g.f. of A052301.
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MAPLE
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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
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CROSSREFS
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Cf. A005263, A005264, A048159, A048160, A052300-A052302.
Sequence in context: A237501 A300124 A308371 * A017942 A149344 A178078
Adjacent sequences: A052300 A052301 A052302 * A052304 A052305 A052306
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KEYWORD
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nonn
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AUTHOR
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Christian G. Bower, Nov 15 1999.
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STATUS
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approved
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