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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 MATHEMATICA b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[g[i], j] b[n - i j, i - 1], {j, 0, n/i}]]]; g[n_] := If[n < 1, 0, b[n - 1, n - 1] + b[n, n - 1]]; a[n_] := If[n == 0, 1, g[n] - Sum[g[j] g[n - j], {j, 0, n}]]; a /@ Range[0, 40] (* Jean-François Alcover, Apr 28 2020, after Alois P. Heinz *) CROSSREFS Cf. A005263, A005264, A048159, A048160, A052300-A052302. Sequence in context: A300124 A343517 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 September 27 20:41 EDT 2023. Contains 365714 sequences. (Running on oeis4.)