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Search: id:A059123
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| A059123 |
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Number of homeomorphically irreducible rooted trees (also known as series-reduced rooted trees, or rooted trees without nodes of degree 2) with n >= 1 nodes. |
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+0
5
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| 0, 1, 1, 0, 2, 2, 4, 6, 12, 20, 39, 71, 137, 261, 511, 995, 1974, 3915, 7841, 15749, 31835, 64540, 131453, 268498, 550324, 1130899, 2330381, 4813031, 9963288, 20665781, 42947715, 89410092, 186447559, 389397778, 814447067, 1705775653
(list; graph; listen)
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OFFSET
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0,5
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REFERENCES
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P. J. Cameron, Some treelike objects, Quart. J. Math. Oxford, 38 (1987), 155-183.
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 62, Eq. (3.3.9).
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LINKS
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N. J. A. Sloane, Table of n, a(n) for n = 0..500
N. J. A. Sloane, Illustration of initial terms
Index entries for sequences related to trees
Index entries for sequences related to rooted trees
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FORMULA
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G.f.: 1 + ((1+x)/x)*f(x) - (f(x)^2+f(x^2))/(2*x) where 1+f(x) is g.f. for A001678 (homeomorphically irreducible planted trees by nodes).
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MAPLE
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with (powseries): with (combstruct): n := 30: Order := n+3: sys := {B = Prod(C, Z), S = Set(B, 1 <= card), C = Union(Z, S)}:
G001678 := (convert(gfseries(sys, unlabeled, x) [S(x)], polynom)) * x^2: G0temp := G001678 + x^2:
G059123 := G0temp / x + G0temp - (G0temp^2+eval(G0temp, x=x^2))/(2*x): A059123 := 0, seq(coeff(G059123, x^i), i=1..n); # from UlrSchimke(AT)aol.com
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CROSSREFS
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Apart from initial term, same as A001679.
Cf. A000055 (trees by nodes), A000014 (homeomorphically irreducible trees by nodes), A000669 (homeomorphically irreducible planted trees by leaves), A000081 (rooted trees by nodes).
Sequence in context: A129860 A028408 A037163 this_sequence A001679 A030435 A063886
Adjacent sequences: A059120 A059121 A059122 this_sequence A059124 A059125 A059126
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jan 09 2001.
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