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A007827
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Number of homeomorphically irreducible (or series-reduced) trees with n pendant nodes, or continua with n non-cut points, or leaves.
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9
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1, 1, 1, 1, 2, 3, 7, 13, 32, 73, 190, 488, 1350, 3741, 10765, 31311, 92949, 278840, 847511, 2599071, 8044399, 25082609, 78758786, 248803504, 790411028, 2523668997, 8095146289, 26076714609, 84329102797, 273694746208
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Also, number of unrooted multifurcating tree shapes with n leaves [see Felsenstein].
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REFERENCES
| M. Cropper, J. Combin. Math. Combin. Comp., Vol. 24 (1997), 177-184.
F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 62.
S. B. Nadler Jr., Continuum Theory, Academic Press.
Joseph Felsenstein, Inferring Phylogenies. Sinauer Associates, Inc., 2004, pg. 33 (Beware errors!).
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LINKS
| P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.
Index entries for sequences related to trees
Index entries for sequences related to rooted trees
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FORMULA
| G.f.: 1+(1+x-B(x))*B(x) where B(x) = x+x^2+2*x^3+5*x^4+12*x^5+33*x^6+90*x^7+... is g.f. for A000669.
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MAPLE
| A := series(1+(1+x-B)*B, x, 30); # where B = g.f. for A000669; A007827 := n->coeff(A, x, n);
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CROSSREFS
| Cf. A000014 (series-reduced trees), A000055 (trees), A000311, A000669 (series-reduced planted trees by leaves), A059123 (homeomorphically irreducible rooted trees by nodes)
Number of row entries of A064060.
Sequence in context: A193530 A003120 A032131 * A129859 A056953 A045611
Adjacent sequences: A007824 A007825 A007826 * A007828 A007829 A007830
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KEYWORD
| nonn,nice,easy
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AUTHOR
| Matthew Cropper (mmcrop01(AT)athena.louisville.edu).
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EXTENSIONS
| Corrected and extended by Christian G. Bower (bowerc(AT)usa.net), Nov 15 1999.
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