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A002988
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Trimmed trees with n nodes.
(Formerly M0777)
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17
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1, 1, 1, 0, 1, 1, 2, 3, 6, 10, 21, 39, 82, 167, 360, 766, 1692, 3726, 8370, 18866, 43029, 98581, 227678, 528196, 1232541, 2888142, 6798293, 16061348, 38086682, 90607902, 216230205, 517482053, 1241778985, 2987268628, 7203242490
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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COMMENTS
| A trimmed tree is a tree with a forbidden limb of length 2.
A tree with a forbidden limb of length k is a tree where the path from any leaf inward hits a branching node or another leaf within k steps.
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REFERENCES
| R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the laddered parenthesis. Amer. Math. Monthly 80 (1973), 868-876.
K. L. McAvaney, personal communication.
A. J. Schwenk, Almost all trees are cospectral, pp. 275-307 of F. Harary, editor, New Directions in the Theory of Graphs. Academic Press, NY, 1973.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the laddered parenthesis (annotated cached copy)
Index entries for sequences related to trees
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FORMULA
| G.f.: 1+B(x)+(B(x^2)-B(x)^2)/2 where B(x) is g.f. of A002955.
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CROSSREFS
| Cf. A002955, A002989-A002992, A052318-A052329.
Sequence in context: A124343 A032291 A063687 * A138347 A036650 A049889
Adjacent sequences: A002985 A002986 A002987 * A002989 A002990 A002991
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms, formula and comments from Christian G. Bower (bowerc(AT)usa.net), Dec 15 1999.
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