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A002990
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Number of n-node trees with a forbidden limb of length 4.
(Formerly M0350)
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0
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1, 1, 1, 1, 2, 2, 5, 9, 19, 38, 86, 188, 439, 1026, 2472, 5997, 14835, 36964, 93246, 236922, 607111, 1565478, 4062797, 10599853, 27797420, 73224806, 193709710, 514406793, 1370937140, 3665714528, 9831891555, 26445886506, 71325268179
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| 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
| 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
| 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 A052327.
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CROSSREFS
| Cf. A002955, A002988-A002992, A052318-A052329.
Sequence in context: A076607 A054229 A052969 * A060405 A003228 A184713
Adjacent sequences: A002987 A002988 A002989 * A002991 A002992 A002993
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KEYWORD
| nonn
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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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