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A002991
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Number of n-node trees with a forbidden limb of length 5.
(Formerly M0725)
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1
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1, 1, 1, 1, 2, 3, 5, 10, 21, 43, 97, 215, 503, 1187, 2876, 7033, 17510, 43961, 111664, 285809, 737632, 1915993, 5008652, 13163785, 34774873, 92282214, 245930746, 657931603, 1766481135, 4758553683, 12858286083, 34844908142, 94681272368
(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 A052328.
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CROSSREFS
| Cf. A002955, A002988-A002992, A052318-A052329.
Sequence in context: A132418 A024494 A131708 * A022861 A001646 A103595
Adjacent sequences: A002988 A002989 A002990 * A002992 A002993 A002994
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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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