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A002989
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Number of n-node trees with a forbidden limb of length 3.
(Formerly M1082)
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1
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1, 1, 1, 1, 1, 2, 4, 7, 14, 28, 61, 131, 297, 678, 1592, 3770, 9096, 22121, 54451, 135021, 337651, 849698, 2152048, 5479408, 14022947, 36048514, 93061268, 241160180, 627179689, 1636448181, 4282964600, 11241488853, 29584389474
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listen;
history;
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OFFSET
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0,6
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COMMENTS
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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
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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
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Table of n, a(n) for n=0..32.
Index entries for sequences related to trees
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FORMULA
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G.f.: 1+B(x)+(B(x^2)-B(x)^2)/2 where B(x) is g.f. of A050321.
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CROSSREFS
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Cf. A002955, A002988-A002992, A052318-A052329.
Sequence in context: A119341 A119342 A119268 * A000671 A199888 A157133
Adjacent sequences: A002986 A002987 A002988 * A002990 A002991 A002992
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms, formula and comments from Christian G. Bower, Dec 15 1999.
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STATUS
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approved
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