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Search: id:A002992
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| A002992 |
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Number of n-node trees with a forbidden limb of length 6.
(Formerly M0778)
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+0
18
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| 1, 1, 1, 1, 2, 3, 6, 10, 22, 45, 102, 226, 531, 1253, 3044, 7456, 18604, 46798, 119133, 305567, 790375, 2057523, 5390759, 14200122, 37598572, 100005401, 267131927, 716318650, 1927758155, 5205240762, 14098580633, 38296720823, 104308468102
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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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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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 A052329.
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CROSSREFS
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Cf. A002955, A002988-A002991, A052318-A052329.
Sequence in context: A125702 A052817 A156803 this_sequence A130867 A122381 A141034
Adjacent sequences: A002989 A002990 A002991 this_sequence A002993 A002994 A002995
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms, formula and comments from Christian G. Bower (bowerc(AT)usa.net), Dec 15 1999.
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