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A002991 Number of n-node trees with a forbidden limb of length 5.
(Formerly M0725)
+0
2
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; listen)
OFFSET

0,5

COMMENT

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.

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).

LINKS

Index entries for sequences related to trees

FORMULA

G.f.: 1+B(x)+(B(x^2)-B(x)^2)/2 where B(x) is g.f. of A052328.

CROSSREFS

Cf. A002955, A002988-A002992, A052318-A052329.

Sequence in context: A132418 A024494 A131708 this_sequence A022861 A001646 A103595

Adjacent sequences: A002988 A002989 A002990 this_sequence A002992 A002993 A002994

KEYWORD

nonn

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

More terms, formula and comments from Christian G. Bower (bowerc(AT)usa.net), Dec 15 1999.

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.


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