%I A000676 M0831 N0316
%S A000676 1,1,0,1,1,2,3,7,12,27,55,127,284,682,1618,3979,9823,24722,62651,
%T A000676 160744,415146,1081107,2831730,7462542,19764010,52599053,140580206,
%U A000676 377244482,1016022191,2745783463,7443742141,20239038700,55178647926
%N A000676 Number of centered trees with n nodes.
%C A000676 A tree has either a center or a bicenter and either a centroid or a bicentroid. 
               (These terms were introduced by Jordan.)
%C A000676 If the number of edges in a longest path in the tree is 2m, then the 
               middle node in the path is the unique center, otherwise the two middle 
               nodes in the path are the unique bicenters.
%D A000676 N. L. Biggs et al., Graph Theory 1736-1936, Oxford, 1976, p. 49.
%D A000676 A. Cayley, On the analytical forms called trees, with application to 
               the theory of chemical combinations, Reports British Assoc. Advance. 
               Sci. 45 (1875), 257-305 = Math. Papers, Vol. 9, 427-460 (see p. 438).
%D A000676 A. Cayley, On the analytical forms called trees, Amer. J. Math., 4 (1881), 
               266-268.
%D A000676 F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1994; pp. 35, 36.
%D A000676 C. Jordan, Sur les assemblages des lignes, J. Reine angew. Math., 70 
               (1869), 185-190.
%D A000676 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000676 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A000676 N. J. A. Sloane, <a href="b000676.txt">Table of n, a(n) for n = 0..200</
               a>
%H A000676 E. M. Rains and N. J. A. Sloane, <a href="http://www.cs.uwaterloo.ca/
               journals/JIS/index.html">On Cayley's Enumeration of Alkanes (or 4-Valent 
               Trees)</a>, J. Integer Sequences, Vol. 2 (1999), Article 99.1.1. 
               [This articles states incorrectly that A000676 and A000677 give the 
               numbers of trees with respectively a centroid and bicentroid.]
%H A000676 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CenteredTree.html">Link to a section of The World of Mathematics.</
               a>
%H A000676 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%Y A000676 Cf. A102911 (trees with a bicentroid), A027416 (trees with a centroid), 
               A000677 (trees with a bicenter), A000055 (trees), A000081 (rooted 
               trees).
%Y A000676 A000676+A000677 = A000055.
%Y A000676 Sequence in context: A054272 A129016 A099163 this_sequence A032173 A130616 
               A089324
%Y A000676 Adjacent sequences: A000673 A000674 A000675 this_sequence A000677 A000678 
               A000679
%K A000676 nonn,nice,easy
%O A000676 0,6
%A A000676 N. J. A. Sloane (njas(AT)research.att.com).