%I A086200
%S A086200 1,3,15,66,406,2775,19900,152076,1206681,9841266,82336528,
%T A086200 702993756,6105180250,53822344278,480681790786,4342078862605,
%U A086200 39621836138886,364831810979041,3386667673687950,31669036266203766
%N A086200 Number of unrooted steric quartic trees with 2n (unlabeled) nodes and 
               possessing a bicentroid; number of 2n-carbon alkanes C(2n)H(4n +2) 
               with a bicentroid when stereoisomers are regarded as different.
%C A086200 The degree of each node is <= 4.
%C A086200 A bicentroid is an edge which connects two subtrees of exactly m/2 nodes, 
               where m is the number of nodes in the tree. If a bicentroid exists 
               it is unique. Clearly trees with an odd number of nodes cannot have 
               a bicentroid.
%C A086200 Regarding stereoisomers as different means that only the alternating 
               group A_4 acts at each node, not the full symmetric group S_4. See 
               A010373 for the analogous sequence when stereoisomers are not counted 
               as different.
%H A086200 <a href="Sindx_Ro.html#rooted">Index entries for sequences related to 
               rooted trees</a>
%H A086200 <a href="Sindx_Tra.html#trees">Index entries for sequences related to 
               trees</a>
%F A086200 G.f.: replace each term x in g.f. for A000625 by x(x+1)/2. Interpretation: 
               ways to pick 2 specific radicals (order not important) from all n 
               carbon radicals is number of 2n carbon bicentered alkanes (join the 
               two radicals with an edge).
%Y A086200 Cf. A000598, A000602, A010732, A010733, A000625, A000628, A086194.
%Y A086200 For even n A000628(n) = A086194(n) + a(n/2), for odd n A000628(n) = A086194(n), 
               since every tree has either a centroid or a bicentroid but not both.
%Y A086200 Sequence in context: A001447 A106732 A052981 this_sequence A122558 A110211 
               A033876
%Y A086200 Adjacent sequences: A086197 A086198 A086199 this_sequence A086201 A086202 
               A086203
%K A086200 nonn
%O A086200 1,2
%A A086200 Steve Strand (snstrand(AT)comcast.net), Aug 28 2003