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Search: id:A010373
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| A010373 |
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Number of unrooted quartic trees with 2n (unlabeled) nodes and possessing a bicentroid; number of 2n-carbon alkanes C(2n)H(4n+2) with a bicentroid, ignoring stereoisomers. |
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7
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| 1, 1, 3, 10, 36, 153, 780, 4005, 22366, 128778, 766941, 4674153, 29180980, 185117661, 1193918545, 7800816871, 51584238201, 344632209090, 2324190638055, 15804057614995, 108277583483391, 746878494484128, 5183852459907628
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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The degree of each node is <= 4.
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.
Ignoring stereoisomers means that the children of a node are unordered. They can be permuted in any way and it is still the same tree. See A086200 for the analogous sequence with stereoisomers counted.
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REFERENCES
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F. Harary, Graph Theory, p. 36, for definition of bicentroid.
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LINKS
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E. M. Rains and N. J. A. Sloane, On Cayley's Enumeration of Alkanes (or 4-Valent Trees)., J. Integer Sequences, Vol. 2 (1999), Article 99.1.1.
Index entries for sequences related to trees
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FORMULA
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a(n)=b(n)*(b(n)+1)/2, where b(n) = A000598[ n ].
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MAPLE
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M[1146] := [ T, {T=Union(Epsilon, U), U=Prod(Z, Set(U, card<=3))}, unlabeled ]:
bicenteredHC := proc(n) option remember; if n mod 2<>0 then 0 else binomial(count(M[ 1146 ], size=n/2)+1, 2) fi end:
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CROSSREFS
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A000602(n) = A010372(n) + a(n/2) for n even, A000602(n) = A010372(n) for n odd.
Cf. A000200, A000598.
Sequence in context: A002212 A129247 A081921 this_sequence A104603 A080625 A138807
Adjacent sequences: A010370 A010371 A010372 this_sequence A010374 A010375 A010376
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KEYWORD
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nonn,easy
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AUTHOR
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Paul.Zimmermann(AT)loria.fr, njas
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EXTENSIONS
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Description revised by Steve Strand (snstrand(AT)comcast.net), Aug 20 2003.
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