|
Search: id:A010373
|
|
|
| A010373 |
|
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. |
|
+0
7
|
|
| 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)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
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.
|
|
REFERENCES
|
F. Harary, Graph Theory, p. 36, for definition of bicentroid.
|
|
LINKS
|
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
|
|
FORMULA
|
a(n)=b(n)*(b(n)+1)/2, where b(n) = A000598[ n ].
|
|
MAPLE
|
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:
|
|
CROSSREFS
|
A000602(n) = A010372(n) + a(n/2) for n even, A000602(n) = A010372(n) for n odd.
Cf. A000200, A000598.
Sequence in context: A149042 A081921 A165792 this_sequence A104603 A080625 A138807
Adjacent sequences: A010370 A010371 A010372 this_sequence A010374 A010375 A010376
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Paul.Zimmermann(AT)loria.fr, N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
Description revised by Steve Strand (snstrand(AT)comcast.net), Aug 20 2003.
|
|
|
Search completed in 0.002 seconds
|
