|
| |
|
|
A010372
|
|
Number of unrooted quartic trees with n (unlabeled) nodes and possessing a centroid; number of n-carbon alkanes C(n)H(2n +2) with a centroid ignoring stereoisomers.
|
|
7
|
|
|
|
1, 0, 1, 1, 3, 2, 9, 8, 35, 39, 159, 202, 802, 1078, 4347, 6354, 24894, 38157, 148284, 237541, 910726, 1511717, 5731580, 9816092, 36797588, 64658432, 240215803, 431987953, 1590507121, 2917928218, 10660307791, 19910436898
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,5
|
|
|
COMMENTS
|
The degree of each node is <= 4.
A centroid is a node with less than n/2 nodes in each of the incident subtrees, where n is the number of nodes in the tree. If a centroid exists it is unique.
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 A086194 for the analogous sequence with stereoisomers counted.
|
|
|
REFERENCES
|
F. Harary, Graph Theory, p. 36, for definition of centroid.
|
|
|
LINKS
|
Table of n, a(n) for n=1..32.
A. Cayley, Über die analytischen Figuren, welche in der Mathematik Bäume genannt werden und ihre Anwendung auf die Theorie chemischer Verbindungen, Chem. Ber. 8 (1875), 1056-1059. (Annotated scanned copy)
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
|
|
|
MAPLE
|
with(combstruct): Alkyl := proc(n) combstruct[count]([ U, {U=Prod(Z, Set(U, card<=3))}, unlabeled ], size=n) end:
centeredHC := proc(n) option remember; local f, k, z, f2, f3, f4; f := 1 + add(Alkyl(k)*z^k, k=0..iquo(n-1, 2));
f2 := series(subs(z=z^2, f), z, n+1); f3 := series(subs(z=z^3, f), z, n+1); f4 := series(subs(z=z^4, f), z, n+1);
f := series(f*f3/3+f4/4+f2^2/8+f2*f^2/4+f^4/24, z, n+1); coeff(f, z, n-1) end: seq(centeredHC(n), n=1..32);
|
|
|
CROSSREFS
|
Cf. A010373, A000022, A086194, A000598, A000602.
A000602(n) = a(n) + A010373(n/2) for n even, A000602(n) = a(n) for n odd.
Sequence in context: A288055 A081233 A050676 * A199455 A287768 A197831
Adjacent sequences: A010369 A010370 A010371 * A010373 A010374 A010375
|
|
|
KEYWORD
|
nonn,easy,nice
|
|
|
AUTHOR
|
Paul Zimmermann, N. J. A. Sloane
|
|
|
EXTENSIONS
|
Description revised by Steve Strand (snstrand(AT)comcast.net), Aug 20 2003
|
|
|
STATUS
|
approved
|
| |
|
|
