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A228606 The Merrifield-Simmons index of the para-polyphenylene chain of length n. 2
1, 18, 299, 4957, 82176, 1362293, 22583749, 374387682, 6206504351, 102889860193, 1705682092824, 28276366556657, 468758456813401, 7770959199931218, 128824997201136899, 2135628238019808757, 35403905065928790576, 586916988454650778493, 9729761468267561700349, 161297526041365993456482 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The Merrifield-Simmons index of a graph is the number of its independent vertex subsets.
REFERENCES
R. E. Merrifield, H. E. Simmons, Topological Methods in Chemistry, Wiley, New York, 1989.
LINKS
T. Doslic, M. S. Litz, Matchings and independent sets in polyphenylene chains, MATCH, Commun. Math. Comput. Chem., 67, 2012, 313-330.
FORMULA
a(n) = ((19+3*sqrt(29))*(17+3*sqrt(29))^n - (19-3*sqrt(29))*(17-3*sqrt(29))^n)/(6*2^n*sqrt(29)).
G.f.: (1+x)/(1-17*x+7*x^2).
MAPLE
gser := series((x+1)/(7*x^2-17*x+1), x = 0, 22): seq(coeff(gser, x, n), n = 0 .. 20);
CROSSREFS
Sequence in context: A166927 A113367 A228604 * A228605 A193317 A161599
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Nov 23 2013
STATUS
approved

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)