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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
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
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Nov 23 2013
STATUS
approved