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A228604
The Merrifield-Simmons index of the ortho-polyphenylene chain of length n.
2
1, 18, 299, 4932, 81301, 1340118, 22089599, 364109832, 6001737001, 98928520218, 1630669938899, 26878845894732, 443052477632701, 7302973450020318, 120377210159548199, 1984215446621359632, 32706447785195768401, 539110673967989840418, 8886330936793922917499
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) = ((9 + 2*sqrt(14))^(n+1) - (9 - 2*sqrt(14))^(n+1))/(4*sqrt(14)).
G.f. = 1/(1 - 18*x + 25*x^2).
a(n) = 18*a(n-1) - 25*a(n-2); a(0)=1, a(1)=18. - Harvey P. Dale, Nov 06 2014
MAPLE
gser := series(1/(25*x^2-18*x+1), x = 0, 22): seq(coeff(gser, x, n), n = 0 .. 20);
MATHEMATICA
CoefficientList[Series[1/(1-18x+25x^2), {x, 0, 20}], x] (* or *) LinearRecurrence[ {18, -25}, {1, 18}, 20] (* Harvey P. Dale, Nov 06 2014 *)
CROSSREFS
Sequence in context: A219670 A166927 A113367 * A228606 A228605 A193317
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Nov 23 2013
STATUS
approved