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A228605
The Merrifield-Simmons index of the meta-polyphenylene chain of length n.
2
1, 18, 299, 4982, 83001, 1382818, 23038099, 383820582, 6394548401, 106534800818, 1774896845499, 29570232336982, 492647582692201, 8207633878782018, 136741265470126499, 2278144220188626182, 37954461443189410401, 632330969513105454418, 10534794588084770785099
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) = (((2+sqrt(3))*(8+5*sqrt(3))^n - (2-sqrt(3))*(8-5*sqrt(3))^n)*(1/2))/sqrt(3).
G.f.: (1+2*x)/(1-16*x -11*x^2).
MAPLE
gser := series((2*x+1)/(1-16*x-11*x^2), x = 0, 22): seq(coeff(gser, x, n), n = 0 .. 20);
CROSSREFS
Sequence in context: A113367 A228604 A228606 * A193317 A161599 A273434
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Nov 23 2013
STATUS
approved